IEEE Fuzzy system Title and Abstract 2016

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2016 TOPICS
A Big Bang-Big Crunch Type-2 Fuzzy Logic System for Machine Vision-Based Event
Detection and Summarization in Real-world Ambient Assisted Living
Abstract - The area of Ambient Assisted Living (AAL) focuses on developing new technologies
which can improve the quality of life and care provided to elderly and disabled people. In this
paper, we propose a novel system based on 3D RGB-D vision sensors and Interval Type-2 Fuzzy
Logic based Systems (IT2FLSs) employing the Big Bang Big Crunch (BB-BC) algorithm for the
real time automatic detection and summarization of important events and human behaviours
from the large-scale data. We will present several real world experiments which were conducted
for AAL related behaviours with various users. It will be shown that the proposed BB-BC
IT2FLSs outperforms the Type-1 FLSs (T1FLSs) counterpart as well as other conventional non-
fuzzy methods, and the performance improvement rises when the amount of subjects increases.
IEEE Transactions on Fuzzy Systems (January 2016)
Adaptive Fuzzy Output Feedback Control for Switched Nonstrict-Feedback Nonlinear
Systems with Input Nonlinearities
Abstract - This paper studies adaptive fuzzy output-feedback tracking control problem for
nonstrict-feedback switched nonlinear systems. The switched systems under consideration
contain unknown nonlinearities, unmeasured states and unknown deadzones. Fuzzy logic
systems are utilized to approximate the unknown nonlinearities, and a switched fuzzy state
observer is designed and thus the immeasurable states are estimated via it. In the framework of
observer-based output feedback control, and by using the certainty equivalence dead zone
inverse, a novel adaptive fuzzy output feedback control design method with the parameters
adaptation laws is developed. The stability of the closed-loop system and the convergence of the
tracking error are proved based on Lyapunov function and the average dwell time methods. Two
simulation examples are provided to check the effectiveness of the proposed approach.
Disturbance Rejection Fuzzy Control for Nonlinear Parabolic PDE Systems via Multiple
Observers

Abstract - A design method of low dimensional disturbance rejection fuzzy control (DRFC) via
multiple observers is proposed for a class of nonlinear parabolic partial differential equation
(PDE) systems, where the disturbance is modeled by an exosystem of ordinary differential
equations (ODEs) and enters into the PDE system through the control channel. In the proposed
scheme, the modal decomposition technique is initially applied to the PDE system to derive a
slow subsystem of low dimensional nonlinear ODEs, which accurately captures the dominant
dynamics of the PDE system. The resulting nonlinear slow subsystem is subsequently
represented by a T-S fuzzy model. From the T-S fuzzy model and the exosystem, a fuzzy slow
mode observer (FSMO) and a fuzzy disturbance observer (FDO) are constructed to estimate the
slow mode and the disturbance, respectively. Furthermore, a nonlinear observation spillover
observer (OSO) is proposed to compensate the effect of observation spillover. Then, based on
these observers, a low dimensional DRFC design is developed in terms of linear matrix
inequalities (LMIs) to guarantee the exponential stability of the closed-loop PDE system in the
presence of the disturbance. Finally, the effectiveness of the proposed design method is
demonstrated on the control of one dimensional Burgers-KPP-Fisher diffusion-reaction system
and the temperature profile of a catalytic rod.
Processing Incomplete k Nearest Neighbor Search
Abstract - Given a set S of multi-dimensional objects and a query object q, a k nearest neighbor
(kNN) query finds from S the k closest objects to q. This query is a fundamental problem in
database, data mining, and information retrieval research. It plays an important role in a wide
spectrum of real applications such as image recognition and location-based services. However,
due to the failure of data transmission devices, improper storage, and accidental loss, incomplete
data exists widely in those applications, where some dimensional values of data items are
missing. In this paper, we systematically study incomplete k nearest neighbor (IkNN) search,
which aims at the kNN query for incomplete data. We formalize this problem, and propose an
efficient LP algorithm using our newly developed index to support exact IkNN retrieval, with the
help of two pruning heuristics, i.e., value pruning and partial distance pruning. Furthermore, we
propose an approximate algorithm, namely HA, to support approximate IkNN search with

improved search efficiency and guaranteed error bound. Extensive experiments using both real
and synthetic data sets demonstrate the effectiveness of newly designed indexes and pruning
heuristics, as well as the performance of our presented algorithms under a variety of
experimental settings.
Fuzzy Multi-Instance Classifiers
Abstract - Multi-instance learning is a setting in supervised learning where the data consists of
bags of instances. Samples in the dataset are groups of individual instances. In classification
problems, a decision value is assigned to the entire bag and the classification of an unseen bag
involves the prediction of the decision value based on the instances it contains. In this paper, we
develop a framework for multi-instance classifiers based on fuzzy set theory. Fuzzy sets have
been used in many machine learning applications, but so far not in the classification of multi-
instance data. We explore its untapped potential here. We interpret the classes as fuzzy sets and
determine membership degrees of unseen bags to these sets based on the available training data.
In doing so, we develop a framework of classifiers, that extract the required membership degrees
either at the level of instances (instance-based) or at the level of bags (bag-based). We offer an
extensive analysis of the different settings within the proposed framework. We experimentally
compare our proposal to state-of-the-art multi-instance classifiers and, based on two evaluation
measures, our methods are shown to perform very well.
Online Local Input Selection Through Evolving Heterogeneous Fuzzy Inference System
Abstract - Recently, online input selection has gained an increasing attention in evolving fuzzy
models. In this paper, we proposed a new evolving fuzzy system referred to as evolving
Heterogeneous Fuzzy Inference System (eHFIS) which can simultaneously perform local input
selection and system identification in an evolving and integrative manner. The introduced eHFIS
is structured by some fuzzy rules with different effective input variables. This was achieved
through inclusion of some parameters (local input selectors) in the structure of Takagi-Sugeno
system. An online learning algorithm is proposed to identify the eHFIS, where:(a) the premise

parameter learning and rule evolution take place with the usage of an incremental and evolving
clustering for partitioning the data space, (b) a local input selection strategy based on switching
to a neighboring model is adopted and then all fuzzy rules with the same input structure form a
new category and (c) for each category the parameters of linear models, in consequent parts, are
updated by weighted recursive fuzzily weighted least squares estimator. The performance of the
proposed eHFIS is evaluated and compared through several simulations on hand made as well as
real life data sets.
Low Design-Cost Fuzzy Controllers for Robust Stabilization of Nonlinear Partial
Differential Systems
Abstract - In general, the design cost of a fuzzy controller for nonlinear partial differential
systems (PDSs) is very expensive. In this paper, a new approach for robust fuzzy H1
stabilization design is developed for a class of N-dimensional nonlinear parabolic PDSs. Further,
two low design-cost robust fuzzy controllers, called the robust fuzzy area-controller and point-
controller, as well as a normal design-cost robust fuzzy fullcontroller are proposed for this
problem. The difference between the three control designs lies in their controller placement in
the spatial domain. First, we present the N-dimensional parabolic Takagi-Sugeno (T-S) fuzzy
PDS based on the knowledge-based fuzzy system technique. Next, these three robust fuzzy
controllers are constructed via solving diffusion matrix inequality (DMI) problems.With the
proposed simple but general method using the Poincar´e inequality, the linear matrix inequality
(LMI) problems are provided to replace DMI problems for the robust fuzzy H1 stabilization
designs for computational simplicity. Further, the comparison of these three robust fuzzy
controllers are demonstrated to enable a designer to select a low cost option. Finally, a
simulation example is provided to illustrate the design procedure and verify the performance of
the proposed designs.

Relationships between Two Types of Intuitionistic Fuzzy Definite Integrals
Abstract - Intuitionistic fuzzy numbers (IFNs) are the basic components of Atanassov’s
intuitionistic fuzzy sets (IFSs), which are very convenient and comprehensive in depicting the
fuzzy characters of things in real life. In the existing literature, there are mainly two different
types of definite integrals with respect to IFNs, which were developed from completely different
aspects. The main purpose of this paper is to demonstrate their relationships in detail by deriving
the definite integrals of two novel intuitionistic fuzzy functions. It is worth pointing out that one
of the two types of definite integrals is shown to be a special case of another one, and finally, we
also derive some other useful results for intuitionistic fuzzy calculus based on the division
derivative.
Weighted Fuzzy Observer-based Fault Detection Approach for Discrete-Time Nonlinear
Systems via Piecewise-Fuzzy Lyapunov Functions
Abstract - The main focus of this paper is on the analysis and integrated design of L2 observer-
based fault detection (FD) systems for discrete-time nonlinear industrial processes. To gain a
deeper insight into this FD framework, the existence condition is introduced first. Then, an
integrated design of L2 observerbased FD approach is realized by solving the proposed existence
condition with the aid of Takagi-Sugeno (T-S) fuzzy dynamic modelling technique and
piecewise-fuzzy Lyapunov functions. Most importantly, a weighted piecewise-fuzzy observer-
based residual generator is proposed aiming at achieving an optimal integration of residual
evaluation and threshold computation into FD systems. The core of this approach is to make use
of the knowledge provided by fuzzy models of each local region and then to weight the local
residual signal by means of different weighting factors. In comparison with the standard norm-
based fuzzy observer-based FD methods, the proposed scheme may lead to a significant
improvement of the FD performance. In the end, the effectiveness of the proposed method is
verified by a numerical example and a case study on the laboratory setup of continuous stirred
tank heater (CSTH) plant.
H-index and Other Sugeno Integrals: Some Defects and Their Compensation

