This document provides citation information for a chapter titled "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems" published in the book "Fuzzy Systems: Concepts, Methodologies, Tools, and Applications". It lists the citation in MLA, APA, and Chicago format. The chapter discusses using the PSK method to solve type-1 and type-3 fuzzy transportation problems.

1. Cite this Chapter as follows:
MLA
Kumar, P. Senthil. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems." Fuzzy Systems: Concepts, Methodologies,
Tools, and Applications. IGI Global, 2017. 367-392. Web. 2 Mar. 2017. doi:10.4018/978-1-5225-1908-9.ch017
APA
Kumar, P. S. (2017). PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems. In Fuzzy Systems: Concepts, Methodologies,
Tools, and Applications (pp. 367-392). Hershey, PA: IGI Global. doi:10.4018/978-1-5225-1908-9.ch017

2. Chicago
Kumar, P. Senthil. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems." In Fuzzy Systems: Concepts, Methodologies,
Tools, and Applications, 367-392 (2017), accessed March 02, 2017. doi:10.4018/978-1-5225-1908-9.ch017

3. Fuzzy Systems:
Concepts, Methodologies, Tools,
and Applications
Information Resources Management Association
USA

4. 
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Editorial Advisory Board
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Names: Information Resources Management Association.
Title: Fuzzy systems : concepts, methodologies, tools, and applications /
Information Resources Management Association, editor.
Description: Hershey PA : Information Science Reference, 2017. | Includes
bibliographical references.
Identifiers: LCCN 2016046977| ISBN 9781522519089 (hardcover) | ISBN
9781522519096 (ebook)
Subjects: LCSH: Fuzzy logic. | Fuzzy systems. | Neural networks (Computer
science) | Intelligent control systems.
Classification: LCC QA9.64 .F8975 2017 | DDC 511.3--dc23 LC record available at https://lccn.loc.gov/2016046977

6. 
Table of Contents

Preface................................................................................................................................................... xx
Volume I
Section 1
Development and Design Methodologies
Chapter 1
Uncertain Static and Dynamic Analysis of Imprecisely Defined Structural Systems............................. 1
S. Chakraverty, National Institute of Technology – Rourkela, India
Diptiranjan Behera, National Institute of Technology – Rourkela, India
Chapter 2
Hierarchical Fuzzy Rule Interpolation and its Application for Hotels Location Selection................... 31
Yanling Jiang, Chongqing University of Science and Technology, China
Shangzhu Jin, Chongqing University of Science and Technology, China
Jun Peng, Chongqing University of Science and Technology, China
Chapter 3
Modified Iterative Methods for Solving Fully Fuzzy Linear Systems................................................... 55
S. A. Edalatpanah, Ayandegan Institute of Higher Education, Tonekabon, Iran
Chapter 4
Comparison of Uncertainties in Membership Function of Adaptive Lyapunov NeuroFuzzy-2 for
Damping Power Oscillations.................................................................................................................. 74
Laiq Khan, COMSATS Institute of Information Technology, Pakistan
Rabiah Badar, COMSATS Institute of Information Technology, Pakistan
Saima Ali, COMSATS Institute of Information Technology, Pakistan
Umar Farid, COMSATS Institute of Information Technology, Pakistan
Chapter 5
Constructing Structural Equation Model Rule-Based Fuzzy System with Genetic Algorithm........... 132
EnDer Su, National Kaohsiung First University of Science and Technology, Taiwan
Thomas W. Knowles, Illinois Institute of Technology, USA
Yu-Gin Fen, National Kaohsiung First University of Science and Technology, Taiwan