Abstract - The famous Hirsch index has been introduced just ca. 10 years ago. Despite that, it is
already widely used in many decision making tasks, like in evaluation of individual scientists,
research grant allocation, or even production planning. It is known that the h-index is related to
the discrete Sugeno integral and the Ky Fan metric introduced in the 1940s. The aim of this
paper is to propose a few modifications of this index as well as other fuzzy integrals – also on
bounded chains – that lead to better discrimination of some types of data that are to be
aggregated. All of the suggested compensation methods try to retain the simplicity of the original
measure.
Interval-valued Atanassov intuitionistic OWA aggregations using admissible linear orders
and their application to decision making
Abstract - Based on the definition of admissible order for interval-valued Atanassov
intuitionistic fuzzy sets, we study OWA operators in these sets distinguishing between the
weights associated to the membership and those associated to the nonmembership degree which
may differ from the latter. We also study Choquet integrals for aggregating information which is
represented using interval-valued Atanassov intuitionistic fuzzy sets. We conclude with two
algorithms to choose the best alternative in a decision making problem when we use this kind of
sets to represent information.
IEEE Transactions on Fuzzy Systems (March 2016)
A New Look at Type-2 Fuzzy Sets and Type-2 Fuzzy Logic Systems
Abstract - We propose the concept of a conditional fuzzy set and prove that a type-2 fuzzy set is
equivalent to a conditional fuzzy set. We show that both the conditional fuzzy sets and the type-2
fuzzy sets are fuzzy relations on the product space of the primary and secondary variables, and
the difference is that the primary and secondary variables in the conditional fuzzy set framework
are usually independent to each other, whereas in the type-2 fuzzy set framework the secondary
variable depends on the primary variable by definition. It is this dependency between the primary
and secondary variables that makes the type-2 fuzzy sets a complex subject, while the
conditional fuzzy sets do not have this built-in dependency and thus are much easier to analyze.
With the fuzzy relation formulation, powerful tools in fuzzy set theory such as Zadeh’s

Compositional Rule of Inference can be used to obtain the marginal fuzzy sets of the type-2 and
conditional fuzzy sets, transforming the type-2 problems back to the conventional type-1 domain.
With the help of the marginal fuzzy set concept, we show that a type-2 fuzzy logic system can be
designed in the same way as designing a type-1 fuzzy logic system.
Non-Fragile Fault-Tolerant Fuzzy Observer-Based Controller Design for Nonlinear
Systems
Abstract - The problem of actuator fault estimation and faulttolerant control for a class of
uncertain nonlinear systems using Takagi-Sugeno (T-S) fuzzy models is investigated. A design
procedure for non-fragile proportional-integral (PI) observer is proposed to estimate the states of
the nonlinear system and reconstruct the abrupt (modeled as step-like faults) and incipient fault
signals. Subsequently, a non-fragile fault-tolerant controller is constructed, which is informed by
the PI observer. Sufficient conditions of the existence of the PI observer and the faulttolerant
controller are provided in the form of linear matrix inequalities. The proposed fault-tolerant
control architecture is tested on two numerical examples.
Dempster-Shafer Fusion of Evidential Pairwise Markov Chains
Abstract - Hidden Markov models have been extended in many directions, leading to pairwise
Markov models, triplet Markov models, or discriminative random fields, all of which have been
successfully applied in many fields covering signal and image processing. The Dempster-Shafer
theory of evidence has also shown its interest in a wide range of situations involving reasoning
under uncertainty and/or information fusion. There are, however, only few works dealing with
both of these modeling tools simultaneously. The aim of this paper, which falls under this
category of works, is to propose a general evidential Markov model offering wide modeling and
processing possibilities regarding information imprecision, sensor unreliability and data fusion.
The main interest of the proposed model relies in the possibility of achieving, easily, the
Dempster-Shafer fusion without destroying the Markovianity.

Mean-Semi-Entropy Models of Fuzzy Portfolio Selection
Abstract - In this paper, a concept of fuzzy semi-entropy is proposed to quantify the downside
uncertainty. Several properties of fuzzy semi-entropy are identified and interpreted. By
quantifying the downside risk with the use of semi-entropy, two mean-semi-entropy portfolio
selection models are formulated and a fuzzy simulation-based genetic algorithm is designed to
solve the models to optimality. We carry out comparative analyses among the fuzzy mean-
entropy models and the fuzzy mean-semientropy models and demonstrate that the mean-semi-
entropy models can significantly improve the dispersion of investment. Several illustrative
examples using stock dataset from the realworld financial market (China Shanghai Stock
Exchange) also show the effectiveness of the models.
Improved Uncertainty Capture for Non-Singleton Fuzzy Systems
Abstract - In non-singleton fuzzy logic systems (NSFLSs), input uncertainties are modelled with
input fuzzy sets in order to capture input uncertainty (e.g., sensor noise). The performance of
NSFLSs in handling such uncertainties depends on both: the appropriate modelling in the input
fuzzy sets of the uncertainties present in the system’s inputs, and on how the input fuzzy sets
(and their inherent model of uncertainty) interact with the antecedent and thus affect the
inference within the remainder of the NSFLS. This paper proposes a novel development on the
latter. Specifically, an alteration to the standard composition method of type-1 fuzzy relations is
proposed, and applied to build a new type of NSFLS. The proposed approach is based on
employing the centroid of the intersection of input and antecedent sets as origin of the firing
degree, rather than the traditional maximum of their intersection, thus making the NSFLS more
sensitive to changes in the input’s uncertainty characteristics. The traditional and novel approach
to NSFLSs are experimentally compared for two well-known problems of Mackey-Glass and
Lorenz chaotic time series predictions, where the NSFLSs’ inputs have been perturbed with
different levels of Gaussian noise. Experiments are repeated for system training under noisy and
noise-free conditions. Analyses of the results show that the new method outperforms the
traditional approach. Moreover, it is shown that while formally more complex, in practice, the
new method has no significant computational overhead compared to the standard approach.

Monotonicity Of SISO Fuzzy Relational Inference with an Implicative Rule Base
Abstract - A Fuzzy Relational Inference (FRI) mechanism is appraised based on the different
desirable properties it possesses. Among these properties, monotonicity of an FRI has not
received much attention. In this work, we investigate the monotonicity of a single input single
output (SISO) FRI with an implicative form of the rule base. In all the previous works that deal
with monotonicity of an FRI with the implicative form of rule base, the employed fuzzy
implications come from a residuated lattice. It can be noticed that this rich underlying structure
plays a major role in proving the results. Further, they also modify the given monotone rule base.
This work differs from the previous works in that (i) the fuzzy implications employed in it do not
come from any known residuated structure on [0; 1] and (ii) the original rule base is employed
without any alteration. We determine conditions under which monotonicity of an FRI, where the
rule base is modeled by a strict fuzzy implication, can be ensured without transforming the
original rule base. Thus the results in this work further augment the case for considering fuzzy
implications, other than those from the residuated setting, to be used in applications.
Uncertain Calculus with Yao Process
Abstract - Uncertain calculus is a branch of mathematics that deals with differentiation and
integration of functions of uncertain processes. This paper investigates the Yao process defined
by the Yao integral and extends the uncertain calculus on Yao process. Some important results is
developed for finite variation and linearity of integral. Moreover, this paper also proposes a
concept of multifactor Yao process and gives a fundamental theorem for multifactor Yao
process.
Finding synergy networks from gene expression data: a fuzzy rule based approach
Abstract - Genes interact among themselves directly as well as indirectly and thereby a gene
regulates the expression levels of other genes. In this work, our objective is to identify a special
type of network called “synergy network”. We want to find synergistic gene pairs that interact
via collaboration with respect to a disease and form a network of such synergistic genes. First we

discuss some issues relating to existing information theoretic methods of finding synergy
networks and then propose a fuzzy rule based approach for discovery of synergy networks.We
justify that fuzzy rule base is a natural choice to realize all the desired attributes of synergistic
relations. To our knowledge, this is the first attempt to exploit fuzzy modeling for finding
synergy networks. The system uses a set of human understandable rules that is generated at a low
cost for every pair of genes. We apply our method on two prostate cancer data sets. We show
that the proposed method is capable of discovering gene pairs that collaborate with each other
with respect to prostate cancer. We demonstrate that our results are statistically significant. We
also discuss the relevance of the identified genes to cancer biology.
Generators of Aggregation Functions and Fuzzy Connectives
Abstract - We show that the class of all aggregation functions on [0; 1] can be generated as a
composition of infinitary supoperation W acting on sets with cardinality not exceeding c, b-
medians Medb, b 2 [0; 1[, and unary aggregation functions 1]0;1] and 1[a;1], a 2]0; 1].
Moreover, we show that we cannot relax the cardinality of argument sets for suprema to be
countable, thus showing a kind of minimality of the introduced generating set. As a by product,
generating sets for fuzzy connectives, such as fuzzy unions, fuzzy intersections and fuzzy
implications are obtained, too.
A self-regulated interval type-2 neuro-fuzzy inference system for handling non-
stationarities in EEG signals for BCI
Abstract - This paper addresses the key problems of nonstationarity and influence of artifacts in
ElectroEncephaloGram (EEG) based Brain-Computer-Interface (BCI) systems. The
nonstationary nature of EEG data arise due to the physiological/ instrumental differences in
intra/inter session of data generation process. This paper proposes a Robust Common Spatial
Pattern feature extraction algorithm (RoCSP) to overcome the effects of artifacts and a Self-
Regulated Interval Type-2 Neuro- Fuzzy Inference System (SRIT2NFIS) to handle this inherent
non-stationarity. Combined together, this approach is referred to as (RoCSP-SRIT2NFIS).
RoCSP algorithm provides better features than the CSP algorithm by excluding those trials that

are affected by the artifacts. SRIT2NFIS uses the features generated by the RoCSP algorithm as
input and handles the non-stationarity as an uncertainty using the interval type-2 fuzzy sets in the
antecedent of fuzzy rules. A self-regulatory learning mechanism is used to evolve the structure
automatically and learn the parameters of the network. A regularized projection based learning
algorithm and a modified rule addition criterion is also proposed to improve the generalization
performance of SRIT2NFIS. Using benchmark data sets, performance evaluation has been
carried out and the results indicate that, compared to other existing algorithms, RoCSP-
SRIT2NFIS produces a higher classification accuracy of 3-5% in simple tasks like leftright
classification and 6-8% in complex tasks like foot-tongue classification. Also a statistical
analysis of the performance results indicates that RoCSP-SRIT2NFIS performs better and is
more suitable for an efficient BCI.
Robust H-infinity based synchronization of the fractional order chaotic systems by using
new self-evolving non-singleton type-2 fuzzy neural networks
Abstract - In this paper a novel H1 based adaptive fuzzy control is presented for the
synchronization of fractional order chaotic systems. A self-evolving non-singleton type-2 fuzzy
neural network (SENST2FNN) is proposed for the estimation of the unknown functions in the
dynamics of the system. The effects of the approximation error and the external disturbances are
eliminated by designing an adaptive compensator, such that the H1 norm of the synchronization
error is minimized and asymptotically stability is achieved. The consequent parameters of SE-
NST2FNN are tuned based on the adaptation laws that are derived from Lyapunov stability
analysis. The antecedent part and the rule database of SE-NST2FNN are optimized based on a
clustering method and the modified invasive weed optimization algorithm, respectively. The
effectiveness of proposed control scheme is verified by simulation examples.
A Generalized C Index for (Internal) Fuzzy Cluster Validity
Abstract - The C index is an internal cluster validity index that was introduced in 1970 as a way
to define and identify a "best" crisp partition on n objects represented by either unlabeled feature

vectors or dissimilarity matrix data. This index is often one of the better performers amongst the
plethora of internal indices available for this task. This article develops a soft generalization of
the C index that can be used to evaluate sets of candidate partitions found by either fuzzy or
probabilistic clustering algorithms. We define four generalizations based on relational
transformations of the soft partition, and then compare their performance to eight other popular
internal fuzzy cluster indices using two methods of comparison (internal "best-c" and
internal/external (I/E) "best match"), 6 synthetic data sets, and 6 real world labeled data sets. Our
main conclusion: the sum-min generalization is the second best performer in the best-c tests, and
the best performer in the I/E tests on small data.
Monotone Fuzzy Rule Relabeling for the Zero-Order TSK Fuzzy Inference System
Abstract - To maintain the monotonicity property of a fuzzy inference system, a monotonically-
ordered and complete set of fuzzy rules is necessary. However, monotonically-ordered fuzzy
rules are not always available, e.g. errors in human judgements lead to non-monotone fuzzy
rules. The focus of this paper is on a new monotone fuzzy rule relabeling (MFRR) method that is
able to relabel a set of non-monotone fuzzy rules to meet the monotonicity property with reduced
computation. Unlike the brute-force approach, which is susceptible to the combinatorial
explosion problem, the proposed MFRR method explores within a reduced search space to find
the solutions; therefore decreasing the computational requirements. The usefulness of the
proposed method in undertaking Failure Mode and Effect Analysis problems is demonstrated
using publicly available information. The results indicate that the MFRR method can produce
optimal solutions with reduced computational time.
Decision Making Support in Telecommunications Networks Management with Matrix
Analysis of Fuzzy Rule-based Systems
Abstract - This paper presents a new general method for Fuzzy analysis, based on mathematical
operations between arrays, which allow the development of simple and fast computational
algorithms, for applications to support decision making in different processes of the

telecommunications network management. The approach is generic enough to be applied at the
operational, tactical and strategic levels of management. To validate the method, prospective
scenarios are analyzed in the period of 2012-2020 for Wire line services in Brazil, developed
through exploratory research, based upon data from official bodies such as Anatel (National
Telecommunications Agency), IBGE (Brazilian Institute of Geography and Statistics) and the
Ministry of Communications.
IEEE Latin America Transactions (March 2016)
Finite-Frequency Model Reduction of Takagi-Sugeno Fuzzy Systems
Abstract - This paper considers the model reduction problem for continuous-time Takagi-
Sugeno (T-S) fuzzy systems. Different from existing full-frequency methods, a finite-frequency
model reduction method is proposed in this paper. The proposed method can get a better
approximation performance when input signals belong to a finite-frequency domain. To this end,
a finite-frequency H1 performance index is firstly defined. Then, a sufficient finite-frequency
performance analysis condition is derived by the aid of Parseval’s theorem and quadratic
functions. Based on this condition and projection lemma, three model reduction algorithms for
T-S fuzzy systems with input signals in low-frequency, middle-frequency, and high-frequency
domain are obtained, respectively. Finally, an example is given to illustrate the effectiveness of
the proposed method.
On Generalized Extended Bonferroni Means for Decision Making
Abstract - The extended Bonferroni mean (EBM) recently proposed differs from the classical
Bonferroni mean as it aims to capture the heterogeneous interrelationship among the attributes
instead of presupposing a homogeneous relation among them. In this study, we generalize the
EBM to explicitly and profoundly understand its aggregation mechanism by defining a
composite aggregation function. We adopt the approach of optimizing the choice of weighting
vectors for the generalized EBM (GEBM) with respect to the least absolute deviation of
residuals. We also investigate several desirable properties of the GEBM. Our special interest in
this study is to investigate the ability of the GEBM to model mandatory requirements. Finally,
the influence of replacing the conjunctive of the GEBM is analyzed to show how the change of

the conjunctive affects the global andness and orness of the GEBM. Meanwhile, the aggregation
mechanism of the EBM is specified and provided with quite intuitive interpretations for
application.
Sparsity-aware Possibilistic Clustering Algorithms
Abstract - In this paper two novel possibilistic clustering algorithms are presented, which utilize
the concept of sparsity. The first one, called sparse possibilistic c-means, exploits sparsity and
can deal well with closely located clusters that may also be of significantly different densities.
The second one, called sparse adaptive possibilistic c-means, is an extension of the first, where
now the involved parameters are dynamically adapted. The latter can deal well with even more
challenging cases, where, in addition to the above, clusters may be of significantly different
variances. More specifically, it provides improved estimates of the cluster representatives, while,
in addition, it has the ability to estimate the actual number of clusters, given an overestimate of
it. Extensive experimental results on both synthetic and real data sets support the previous
statements.
Dissimilarity Metric Learning in the Belief Function Framework
Abstract - The Evidential K-Nearest-Neighbor (EK-NN) method provided a global treatment of
imperfect knowledge regarding the class membership of training patterns. It has outperformed
traditional K-NN rules in many applications, but still shares some of their basic limitations, e.g.,
1) classification accuracy depends heavily on how to quantify the dissimilarity between different
patterns and 2) no guarantee for satisfactory performance when training patterns contain
unreliable (imprecise and/or uncertain) input features. In this paper, we propose to address these
issues by learning a suitable metric, using a low-dimensional transformation of the input space,
so as to maximize both the accuracy and efficiency of the EK-NN classification. To this end, a
novel loss function to learn the dissimilarity metric is constructed. It consists of two terms: the
first one quantifies the imprecision regarding the class membership of each training pattern;
while, by means of feature selection, the second one controls the influence of unreliable input
features on the output linear transformation. The proposed method has been compared with some

other metric learning methods on several synthetic and real data sets. It consistently led to
comparable performance with regard to testing accuracy and class structure visualization.
Adaptive Fuzzy Tracking Control Design for Uncertain Non-Strict Feedback Nonlinear
Systems
Abstract - This paper investigates an adaptive fuzzy tracking control design problem for single-
input and single-output (SISO) uncertain non-strict feedback nonlinear systems. For the cases of
the states measurable and the states immeasurable, fuzzy logic systems are separately adopted to
approximate the unknown nonlinear functions or model the uncertain nonlinear systems. In the
unified framework of adaptive backstepping control design, both adaptive fuzzy state feedback
and observer-based output feedback control design schemes are proposed. The stability of the
closed-loop systems is proved by using Lyapunov function theory. The simulation examples are
provided to confirm the effectiveness of the proposed control methods.
Uncertain Random Renewal Reward Process with Application to Block Replacement
Policy
Abstract - As a mixture of uncertain variable and random variable, uncertain random variable is
an important tool to describe indeterminacy phenomena. In order to model the evolution of
uncertain random phenomena, a concept of uncertain random process has been proposed, and
uncertain random renewal process has been designed as an example. This paper aims at
proposing a new type of uncertain random process, called uncertain random renewal reward
process, in which the inter-arrival times and the rewards are assumed to be random variables and
uncertain variables, respectively. The chance distribution of the renewal reward process is
obtained, and the reward rate is derived. A renewal reward theorem is verified which shows the
reward rate converges in distribution to an uncertain variable derived from the random inter-
arrival times and the uncertain rewards. As an application, this paper also proposes an uncertain
random block replacement problem, and formulates an unconstrained optimization model by
using uncertain random renewal reward process.