7. 
Chapter 6
A Novel Approach of Restoration of Digital Images Degraded by Impulse Noise............................. 153
Rashmi Kumari, JJTU, India
Anupriya Asthana, Galgotias University, India
Vikas Kumar, Asia-Pacific Institute of Management, India
Chapter 7
Imprecise Knowledge and Fuzzy Modeling in Materials Domain...................................................... 170
Subhas Ganguly, National Institute Technology Raipur, India
Shubhabrata Datta, Calcutta Institute of Engineering and Management, India
Chapter 8
Assessment of Clinical Decision Support Systems for Predicting Coronary Heart Disease............... 184
Sidahmed Mokeddem, University of Oran 1 Ahmed Ben Bella, Algeria
Baghdad Atmani, University of Oran 1 Ahmed Ben Bella, Algeria
Chapter 9
Early Warning System Framework Proposal Based on Structured Analytical Techniques, SNA,
and Fuzzy Expert System for Different Industries............................................................................... 202
Goran Klepac, University College for Applied Computer Engineering Algebra, Zagreb,
Croatia
Robert Kopal, University College for Applied Computer Engineering Algebra, Zagreb,
Croatia
Leo Mrsic, University College for Applied Computer Engineering Algebra, Zagreb, Croatia
Chapter 10
Stability Enhancement in Multi-Machine Power Systems by Fuzzy-Based Coordinated 
AVR-PSS.............................................................................................................................................. 235
Rahmat Khezri, University of Kurdistan, Iran
Hassan Bevrani, University of Kurdistan, Iran
Chapter 11
Fuzzy Finite Element Method in Diffusion Problems......................................................................... 250
S. Chakraverty, National Institute of Technology – Rourkela, India
S. Nayak, National Institute of Technology, India
Chapter 12
A Hybrid Model for Rice Disease Diagnosis Using Entropy Based Neuro Genetic Algorithm......... 273
K. Lavanya, VIT University, Vellore, India
M.A. Saleem Durai, VIT University, Vellore, India
N.Ch.S.N. Iyengar, VIT University, Vellore, India

8. 
Chapter 13
A Fuzzy Model with Thermodynamic Based Consequents and a Niching Swarm-Based
Supervisor to Capture the Uncertainties of Damavand Power System................................................ 292
Ahmad Mozaffari, University of Waterloo, Canada
Moein Mohammadpour, Babol University of Technology, Iran
Alireza Fathi, Babol University of Technology, Iran
Mofid Gorji-Bandpy, Babol University of Technology, Iran
Chapter 14
Design of a Hybrid Adaptive Neuro Fuzzy Inference System (ANFIS) Controller for Position and
Angle Control of Inverted Pendulum (IP) Systems............................................................................. 308
Ashwani Kharola, Institute of Technology Management (ITM), India
Chapter 15
Intuitionistic Fuzzy Set Theory with Fair Share CPU Scheduler: A Dynamic Approach................... 321
Supriya Raheja, NorthCap University, India
Chapter 16
Classification of EEG Signals for Motor Imagery Based on Mutual Information and Adaptive
Neuro Fuzzy Inference System............................................................................................................ 347
Shereen A. El-aal, Al-Azhar University, Egypt
Rabie A. Ramadan, Cairo University, Egypt
Neveen Ghali, Al-Azhar University, Egypt
Chapter 17
PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems................................... 367
P. Senthil Kumar, Jamal Mohamed College (Autonomous), India
Chapter 18
Fault Detection and Isolation for an Uncertain Takagi-Sugeno Fuzzy System using the Interval
Approach.............................................................................................................................................. 393
Hassene Bedoui, University of Monastir, Tunisia
Atef Kedher, University of Tunis Manar, Tunisia
Kamel Ben Othman, University of Tunis Manar, Tunisia
Section 2
Tools and Technologies
Chapter 19
Fuzzy Expert System to Diagnose Diabetes Using S Weights for S Fuzzy Assessment
Methodology........................................................................................................................................ 418
A. V. Senthil Kumar, Hindusthan College of Arts and Science, India
M. Kalpana, Tamil Nadu Agricultural University, India

9. 
Chapter 20
Hybrid Fuzzy Neural Search Retrieval System................................................................................... 443
Rawan Ghnemat, Princess Sumaya University for Technology, Jordan
Adnan Shaout, The University of Michigan – Dearborn, USA
Chapter 21
A Multi-Objective Fuzzy Ant Colony Optimization Algorithm for Virtual Machine Placement....... 459
Boominathan Perumal, VIT University, Vellore, India
Aramudhan M., Perunthalaivar Kamarajar Institute of Engineering and Technology, India
Chapter 22
Fuzzy Adaptive Controller for Uncertain Multivariable Nonlinear Systems with Both Sector
Nonlinearities and Dead-Zones........................................................................................................... 487
Abdesselem Boulkroune, University of Jijel, Algeria
Chapter 23
A Two-Level Fuzzy Value-Based Replica Replacement Algorithm in Data Grids............................. 516
Nazanin Saadat, Science and Research Branch, Islamic Azad University, Iran
Amir Masoud Rahmani, Science and Research Branch, Islamic Azad University, Iran
Chapter 24
A Fuzzy Expert System for Star Classification Based on Photometry................................................ 540
Aida Pakniyat, Kharazmi University, Iran
Rahil Hosseini, Shahr-e-Qods Branch, Islamic Azad University, Iran
Mahdi Mazinai, Shahr-e-Qods Branch, Islamic Azad University, Iran
Chapter 25
Personalized Neuro-Fuzzy Expert System for Determination of Nutrient Requirements................... 551
Priti Srinivas Sajja, Sardar Patel University, India
Jeegar Ashokkumar Trivedi, Sardar Patel University, India
Volume II
Chapter 26
Movie Recommendation System Based on Fuzzy Inference System and Adaptive Neuro Fuzzy
Inference System.................................................................................................................................. 573
Mahfuzur Rahman Siddiquee, North South University, Bangladesh
Naimul Haider, North South University, Bangladesh
Rashedur M. Rahman, North South University, Bangladesh
Chapter 27
Fuzzy Logic-Based Cluster Heads Percentage Calculation for Improving the Performance of the
LEACH Protocol.................................................................................................................................. 609
Omar Banimelhem, Jordan University of Science and Technology, Jordan
Eyad Taqieddin, Jordan University of Science and Technology, Jordan
Moad Y. Mowafi, Jordan University of Science and Technology, Jordan
Fahed Awad, Jordan University of Science and Technology, Jordan
Feda’ Al-Ma’aqbeh, Jordan University of Science and Technology, Jordan

10. 
Chapter 28
Evaluation of Human Machine Interface (HMI) on a Digital and Analog Control Room in Nuclear
Power Plants Using a Fuzzy Logic Approach...................................................................................... 628
Pola Lydia Lagari, Purdue University, USA
Antonia Nasiakou, Purdue University, USA
Miltiadis Alamaniotis, Purdue University, USA
Chapter 29
Including Client Opinion and Employee Engagement in the Strategic Human Resource
Management: An Advanced SWOT- FUZZY Decision Making Tool................................................ 647
Rachid Belhaj, Mohammed V University, Morocco
Mohamed Tkiouat, Mohammed V University, Morocco
Chapter 30
An Optimal Fuzzy Load Balanced Adaptive Gateway Discovery for Ubiquitous Internet Access in
MANET............................................................................................................................................... 663
Prakash Srivastava, Madan Mohan Malaviya University of Technology, India
Rakesh Kumar, Madan Mohan Malaviya University of Technology, India
Chapter 31
A Hybrid System Based on FMM and MLP to Diagnose Heart Disease............................................ 682
Swati Aggarwal, NSIT, India
Venu Azad, Government Girls PG College, India
Chapter 32
Strictness Petroleum Prediction System Based on Fuzzy Model........................................................ 715
Senan A. Ghallab, Ain Shams University, Egypt
Nagwa. L. Badr, Ain Shams University, Egypt
Abdel Badeeh Salem, Ain Shams University, Egypt
M. F. Tolba, Ain Shams University, Egypt
Chapter 33
Fuzzy-Based Matrix Converter Drive for Induction Motor................................................................. 738
Chitra Venugopal, University of KwaZulu-Natal, South Africa
Chapter 34
A Fuzzy-Based Calorie Burn Calculator for a Gamified Walking Activity Using Treadmill............. 763
Prabhakar Rontala Subramaniam, University of KwaZulu-Natal, South Africa
Chitra Venugopal, University of KwaZulu-Natal, South Africa
Arun Kumar Sangaiah, VIT University, India
Chapter 35
Application of Fuzzy Logic for Mapping the Agro-Ecological Zones................................................ 782
Bistok Hasiholan Simanjuntak, Satya Wacana Christian University, Indonesia
Sri Yulianto Joko Prasetyo, Satya Wacana Christian University, Indonesia
Kristoko Dwi Hartomo, Satya Wacana Christian University, Indonesia
Hindriyanto Dwi Purnomo, Satya Wacana Christian University, Indonesia