Characterization of fuzzy implication functions with a continuous natural negation
satisfying the law of importation with a fixed t-norm
Abstract - The law of importation is an important property of fuzzy implication functions with
interesting applications in approximate reasoning and image processing. This property has been
extensively studied and some open problems have been posed in the literature. In particular, in
this paper, we partially solve an open problem related to this property posed some years ago.
Specifically, given a fixed t-norm T, all fuzzy implication functions with continuous natural
negation that satisfy the law of importation with this t-norm T are characterized. This
characterization is specially detailed for the case of any continuous tnorm T and particular cases
are given for the minimum t-norm, for any continuous Archimedean t-norm and for any ordinal
sum of continuous Archimedean t-norms. For non-continuous t-norms, the particular cases of the
drastic t-norm and the nilpotent minimum t-norm are also presented separately. Finally,
characterizations of some well-known fuzzy implication functions are also deduced from the
presented results.
IEEE Transactions on Fuzzy Systems (April 2016)
An Optimal Fuzzy System for Edge Detection in Color Images using Bacterial Foraging
Algorithm
Abstract - This paper presents a fuzzy system for edge detection, using Smallest Univalue
Segment Assimilating Nucleus (SUSAN) principal and Bacterial Foraging Algorithm (BFA).
The proposed algorithm fuzzifies the Univalue Segment Assimilating Nucleus (USAN) area
obtained from the original image, using a USAN area histogram based Gaussian membership
function. A parametric fuzzy intensifier operator (FINT) is proposed to enhance the weak edge
information, which results in another fuzzy set. The fuzzy measures: fuzzy edge quality factors
and sharpness factor are defined on fuzzy sets. BFA is used to optimize the parameters involved
in fuzzy membership function and FINT. The fuzzy edge map is obtained using optimized
parameters. The adaptive thresholding is used to de-fuzzify the fuzzy edge map to obtain a
binary edge map. The experimental results are analyzed qualitatively and quantitatively. The
quantitative measures: Pratt’s FOM, Cohen’ Kappa, Shannon’s Entropy and edge strength

similarity based edge quality metric, are used. The quantitative results are statistically analyzed
using t-test. The proposed algorithm outperforms many of the traditional and state-of-art edge
detectors.
A Note on Fuzzy Joint Points Clustering Methods for Large Data Sets
Abstract - Integrating clustering algorithms with fuzzy logic typically yields more robust
methods, which require little to no supervision of user. The fuzzy joint points (FJP) method is a
density based fuzzy clustering approach that can achieve quality clustering. However, early
versions of the method hold high computational complexity. In a recent work, the speed of the
method was significantly improved without sacrificing clustering efficiency and an even faster
but parameter dependent method was also suggested. Yet, the clustering performance of the
latter was left as an open discussion and subject of study. In this study, we prove the existence of
the appropriate parameter value and give an upper bound on it to discuss whether and how the
parameter dependent method can achieve the same clustering performance with the original
method.
Adaptive Inversion-Based Fuzzy Compensation Control of Uncertain Pure-Feedback
Systems With Asymmetric Actuator Backlash
Abstract - This research concerns with the problem of adaptive inverse compensation control for
a class of uncertain purefeedback nonlinear systems with asymmetric actuator backlash. By
resorting to the mean-value theorem, the considered system can be transformed into the strict-
feedback form with unknown states-dependent virtual control coefficients. Then the most
challenging difficulty is how to design the adaptive backlash inverse compensator in face of
uncertain control gain function. To overcome this challenge, we first propose a smooth inverse
model for asymmetric backlash, and based on it, a new expression of adaptive compensation
error is further developed in Propositions 1–2, which also paves the way to the embeddedness of
fuzzy logic systems to cancel the unknown gain function. Moreover, two mutually learning
mechanisms (one is for predicting unknown backlash parameters, while another is to search for
optimal fuzzy weights) are further constructed such that the inverse compensator can be updated

online. With the backstepping iteration design of compensator input, an adaptive fuzzy
compensation controller (i.e., the compensator output) is developed to ensure the asymptotic
stability of closed-loop system. Finally, comparative simulations are conducted to validate the
effectiveness and applicability of the proposed control theory.
Assessing a Fuzzy Extension of Rand Index and Related Measures
Abstract - This empirical study extends the results of Hüllermeier et al. (2012). It examines the
ability of a generalisation of the Rand index and four related measures of similarity to recover
the cluster structure of the data in the framework of fuzzy c-means clustering. The index range is
also used as a criterion statistic. A Monte Carlo simulation is conducted for both the null case
and where the data have a well-defined cluster structure. The fuzzy extension of the related
measures is not so effective for imbalanced data. On the contrary, whether the index is Dice,
Fowlkes and Mallows, Hurbert and Arabie, or Jaccard, it provides reliable results for noise data
or for data containing fairly balanced clusters. The criticisms of the Rand index in the context of
crisp clustering can also be extended to its fuzzy version.
Fractional Differential Systems: A Fuzzy Solution based on Operational Matrix of Shifted
Chebyshev Polynomials and its Applications
Abstract - In this paper, a new formula of fuzzy Caputo fractional-order derivatives (0 < v 1) in
terms of shifted Chebyshev polynomials is derived. The proposed approach introduces shifted
Chebyshev operational matrix in combination with shifted Chebyshev tau technique for the
numerical solution of linear fuzzy fractional order differential equations. The main advantage of
the propose approach is that it simplifies the problem alike in solving a system of fuzzy algebraic
linear equation. An approximated error bound between the exact solution and the proposed fuzzy
solution with respect to the number of fuzzy rules and solution errors is derived. Furthermore, we
also discuss the convergence of the proposed method from the fuzzy perspective.
Experimentally, we show the strength of the proposed method in solving a variety of FDE
models under uncertainty encountered in engineering and physical phenomena (i.e

viscoelasticity, oscillations and Resistor-Capacitor (RC) circuits). Comparisons are also made
with solutions obtained by the Laguerre polynomials and fractional Euler method.
Finite-Time Stabilization of Discrete-Time Switched Nonlinear Systems without Stable
Subsystems via Switching Signals Design
Abstract - This paper investigates the finite-time exponential stability analysis and stabilization
problem of discrete-time switched nonlinear systems without stable subsystems. In the stability
analysis, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate nonlinear
subsystems. With two level functions, namely, crisp switching functions and local fuzzy
weighting functions, we introduce switched fuzzy systems with approximation errors, which
inherently contain both the features of the switched systems and T-S fuzzy systems. By
constructing the “decreasing-jump” piecewise Lyapunov-like functions and minimum dwell time
technique, a finite-time exponential stability of switched fuzzy systems with bounded
approximation errors is obtained. Then based on the finite-time exponential stability, a multi-
objective evolution algorithm (EA) (non-dominated sorting genetic algorithm, NSGA-II), which
considers two conflicting objectives, such as the average convergence error and the average
switching cost, is proposed to generate trade-off switching sequences to stabilize the discrete-
time switched nonlinear systems over a finite-time interval. A numerical example and a practical
example are provided to illustrate the effectiveness of the stability and the algorithm,
respectively.
FN-TOPSIS: Fuzzy Networks for Ranking Traded Equities
Abstract - Fuzzy systems consisting of networked rule bases, called fuzzy networks, capture
various types of imprecision inherent in financial data and in the decision-making processes on
them. This paper introduces a novel extension of the Technique for Ordering of Preference by
Similarity to Ideal Solution (TOPSIS) method and uses fuzzy networks to solve multi criteria
decision-making problems where both benefit and cost criteria are presented as subsystems.