11. 
Chapter 36
Prediction of Solar and Wind Energies by Fuzzy Logic Control......................................................... 807
Sanaa Faquir, University Sidi Mohamed Ben Abdallah, Morocco
Ali Yahyaouy, University Sidi Mohamed Ben Abdallah, Morocco
Hamid Tairi, University Sidi Mohamed Ben Abdallah, Morocco
Jalal Sabor, Ecole Nationale Superieure d’Arts et Metiers (ENSAM), Morocco
Chapter 37
Enhancement of Turbo-Generators Phase Backup Protection Using Adaptive Neuro Fuzzy
Inference System.................................................................................................................................. 835
Mohamed Salah El-Din Ahmed Abdel Aziz, Dar Al-Handasah (Shair and partners), Egypt
Mohamed Elsamahy, The Higher Institute of Engineering, El-Shorouk Academy, Egypt
Mohamed A. Moustafa Hassan, Cairo University, Egypt
Fahmy M. A. Bendary, Benha University, Egypt
Chapter 38
Fuzzy Rule Based Environment Monitoring System for Weather Controlled Laboratories Using
Arduino................................................................................................................................................ 855
S. Sasirekha, SSN College of Engineering, India
S. Swamynathan, Anna University, India
Chapter 39
Fuzzy Labeled Transition Refinement Tree: Application to Stepwise Designing Multi Agent
Systems................................................................................................................................................ 873
Sofia Kouah, University of Constantine 2, Algeria University of Oum El Bouaghi, Algeria
Djamel-Eddine Saidouni, University of Constantine 2, Algeria
Chapter 40
Rule-Based Systems for Medical Diagnosis........................................................................................ 906
V. S. Giridhar Akula, Methodist College of Engineering and Technology, India
Section 3
Utilization and Application
Chapter 41
Implementation of Fuzzy Technology in Complicated Medical Diagnostics and Further 
Decision............................................................................................................................................... 935
A. B. Bhattacharya, University of Kalyani, India
Arkajit Bhattacharya, M. G. M. Medical College and Hospital, India
Chapter 42
Intelligent Decision Making and Risk Analysis of B2c E-Commerce Customer Satisfaction............ 969
Masoud Mohammadian, University of Canberra, Australia