Thus, the decision maker evaluates the performance of each alternative for portfolio optimisation
and further observes the performance for both benefit and cost criteria. This approach improves
significantly the transparency of the TOPSIS methods, while ensuring high effectiveness in
comparison to established approaches. The proposed method is further tested to solve the
problem of selection/ranking of traded equity covering developed and emergent financial
markets. The ranking produced by the method is validated using Spearman rho rank correlation.
Based on the case study, the proposed method outperforms the existing TOPSIS approaches in
terms of ranking performance.
Robust H-infinity Filtering for A Class of Two-Dimensional Uncertain Fuzzy Systems with
Randomly Occurring Mixed Delays
Abstract - This paper is concerned with the robust H1 filtering problem for a class of two-
dimensional (2-D) uncertain fuzzy systems with randomly occurring mixed delays (ROMDs).
The underlying 2-D systems are described by the Fornasini- Marchesini (FM) model and the
uncertainty is expressed in a linear fraction form. An improved Takagi-Sugeno (T-S) fuzzy
model corresponding to the spatial promise variables is adopted to represent the complicated 2-D
nonlinear system. The mixed delays consisting of both discrete and distributed delays are
allowed to appear in a random manner governed by two sets of Bernoulli distributed white
sequences with known probability. A full-order fuzzy filter is constructed to estimate the output
signal such that, in the presence of parameter uncertainties and ROMDs, the dynamics of the
estimation errors is asymptotically stable with a prescribed H1 disturbance attenuation level.
Based on the stochastic analysis technique and the Lyapunovlike functional, sufficient conditions
are established to ensure the existence of the desired filters and the explicit expressions of such
filters are derived by means of the solution to a class of convex optimization problems that can
be solved via standard software packages. A numerical example is provided to demonstrate the
effectiveness of the developed filter design algorithms and the filter performances with and
without fuzzy rules are also compared.
Non-Parametric Kernel Estimation based on Fuzzy Random Variables

Abstract - This paper extends the classical non-parametric curve fitting methods for fuzzy
random variables. The study was conducted in two parts: 1) fuzzy density estimation and 2) non-
parametric regression. The classical non-parametric density estimation was first developed based
on kernel method for a given fuzzy random sample at crisp and/or fuzzy point based on crisp or
fuzzy bandwidth. The classical bandwidth selection was also extended when the underlying
population was normal with known or unknown fuzzy variance. Moreover, the classical non-
parametric kernel-based regression model with crisp and/or input or output is extended whenever
a given bandwidth is a crisp or fuzzy number. The cross-validation procedure for selecting the
optimal value of the (crisp) smoothing parameter is also extended to fit the proposed non-
parametric regression model. The large sample properties of the proposed fuzzy estimators were
also investigated by some theorems. Several numerical examples including that of a real life data
are used to illustrate the proposed methods in curve fitting estimation with crisp and/or fuzzy
information. Moreover, the proposed methods were examined in comparison with some other
existing methods and their effectiveness were clarified via some numerical examples and
simulation studies. Both theatrical and numerical results indicated that the non-parametric curve
fitting methods significantly reduced the sum of square errors as well as the spreads of the fuzzy
curve fitting estimation.
A Profit Maximizing Solid Transportation Model under Rough Interval Approach
Abstract - The present study attempts to establish an innovative solid transportation problem
that intends to maximize profit under the rough interval approximation methodology. Two
transportation problems were constructed in this regard with interval coefficients corresponding
to the upper approximations and the lower approximations of the rough intervals under study.
Furthermore, from the contingent solid transportation problems, four different classical solid
transportation problems were derived which were subsequently solved on the LINGO® iteration
platform. The concept of completely satisfactory solution and rather satisfactory solution, surely
optimal range, possibly optimal range and rough optimal range have been discussed with a
perspective to its relevance to real world practical problems. The rough chance constrained
programming and the expected value operator for rough interval have been applied to solve the

problem under study. The distinct advantages of the proposed method over those existing have
been outlined. Numerical examples have also been provided to illustrate the solution procedure
and the methodologies adopted.
Fuzzy Adaptive Inverse Compensation Method to Tracking Control of Uncertain
Nonlinear Systems With Generalized Actuator Dead Zone
Abstract - This paper solves the problem of adaptive fuzzy inverse compensation control for
uncertain nonlinear system whose actuator is subjected to generalized dead-zone nonlinearity. By
defining a continuous connection function and combining with mean-value theorem, the
generalized dead zone is firstly decomposed into a nominal asymmetric dead zone multiplying
an uncertain continuous input function. Afterwards, a smooth inversion and its parameterization
are further proposed such that a new expression of adaptive asymmetric dead-zone compensation
error is established in Theorems 1–2. With such an expression, the fuzzy systems can be
successfully embedded into compensation structure to indirectly handle uncertain input
dynamics. In addition, a separation scheme is developed to construct two online estimators.
Based on above design procedure, an adaptive inverse compensator for generalized dead zone is
built eventually. With backstepping iteration design of compensator input, an adaptive fuzzy
controller is developed to establish the closed-loop system stability. Finally, two simulations are
conducted to illustrate the effectiveness and applicability of the proposed control scheme.
Sampled-data fuzzy stabilization of nonlinear systems under nonuniform sampling
Abstract - This paper investigates the sampled-data fuzzy stabilization problem for a class of
nonlinear systems that is exactly modeled in T-S fuzzy form at least locally. A new method for
designing parallel distribution compensation (PDC) fuzzy controller is proposed, which just
requires that the nonlinear function is locally Lipschitz. By considering the sample-andhold
behavior of the system and using Jensen’s integral inequality, an inequality constrain condition is
derived from the locally Lipschitz property. Further, by defining a time-dependent Lyapunov-
Krasovskii functional (LKF) term, a new technique instead of the use of S-procedure is
developed, and stabilization conditions for state feedback and observer-based output feedback

under nonuniform sampling are obtained, respectively. Compared with the existing ones, the new
design method not only avoids the difficulty of finding exact upper bounds of asynchronous
errors of mismatch membership functions, but also contains less conservatism and less numerical
complexity. Finally, some illustrative examples are given to show the effectiveness of the
proposed design method and the significant improvement over the existing results.
Parametrization and Adaptive Control of Multivariable Non-Canonical T-S Fuzzy Systems
Abstract - This paper conducts a new study for adaptive Takagi-Sugeno (T-S) fuzzy
approximation based control of multiinput and multi-output (MIMO) non-canonical form
nonlinear systems. Canonical-form nonlinear systems have explicit relative degree structures,
whose approximation models can be directly used to derive desired parametrized controllers.
Non-canonical form nonlinear systems usually do not have such a feature, nor do their
approximation models which are also in noncanonical forms. This paper shows that it is
desirable to reparametrize non-canonical form T-S fuzzy system models with smooth
membership functions for adaptive control and such system re-parametrization can be realized
using relative degrees, a concept yet to be studied for MIMO non-canonical form T-S fuzzy
systems. The paper develops an adaptive feedback linearization scheme for control of such
general system models with uncertain parameters, by first deriving various relative degree
structures and normal forms for such systems. Then, a reparametrization procedure is developed
for such system models, based on which adaptive control designs are derived, with desired
stability and tracking properties analyzed. A detailed example is presented with simulation
results to show the new control design procedure and desired control system performance.
Stability and Stabilization of Discrete-Time T-S Fuzzy Systems with Time-Varying Delay
via Cauchy-Schwartz-Based Summation Inequality
Abstract - This paper proposes new stability and stabilization conditions for discrete-time fuzzy
systems with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional
and introducing a new summation inequality based on the inequality of Cauchy-Schwartz form,
which enhances the feasible region of the stability criterion for discrete-time systems with time-

varying delay, a stability criterion for such systems is established. In order to show the
effectiveness of the proposed inequality, which provides more tight lower bound of a summation
term of quadratic form, a delay-dependent stability criterion for such systems is derived within
the framework of linear matrix inequalities (LMIs) which can be easily solved by various
effective optimization algorithms. Going one step forward, the proposed inequality is applied to
a stabilization problem in discrete-time fuzzy systems with time-varying delays. The advantages
of proposed stability and stabilization criteria are illustrated via two numerical examples.
Adaptive fuzzy leader-following consensus control for stochastic multi-agent systems with
heterogeneous nonlinear dynamics
Abstract - This paper focuses on the leader-following consensus control problem of multi-agent
systems in random vibration environment. The Itˆo stochastic systems with heterogeneous
unknown dynamics and external disturbances are established to describe the agents in random
vibration environment. The fuzzy logic systems are applied to approximate the unknown
nonlinear dynamics and one adaptive parameter is designed to decay the effect of external
disturbances. We present a new distributed consensus controller for each follower agent only
based on local information which is measured or received from its neighbors and itself. Under
the consensus controller, we prove that all the follower agents can keep consensus with the
leader even though only a very small part of follower agents can measure or receive the state
information of the leader. Furthermore, the states of all the follower agents are bounded in
probability. Finally, the simulation results are provided to illustrate the effectiveness of designed
algorithm.
Adaptive Fuzzy Backstepping Tracking Control for Strict-Feedback Systems with Input
Delay
Abstract - This paper investigates the problem of adaptive fuzzy tracking control for nonlinear
strict-feedback systems with input delay and output constraint. Input delay is handled based on
the information of Pade approximation and output constraint problem is solved by barrier
Lypaunov function. Some adaptive parameters of the controller need to be updated online

through considering the norm of membership function vector instead of all sub-vectors. A novel
adaptive fuzzy tracking control scheme is developed to guarantee all variables of the closed-loop
systems are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error can be
adjusted around the origin with a small neighborhood. The stability of the closed-loop systems is
proved and simulation results are given to demonstrate the effectiveness of the proposed control
approach.
IEEE Transactions on Fuzzy Systems (May 2016)
Teleoperation Control of An Exoskeleton Robot Using Brain Machine Interface and Visual
Compressive Sensing
Abstract - This paper presents a teleoperation control for an exoskeleton robotic system based
on the brain-machine interface (BMI) and vision feedback. Vision compressive sensing,
brainmachine reference commands, and adaptive fuzzy controllers in joint-space have been
effectively integrated to enable robot performing manipulation tasks guided by human operator’s
mind. First, a visual-feedback link is implemented by video captured by a camera, allowing
him/her to visualize the manipulator’s workspace and the movements being executed. Then,
compressed images are used as feedback errors in a nonvector space for producing SSVEP
(Steady-State Visual Evoked Potentials) electroencephalography (EEG) signals, and it requires
no prior information on features in contrast to the traditional visual servoing. The proposed EEG
decoding algorithm generates control signals for the exoskeleton robot using features extracted
from neural activity. Considering coupled dynamics and actuator input constraints during the
robot manipulation, a local adaptive fuzzy controller has been designed following Lyapunov
synthesis to drive the exoskeleton tracking the intended trajectories in human operator’s mind
and to provide a convenient way of dynamics compensation with minimal knowledge of the
dynamics parameters of the exoskeleton robot. Extensive experiment studies employing three
subjects have been performed to verify the validity of the proposed method.
Varying Spread Fuzzy Regression for Affective Quality Estimation
Abstract - Design of preferred products requires affective quality information which relates to
human emotional satisfaction. However, it is expensive and time consuming to conduct a full

survey to investigate affective qualities regarding all objective features of a product. Therefore,
developing a prediction model is essential in order to understand affective qualities on a product.
This paper proposes a novel fuzzy regression method in order to predict affective quality and
estimate fuzziness in human assessment, when objective features are given. The proposed fuzzy
regression also improves on traditional fuzzy regression that simulate only a single characteristic
with the resulting limitation that the amount of fuzziness is linear correlated with the independent
and dependent variables. The proposed method uses a varying spread to simulate nonlinear and
nonsymmetrical fuzziness caused by affective quality assessment. The effectiveness of the
proposed method is evaluated by two very different case studies, affective design of an electric
iron and image quality assessment, which involve different amounts of data, varying fuzziness,
and discrete and continuous data. The results obtained by the proposed method are compared
with those obtained by the state-of-art and the recently-developed fuzzy regression methods. The
results show that the proposed method can generate better prediction models in terms of three
fuzzy criteria which address both predictions of magnitudes and fuzziness.
Adaptive Predefined Performance Control for MIMO Systems with Unknown Direction
via Generalized Fuzzy Hyperbolic Model
Abstract - Adaptive predefined performance control problem is investigated for a class of
multiple-input-multiple-output systems with unknown control direction and unknown backlash-
like hysteresis nonlinearities by using generalized fuzzy hyperbolic model (GFHM). Compared
with the existing methods, the main features are as follows: 1) the prediction error is introduced
to construct the adaptive laws, which means that the approximate accuracy of the GFHM is
solved, 2) the Nussbaum-type gain is utilized to deal with the unknown control direction, which
avoids the requirement of direction a priori, and 3) by transforming the tracking errors into new
error variables, the prescribed steady state and transient performance can be ensured. It is shown
that the proposed control approach can guarantee that all the signals of the resulting closed-loop
systems are bounded and the output tracks a desired trajectory while the tracking errors are
confined all times within the prescribed bounds. Finally, two simulation results and some
comparisons are provided to verify the effectiveness of the proposed approach. Since the

proposed control strategy is only implemented in a healthy case, how to extend the strategy to a
faulty case will be a further topic.
Revisiting fuzzy set and fuzzy arithmetic operators and constructing new operators in the
land of probabilistic linguistic computing
Abstract - In this study, we use a framework known as probabilistic linguistic computing (PLC)
to achieve two goals. First, we demonstrate it as an easy-to-use laboratory for understanding
existing fuzzy operators. This is achieved by projecting a fuzzy operator of interest into the PLC
setting, arriving at a corresponding PLC operator and hence revealing assumptions initially
hidden in that operator. Second, we demonstrate PLC as a simple and general approach for the
engineers to construct a wide range of fuzzy operators and measures that can be robustly used in
their specialized applications. In particular, by explicating the assumptions hidden in the
commonly used fuzzy set and fuzzy arithmetic operators, one is in position to develop other
potentially more complex operators (such as fuzzy entropy measure or fuzzy partial correlation
measures) that possess the same assumptions – these complex operators so developed can then
be viewed as compatible and consistent with the commonly used fuzzy set and arithmetic
operators.
Dynamic Output-Feedback Dissipative Control for T-S Fuzzy Systems with Time-Varying
Input Delay and Output Constraints
Abstract - This paper develops a new fuzzy dynamic outputfeedback control scheme for Takagi-
Sugeno (T-S) fuzzy systems with time-varying input delay and output constraints based on (Q;
S;R)--dissipativity. The proposed controller, called a (Q; S;R)--dissipative output-feedback fuzzy
controller, takes into consideration the abstract energy, storage function, and supply rate for the
disturbance attenuation and provides a unified framework that can incorporate existing results for
H1 and passivity controllers as special cases for T-S fuzzy systems with time-varying input delay
and output constraints. A dynamic parallel distributed compensator is used to design the (Q;

S;R)--dissipative output-feedback fuzzy controller to ensure the asymptotic stability and strict
(Q; S;R)--dissipativity of closed-loop systems described by a T-S fuzzy model that satisfies some
output constraints. By employing the reciprocally convex approach, a new set of delay-
dependent conditions for the desired controller is formulated in terms of the linear matrix
inequality. The effectiveness and the applicability of the proposed design techniques are
validated by an example of control for active suspension systems for different road conditions.
Asymptotic Fuzzy Tracking Control for a Class of Stochastic Strict-Feedback Systems
Abstract - This paper presents an asymptotic tracking control design method for stochastic
strict-feedback systems via fuzzy logic systems. In the existing results, stochastic controls are
usually limited to be bounded in probability. But, how to realize the asymptotic tracking control
for stochastic strict-feedback systems remains a control dilemma. This paper achieves the
asymptotic tracking control by proposing a novel gain suppressing inequality approach.
Specifically, the three-part construction is performed to achieve such control objective for
stochastic systems. Firstly, the novel gain suppressing inequality technique is developed to lay
the foundation for carrying out the Lyapunov stability analysis. Secondly, the developed
inequality technique is integrated with each step of the backstepping based adaptive control
design procedure. Thirdly, analyses are provided to realize the asymptotic tracking control of
stochastic strict-feedback systems.
Teleoperation Control of An Exoskeleton Robot Using Brain Machine Interface and Visual
Compressive Sensing
Abstract - This paper presents a teleoperation control for an exoskeleton robotic system based
on the brain-machine interface (BMI) and vision feedback. Vision compressive sensing,
brainmachine reference commands, and adaptive fuzzy controllers in joint-space have been
effectively integrated to enable robot performing manipulation tasks guided by human operator’s
mind. First, a visual-feedback link is implemented by video captured by a camera, allowing
him/her to visualize the manipulator’s workspace and the movements being executed. Then,
compressed images are used as feedback errors in a nonvector space for producing SSVEP

(Steady-State Visual Evoked Potentials) electroencephalography (EEG) signals, and it requires
no prior information on features in contrast to the traditional visual servoing. The proposed EEG
decoding algorithm generates control signals for the exoskeleton robot using features extracted
from neural activity. Considering coupled dynamics and actuator input constraints during the
robot manipulation, a local adaptive fuzzy controller has been designed following Lyapunov
synthesis to drive the exoskeleton tracking the intended trajectories in human operator’s mind
and to provide a convenient way of dynamics compensation with minimal knowledge of the
dynamics parameters of the exoskeleton robot. Extensive experiment studies employing three
subjects have been performed to verify the validity of the proposed method.
An Extended Type-Reduction Method for General Type-2 Fuzzy Sets
Abstract - A centroid type-reduction strategy for computing the centroids of type-2 fuzzy sets
based on decomposed -planes was proposed by Liu. However, it cannot be applied to type-2
fuzzy sets with concave secondary membership functions. In this paper, we extend the Liu’s
method so that the centroids of type- 2 fuzzy sets with concave secondary membership functions
can be derived. For each decomposed -plane, we convert it into a group of interval type-2 fuzzy
sets. The union of the centroids of its member interval type-2 fuzzy sets constitutes the centroid
of the -plane. Then the weighted union of the centroids of the decomposed -planes becomes the
centroid type-reduced set of the original type-2 fuzzy set. When dealing with type-2 fuzzy sets
with convex secondary membership functions, our proposed method is reduced to the Liu’s
method.
LMI-based Stability Analysis for Piecewise Multi-Afﬁne Systems
Abstract - This paper provides a computational method to study the asymptotic stability of
piecewise multi-affine systems. Such systems stem from a class of fuzzy systems with singleton
consequents and can be used to approximate any smooth nonlinear system with arbitrary
accuracy. Based on the choice of piecewise Lyapunov functions, stability conditions are
expressed as a feasibility test of a convex optimization with linear matrix inequality constraints.