12. 
Chapter 43
Fuzzy Logic Based Approach for Power System Fault Section Analysis............................................ 987
Neeti Dugaya, Sagar Institute of Research, Technology and Science, India
Smita Shandilya, Sagar Institute of Research, Technology and Science, India
Chapter 44
Some Recent Defuzzification Methods.............................................................................................. 1003
Harendra Kumar, Gurukula Kangari University, India
Chapter 45
Application of Fuzzy Expert System in Medical Treatment............................................................. 1020
Kajal Ghosal, Chronic Disease and Oncological Homeopathic Consultant, India
Partha Haldar, Jadavpur University, India
Goutam Sutradhar, Jadavpur University, India
Chapter 46
Predicting Uncertain Behavior and Performance Analysis of the Pulping System in a Paper
Industry Using PSO and Fuzzy Methodology................................................................................... 1070
Harish Garg, Indian Institute of Technology-Roorkee, India
Monica Rani, Indian Institute of Technology-Roorkee, India
S.P. Sharma, Indian Institute of Technology-Roorkee, India
Chapter 47
Vague Correlation Coefficient of Interval Vague Sets and its Applications to Topsis in MADM
Problems............................................................................................................................................ 1110
John Robinson P., Bishop Heber College (Autonomous), India
Henry Amirtharaj E. C., Bishop Heber College (Autonomous), India
Volume III
Chapter 48
A Fuzzy-Based Approach to Support Decision Making in Complex Military Environments.......... 1150
Timothy P. Hanratty, US Army Research Laboratory, Aberdeen Proving Ground, USA
E. Allison Newcomb, Towson University, USA
Robert J. Hammell II, Towson University, USA
John T. Richardson, US Army Research Laboratory, Aberdeen Proving Ground, USA
Mark R. Mittrick, US Army Research Laboratory, Aberdeen Proving Ground, USA
Chapter 49
Nonlinear System Identification of Smart Buildings......................................................................... 1183
Soroush Mohammadzadeh, University of Oklahoma, USA
Yeesock Kim, Worcester Polytechnic Institute (WPI), USA

13. 
Chapter 50
Fuzzy Logic-Based Intelligent Control System for Active Ankle Foot Orthosis.............................. 1203
M. Kanthi, Manipal University, India
Chapter 51
Knowledge Representation Using Fuzzy XML Rules in Web-Based Expert System for Medical
Diagnosis........................................................................................................................................... 1237
Priti Srinivas Sajja, Sardar Patel University, India
Chapter 52
Improvement of JXTA-Overlay P2P Platform: Evaluation for Medical Application and 
Reliability........................................................................................................................................... 1268
Yi Liu, Fukuoka Institute of Technology (FIT), Japan
Shinji Sakamoto, Fukuoka Institute of Technology (FIT), Japan
Keita Matsuo, Fukuoka Prefectural Fukuoka Technical High School, Japan
Makoto Ikeda, Fukuoka Institute of Technology (FIT), Japan
Leonard Barolli, Fukuoka Institute of Technology (FIT), Japan
Fatos Xhafa, Technical University of Catalonia, Spain
Chapter 53
Bio-Inspired Computing through Artificial Neural Network............................................................. 1285
Nilamadhab Dash, C. V. Raman College of Engineering, India
Rojalina Priyadarshini, C. V. Raman College of Engineering, India
Brojo Kishore Mishra, C. V. Raman College of Engineering, India
Rachita Misra, C. V. Raman College of Engineering, India
Chapter 54
Trust Calculation Using Fuzzy Logic in Cloud Computing.............................................................. 1314
Rajanpreet Kaur Chahal, Panjab University, India
Sarbjeet Singh, Panjab University, India
Chapter 55
Fuzzy Decision Support System for Coronary Artery Disease Diagnosis Based on Rough Set
Theory................................................................................................................................................ 1367
Noor Akhmad Setiawan, Universitas Gadjah Mada, Indonesia
Chapter 56
Artificial Intelligent Approaches for Prediction of Longitudinal Wave Velocity in Rocks............... 1385
A. K. Verma, Indian School of Mines, India
T. N. Singh, Indian Institute of Technology, India
Sachin Maheshwar, Indian School of Mines, India