The basic idea behind these conditions is to exploit the parametric expressions of piecewise
multi-affine systems by means of Finsler’s lemma. Numerical examples are given to point out
the effectiveness of the proposed method.
Design of state feedback adaptive fuzzy controllers for second order-systems using a
frequency stability criterion
Abstract - This paper proposes a design method for secondorder systems that guarantees the
stability of an adaptive fuzzy controller with state feedback. The system consists of a linear
unstable plant, the Takagi-Sugeno controller, a nonlinear reference model and an adaptation
mechanism. In this paper, gradient-based adaptation is used to change the consequents of the
controller rules so that the closed-loop system behaves like the reference model. The proposed
method utilizes a frequencydomain criterion in the form of the modified circle theorem. The
controller function is assumed to be a nonlinearity described by a sector condition, which means
that the function lies between two planes. During the process of adaptation this function is
verified so it stays in the sector guaranteeing stability. The method described here is illustrated
by an example of a control system containing an unstable plant with an unknown pole in the
right half-plane. The motivation of this paper is to propose a frequency-domain method for the
design of state feedback adaptive fuzzy controllers. Comparing with time domain methods that
require advanced software tools, the proposed method offers simple graphical interpretation on
the Nyquist plane.
IEEE Transactions on Fuzzy Systems (May 2016)|
The spatial disaggregation problem: simulating reasoning using a fuzzy inference system
Abstract - The spatial disaggregation problem is an interesting problem when investigating and
processing geographically correlated data; it is a special case of the map overlay problem. The
map overlay problem occurs when data that are presented in incompatible grids need to be
combined or compared; the spatial disaggregation problem is a special case in which the cells of
one grid partition the cells of the other grid. The main reason for spatial disaggregation is to
increase the spatial resolution of the data. Traditionally, similar methods as for the map overlay
problem are used; fairly straightforward assumptions on the geographical distribution of the data

are made, but these assumptions do not match the real world situation. The approach presented in
this contribution uses additionally available data (proxy data) that provides information on the
geographic distribution of the input data. As will be illustrated, having this proxy data still does
not provide for a straight forward solution and incorporating it inquires some form of reasoning
which will be achieved by means of a dynamically constructed fuzzy inference system.
The ranking of multi-dimensional uncertain information based on metrics on the fuzzy
ellipsoid number space
Abstract - On the usual high dimensional fuzzy number space, the usual supremum metric D
(derived by the Hausdorff metric between the level sets of usual n- dimension fuzzy numbers)
and the “p” metric p are the most common metrics. However, due to the complexity of the level
sets of usual n-dimensional fuzzy numbers, the two kinds of metrics not only have a tendency to
be rougher, but also are difficult to give concrete expression formulas (this affects their theory
and application research). In this paper, some new metrics on fuzzy ellipsoid number space are
introduced, which not only can better reveal the difference between two different fuzzy ellipsoid
numbers, but also have concrete expression formulas (expressed with the level set functions of
fuzzy ellipsoid numbers). And the properties of the new introduced metrics and the relationships
between the new metrics and the usual metrics (D and p) are studied, and some results are
obtained. Then, we give the concept of supremum (infimum) of bounded subsets of fuzzy
ellipsoid number space, and obtain its concrete calculation formula. And then, by using the
obtained results, we propose a method to rank multidimensional uncertain information, and give
a practical example to show the application and the rationality of the proposed techniques.
A Fitting Model for Feature Selection with Fuzzy Rough Sets
Abstract - Fuzzy rough set is an important rough set model used for feature selection. It uses the
fuzzy rough dependency as a criterion for feature selection. However, this model can merely
maintain a maximal dependency function. It does not fit a given data set well and cannot ideally
describe the differences in sample classification. Therefore, in this study, we introduce a new
model for handling this problem. First, we define the fuzzy decision of a sample using the

concept of fuzzy neighborhood. Then, a parame- terized fuzzy relation is introduced to
characterize the fuzzy information granules, using which the fuzzy lower and upper
approximations of a decision are reconstructed and a new fuzzy rough set model is introduced.
This can guarantee that the membership degree of a sample to its own category reaches the
maximal value. Furthermore, this approach can fit a given data set and effectively prevents
samples from being misclassified. Finally, we define the significance measure of a candidate
attribute and design a greedy forward algorithm for feature selection. Twelve data sets selected
from public data sources are used to compare the proposed algorithm with certain existing
algorithms, and the experimental results show that the proposed reduction algorithm is more
effective than classical fuzzy rough sets, especially for those data sets for which different
categories exhibit a large degree of overlap.
IEEE Transactions on Fuzzy Systems (June 2016)
Admissibility Analysis and Control Synthesis for T-S Fuzzy Descriptor Systems
Abstract - The problem of admissibility analysis and control synthesis for Takagi-Sugeno (T-S)
fuzzy descriptor systems is investigated. Firstly, based on Nonquadratic fuzzy Lyapunov
function and fully using the information of fuzzy membership functions, a new relaxed sufficient
condition ensuring a fuzzy descriptor system to be admissible (regular, impulse-free and stable)
is proposed, in which it is not necessary to require every fuzzy subsystem to be stable. Secondly,
the other sufficient condition for the admissibility is obtained without the information of time
derivatives of fuzzy membership functions. Following the analysis, both parallel and nonparallel
distributed compensation controllers are designed, linear matrix inequalities (LMIs) conditions
are given to construct the controllers. Finally, some examples are provided to illustrate the main
results in the paper less conservative than some earlier related results.
Subspace-Based Takagi-Sugeno Modeling for Improved LMI Performance
Abstract - Given a nonlinear system, the sector-nonlinearity methodology provides a systematic
way of transforming it in an equivalent Takagi-Sugeno model. However, such transformation is
not unique: conservatism of shape-independent performance conditions in the form of linear
matrix inequalities results in some models yielding better results than others. This paper provides

some guidelines on choosing a sector-nonlinearity Takagi-Sugeno model, with provable
optimality (in a particular sense) in the case of quadratic nonlinearities. The approach is based on
Hessian and restrictions of a function onto a subspace.
Measuring Similarity and Ordering based on Interval Type-2 Fuzzy Numbers
Abstract - This paper extends a preference degree to rank interval type-2 fuzzy numbers. A
general method to measure the similarity between interval type-2 fuzzy numbers is also
introduced. Using some theorems and lemmas, it is proven that the extended similarity measures
satisfy many common and desired properties based on the common axiomatic definitions
introduced for similarity measures. The main properties of the extended preference degree are
studied. In addition, several possible applications of the proposed methods are illustrated by
some application examples in pattern recognition and multi-criteria group decision-making.
Moreover, the proposed methods are examined in order to compare them with other existing
methods and the feasibility and effectiveness of the proposed methods are cleared via some
lemmas and numerical comparisons.
Statistical Inference in Rough Set Theory Based on Kolmogorov-Smirnov Goodness-of-Fit
Test
Abstract - Dependency degree (DD) and importance degree (ID) of patterns is crucial for
patterns appraisement and model reconstruction. In rough set data analysis (RSDA), DD and ID
lack robustness because the lower approximation set is terribly unstable under the indiscernibility
relation perturbation. Statistical inference is a good way to deal with this instability. However,
the fixed value hypothesis testing and interval estimation of DD and ID were only discussed by 2
test, which merely suits for two contingency tables with the same number of elements and their
nonzero elements must exist at the same positions. These requirements are too strict for practical
applications. In this paper, Kolmogorov-Smirnov goodness-of-fit test is introduced to generalize
the statistical inferences of DD and ID. As the bridge between data and corresponding measures,

contingency table lies at the core of RSDA. By transforming contingency table to a random
sample of a hypothesized random variable, algorithms EGoFTCT and AGoFTCT are proposed
based on Kolmogorov-Smirnov statistic to implement goodnessof- fit tests of contingency tables.
Better than 2 test, all contingency tables, even with different numbers and different positions of
nonzero elements, are permitted. Subsequently, by generating a contingency table with expected
DD value, the fixed value hypothesis of DD is transformed to the goodness-of fit test between
the original and expected contingency tables. Three algorithms, HToDD-ks, REoDD-ks, and
ST&REoID-ks, are proposed as fixed value hypothesis tests and region estimations of DD and
ID. These algorithms can be used to verify the importance of attributes and choose the attribute
subset with the highest likelihood of maintaining the original discrimination ability. Experiments
varify that the discrimination ability, disturbance tolerance ability and stability under varying
discretization strategies of DD and ID are significantly enhanced by the proposed algorithms.
A Fuzzy Control Model for Restraint of Bullwhip Effect in Uncertain Closed-Loop Supply
Chain with Hybrid Recycling Channels
Abstract - By considering the uncertainties in the closed-loop supply chain system with hybrid
recycling channels, a fuzzy control model is constructed to restrain the bullwhip effect. Firstly,
the basic models of the uncertain closed-loop supply chain with hybrid recycling channels are
established where the manufacturer and the third party recovery provider collect the recycled
products at the same time. Then, the basic models of the closed-loop supply chain are converted
into a nonlinear fuzzy switching model based on the discrete Takagi-Sugeno (T-S) fuzzy control
system. Secondly, a fuzzy robust control method is utilized to reduce the impacts caused by the
internal and external uncertain factors on the closed-loop supply chain. This method can not only
restrain the bullwhip effect, but also make supply chain remain robust stability. Finally, the
simulation results show the feasibility and effectiveness of the constructed fuzzy control system.
Type-2 Fuzzy Alpha-Cuts