14. 
Chapter 57
An Adaptive Path Planning Based on Improved Fuzzy Neural Network for Multi-Robot 
Systems.............................................................................................................................................. 1396
Zhiguo Shi, University of Science and Technology, China
Huan Zhang, University of Science and Technology, China
Jingyun Zhou, University of Science and Technology, China
Junming Wei, Australian National University, Australia
Chapter 58
Information Systems on Hesitant Fuzzy Sets.................................................................................... 1425
Deepak D., National Institute of Technology Calicut, India
Sunil Jacob John, National Institute of Technology Calicut, India
Chapter 59
Artificial Intelligence Methods and Their Applications in Civil Engineering.................................. 1453
Gonzalo Martínez-Barrera, Universidad Autónoma del Estado de México, Mexico
Osman Gencel, Bartin University, Turkey
Ahmet Beycioglu, Düzce University, Turkey
Serkan Subaşı, Düzce University, Turkey
Nelly González-Rivas, Joint Center for Research in Sustainable Chemistry (CCIQS), Mexico
Chapter 60
Contrasting Correlation Coefficient with Distance Measure in Interval Valued Intuitionistic
Trapezoidal Fuzzy MAGDM Problems............................................................................................. 1478
John P. Robinson, Bishop Heber College, India
Chapter 61
A Study on Hybridization of Intelligent Techniques in Bioinformatics............................................ 1518
Peyakunta Bhargavi, Sri Padmavati Mahila University, India
S. Jyothi, Sri Padmavati Mahila University, India
D. M. Mamatha, Sri Padmavati Mahila Univeristy, India
Chapter 62
Dynamic Behaviour and Crack Detection of a Multi Cracked Rotating Shaft using Adaptive
Neuro-Fuzzy-Inference System: Vibration Analysis of Multi Cracked Rotating Shaft..................... 1540
Rajeev Ranjan, Haldia Institute of Technology, India
Section 4
Organizational and Social Implications
Chapter 63
Modeling Conflict Dynamics: System Dynamic Approach............................................................... 1553
Janez Usenik, University of Maribor, Slovenia
Tit Turnsek, Landscape Governance College Grm, Slovenia

15. 
Chapter 64
Fuzzy Opinion: Detection of Opinion Based on SentiWordNet Dictionary by Using Fuzzy 
Logic.................................................................................................................................................. 1576
Mohamed Amine Boudia, Dr. Tahar Moulay University of Saida, Algeria
Reda Mohamed Hamou, Dr. Tahar Moulay University of Saida, Algeria
Abdelmalek Amine, Dr. Tahar Moulay University of Saida, Algeria
Chapter 65
Adjust Fuzzy Model Parameters for Head Election in Wireless Sensor Network Protocols............. 1596
Walaa Abd el Aal Afifi, ISSR-Cairo University, Egypt
Hesham Ahmed Hefny, ISSR-Cairo University, Egypt
Chapter 66
Bidder Selection in Public Procurement using a Fuzzy Decision Support System........................... 1620
Vjekoslav Bobar, University of Belgrade, Serbia
Ksenija Mandic, University of Belgrade, Serbia
Milija Suknovic, University of Belgrade, Serbia
Chapter 67
Fuzzy Dynamic Load Balancing in Virtualized Data Centers of SaaS Cloud Provider.................... 1643
Md. S. Q. Zulkar Nine, North South University, Bangladesh
Abul Kalam Azad, North South University, Bangladesh
Saad Abdullah, North South University, Bangladesh
Rashedur M. Rahman, North South University, Bangladesh
Section 5
Emerging Trends
Chapter 68
Emerging Application of Fuzzy Expert System in Medical Domain................................................ 1667
A. V. Senthil Kumar, Hindusthan College of Arts and Science, India
M. Kalpana, Tamil Nadu Agricultural University, India
Chapter 69
Fuzzy Critical Path Method Based on a New Approach of Ranking Fuzzy Numbers Using
Centroid of Centroids......................................................................................................................... 1690
N. Ravi Shankar, GITAM University, India
B. Pardha Saradhi, Dr. L.B. College, India
S. Suresh Babu, GITAM University, India
Chapter 70
MAGDM-Miner: A New Algorithm for Mining Trapezoidal Intuitionistic Fuzzy Correlation
Rules.................................................................................................................................................. 1708
John P. Robinson, Bishop Heber College, India
Henry Amirtharaj, Bishop Heber College, India