Abstract - Type-2 fuzzy logic systems make use of type-2 fuzzy sets. To be able to deliver
useful type-2 fuzzy logic applications we need to be able to perform meaningful operations on
these sets. These operations should also be practically tractable. However, type-2 fuzzy sets
suffer the shortcoming of being complex by definition. Indeed, the third dimension, which is the
source of extra parameters, is in itself the origin of extra computational cost. The quest for a
representation that allow practical systems to be implemented is the motivation for our work. In
this paper we define the alpha-cut decomposition theorem for type- 2 fuzzy sets which is a new
representation analogous to the alpha-cut representation of type-1 fuzzy sets and the extension
principle. We show that this new decomposition theorem forms a methodology for extending
mathematical concepts from crisp sets to type-2 fuzzy sets directly. In the process of developing
this theory we also define a generalisation that allows us to extend operations from interval type-
2 fuzzy sets or interval valued fuzzy sets to type-2 fuzzy sets. These results will allow for the
more applications of type-2 fuzzy sets by expiating the parallelism that the research here affords.
Mean-variance portfolio selection with the ordered weighted average
Abstract - Portfolio selection is the theory that studies the process of selecting the optimal
proportion of different assets. The first approach was introduced by Harry Markowitz and was
based on a mean-variance framework. This paper introduces the ordered weighted average
(OWA) in the mean-variance model. The main idea is to replace the classical mean and variance
by the OWA operator. By doing so, the new model is able to study different degrees of optimism
and pessimism in the analysis being able to develop an approach that considers the decision
makers attitude in the selection process. This work also suggests a new framework for dealing
with the attitudinal character of the decision maker based on the numerical values of the
available arguments. The main advantage of this method is the ability to adapt to many situations
offering a more complete representation of the available data from the most pessimistic situation
to the most optimistic one. An illustrative with fictitious data and a real example are studied.
Evolving Possibilistic Fuzzy Modeling for Realized Volatility Forecasting with Jumps

Abstract - Equity assets volatility modeling and forecasting provide key information for risk
management, portfolio construction, financial decision making and derivatives pricing. Realized
volatility models outperform autoregressive conditional heteroskedasticity and stochastic
volatility models in out-ofsample forecasting. Gain in forecasting performance is achieved when
models comprise volatility jump components. This paper suggests evolving possibilistic fuzzy
modeling to forecast realized volatility with jumps. The modeling approach is based on an
extension of the possibilistic fuzzy c-means clustering and on functional fuzzy rule-based
models. It employs memberships and typicalities to recursively update cluster centers. The
evolving nature of the model allows adding or removing clusters using statistical distance-like
criteria to update the model as dictated by input data. The possibilistic model improves
robustness to noisy data and outliers, an essential requirement in financial markets volatility
modeling and forecasting. Computational experiments and statistical analysis are done using
Value-at-Risk estimates to evaluate and to compare the performance of the evolving possibilistic
fuzzy modeling with the Heterogeneous Autoregressive, neural networks models and current
state of the art evolving fuzzy methods. The experiments use actual data from S&P 500 and
Nasdaq (United States), FTSE (United Kingdom), DAX (Germany), IBEX (Spain) and Ibovespa
(Brazil), major equity market indexes in global markets. The results show that the evolving
possibilistic fuzzy model is highly efficient to model realized volatility with jumps in terms of
forecasting accuracy.
An SOS-based Control Lyapunov Function Design for Polynomial Fuzzy Control of
Nonlinear Systems
Abstract - This paper deals with a sum-of-squares (SOS) based control Lyapunov function
(CLF) design for polynomial fuzzy control of nonlinear systems. The design starts with exactly
replacing (smooth) nonlinear systems dynamics with polynomial fuzzy models which are known
as universal approximators. Next, global stabilization conditions represented in terms of SOS are
provided in the framework of the CLF design, i.e., a stabilizing controller with non parallel
distributed compensation form is explicitly designed by applying Sontag’s control law once a
CLF for a given nonlinear system is constructed. Furthermore, semiglobal stabilization

conditions on operation domains are derived in the same fashion as in the global stabilization
conditions. Both global and semi-global stabilization problems are formulated as SOS
optimization problems which reduce to numerical feasibility problems. Five design examples are
given to show the effectiveness of our proposed approach over the existing linear matrix
inequality (LMI) and SOS approaches.
Stock picking by Probability-Possibility approaches
Abstract - This paper presents a performance evaluation of stock picking by merging several
technical indicators. Several fusion operators have been proposed either in the probabilistic or in
the possibilistic framework. The latter fuzzy framework has been introduced to manage the
uncertain information embedded in financial time series due to human biases as studied by
behavioral finance. Performances of portfolio resulting from the proposed systems, are evaluated
according to cumulative returns but also through a risk analysis point of view (Sharpe ratio).
Two fusion mechanisms (one probabilistic, one possibilistic) aiming at discriminating common
information from merged technical indicators, produce the higher portfolio performances. It also
appears that selecting specific technical indicators affects the overall performances of the
proposed stock picking systems. Indeed, studying the technical indicators selection through a
shared/non shared information point of view, reveals possibilistic framework is more robust to
redundant sources than probabilistic framework. Effects of some parameters used in the fusion
algorithms (amount of assets, window length analysis, . . .) are also investigated. Results from all
these tests clearly show the high potentiality of technical indicators fusion to improve portfolio
performances. However, these first promising results have to be further inspected within wider
contexts, as discussed at the end of the paper.
H∞ Filtering for Continuous-Time T-S Fuzzy Systems With Partly Immeasurable Premise
Variables
Abstract - This paper is concerned with the H∞ filtering problem for T-S fuzzy systems with
partly immeasurable premise variables. By using measurable premise variables of fuzzy models
as the premise variables of fuzzy filters, a new fuzzy filter scheme is constructed. Further based

on the new filter scheme and a class of new line integral fuzzy Lyapunov functions, a convex
condition for designing H∞ filters is proposed. In contrast to the existing approaches, the new
condition can take full use of measurable premise variables for less conservative design. A
numerical example is given to illustrate the effectiveness of the proposed method.
IEEE Transactions on Systems, Man, and Cybernetics: Systems (June 2016)
Multi-Objective Evolutionary Optimization of Type-2 Fuzzy Rule-based Systems for
Financial Data Classification
Abstract - Classification techniques are becoming essential in the financial world for reducing
risks and possible disasters. Managers are interested in not only high accuracy but also in
interpretability and transparency. It is widely accepted now that the comprehension of how
inputs and output are related to each other is crucial for taking operative and strategic decisions.
Furthermore, inputs are often affected by contextual factors and characterized by a high level of
uncertainty. In addition, financial data are usually highly skewed towards the majority class.
With the aim of achieving high accuracies, preserving the interpretability and managing
uncertain and unbalanced data, the paper presents a novel method to deal with financial data
classification by adopting type-2 fuzzy rule-based classifiers (FRBCs) generated from data by a
multi-objective evolutionary algorithm (MOEA). The classifiers employ an approach, denoted as
scaled dominance, for defining rule weights in such a way to help minority classes to be
correctly classified. In particular, we have extended PAES-RCS, an MOEA-based approach to
learn concurrently the rule and data bases of FRBCs, for managing both interval type-2 fuzzy
sets and unbalanced datasets. To the best of our knowledge, this is the first work that generates
type-2 FRBCs by concurrently maximizing accuracy and minimizing the number of rules and the
rule length with the objective of producing interpretable models of real-world skewed and
incomplete financial datasets. The rule bases are generated by exploiting a rule and condition
selection (RCS) approach, which selects a reduced number of rules from a heuristically
generated rule base and a reduced number of conditions for each selected rule during the
evolutionary process. The weight associated with each rule is scaled by the scaled dominance
approach on the fuzzy frequency of the output class, in order to give a higher weight to the
minority class. As regards the data base learning, the me- bership function parameters of the

interval type-2 fuzzy sets used in the rules are learned concurrently to the application of RCS.
Unbalanced datasets are managed by using, in addition to complexity, selectivity and specificity
as objectives of the MOEA rather than only the classification rate. We tested our approach,
named IT2-PAES-RCS, on eleven financial datasets and compared our results with the ones
obtained by the original PAES-RCS with three objectives and with and without scaled
dominance, the fuzzy rule-based classifiers FARC-HD and FURIA, the classical C4.5 decision
tree algorithm and its cost-sensitive version. Using non-parametric statistical tests, we will show
that IT2-PAES-RCS generates FRBCs with, on average, accuracy statistically comparable to and
complexity lower than the ones generated by the two versions of the original PAES-RCS.
Further, the FRBCs generated by FARC-HD and FURIA and the decision trees computed by
C4.5 and its cost-sensitive version, despite the highest complexity, result to be less accurate than
the FRBCs generated by IT2-PAES-RCS. Finally, we will highlight how these FRBCs are easily
interpretable by showing and discussing one of them.
Modeling Stock Price Dynamics with Fuzzy Opinion Networks
Abstract - We propose a mathematical model for the word-of-mouth communications among
stock investors through social networks and explore how the changes of the investors’ social
networks influence the stock price dynamics and vice versa. An investor is modeled as a
Gaussian fuzzy set (a fuzzy opinion) with the center and standard deviation as inputs and the
fuzzy set itself as output. Investors are connected in the following fashion: the center input of an
investor is taken as the average of the neighbors’ outputs, where two investors are neighbors if
their fuzzy opinions are close enough to each other, and the standard deviation (uncertainty)
input is taken with local, global or external reference schemes to model different scenarios of
how investors define uncertainties. The centers and standard deviations of the fuzzy opinions are
the expected prices and their uncertainties, respectively, that are used as inputs to the price
dynamic equation. We prove that with the local reference scheme the investors converge to
different groups in finite time, while with the global or external reference schemes all investors
converge to a consensus within finite time and the consensus may change with time in the
external reference case. We show how to model trend followers, contrarians and manipulators

IEEE Fuzzy system Title and Abstract 2016

IEEE Fuzzy system Title and Abstract 2016

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