16. 
Chapter 71
Advances in QoS/E Characterization and Prediction for Next Generation Mobile Communication
Systems.............................................................................................................................................. 1739
Charalampos N. Pitas, National Technical University of Athens, Greece
Apostolos G. Fertis, SMA und Partner AG, Zurich, Switzerland
Dimitris E. Charilas, National Technical University of Athens, Greece
Athanasios D. Panagopoulos, National Technical University of Athens, Greece
Index....................................................................................................................................................xxii

17. 367
Copyright © 2017, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
Chapter 17
DOI: 10.4018/978-1-5225-1908-9.ch017
ABSTRACT
In conventional transportation problem (TP), supplies, demands and costs are always certain. In this
paper, the author tried to categories the TP under the mixture of certain and uncertain environment and
formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers (TFNs) and trapezoidal
fuzzy numbers (TrFNs) to solve the TP. The existing ranking procedure of Liou and Wang is used to
transform the type-1 and type-3 fuzzy transportation problem (FTP) into a crisp one so that the con-
ventional method may be applied to solve the TP. The solution procedure differs from TP to type-1 and
type-3 FTP in allocation step only. Therefore, the new method called PSK method and new multiplication
operation on TrFN is proposed to find the mixed optimal solution in terms of crisp numbers, TFNs and
TrFNs. The main advantage of this method is computationally very simple, easy to understand and also
the optimum objective value obtained by our method is physically meaningful. The effectiveness of the
proposed method is illustrated by means of a numerical example.
1. INTRODUCTION
The transportation problem is a special class of linear programming problem which deals with the dis-
tribution of single homogeneous product from various origins(sources) to various destinations(sinks).
The objective of the transportation problem is to determine the optimal amount of a commodity to be
transported from various supply points to various demand points so that the total transportation cost
is minimum for a minimization problem or total transportation profit is maximum for a maximization
problem.
The unit costs, that is, the cost of transporting one unit from a particular supply point to a particular
demand point, the amounts available at the supply points and the amounts required at the demand points
PSK Method for Solving
Type-1 and Type-3 Fuzzy
Transportation Problems
P. Senthil Kumar
Jamal Mohamed College (Autonomous), India

18. 368
PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems

are the parameters of the transportation problem. Efficient algorithms have been developed for solving
transportationproblemswhenthecostcoefficients,thedemandandsupplyquantitiesareknownprecisely.
In the history of mathematics, Hitchcock (1941) originally developed the basic transportation prob-
lem. Charnes and Cooper (1954) developed the stepping stone method which provides an alternative
way of determining the simplex method information. Appa (1973) discussed several variations of the
transportation problem. Arsham et al. (1989) proposed a simplex type algorithm for general transporta-
tion problems. An Introduction to Operations Research Taha (2008) deals the transportation problem.
In today’s real world problems such as in corporate or in industry many of the distribution problems
are imprecise in nature due to variations in the parameters. To deal quantitatively with imprecise infor-
mation in making decision, Zadeh (1965) introduced the fuzzy set theory and has applied it successfully
in various fields. The use of fuzzy set theory becomes very rapid in the field of optimization after the
pioneering work done by Bellman and Zadeh (1970). The fuzzy set deals with the degree of membership
(belongingness) of an element in the set. In a fuzzy set the membership value (level of acceptance or
level of satisfaction) lies between 0 and 1 where as in crisp set the element belongs to the set represent
1 and the element not belongs to the set represent 0.
Due to the applications of fuzzy set theory, several authors like Oheigeartaigh (1982) presented an
algorithm for solving transportation problems where the availabilities and requirements are fuzzy sets
with linear or triangular membership functions. Chanas et al. (1984) presented a fuzzy linear program-
ming model for solving transportation problems with fuzzy supply, fuzzy demand and crisp costs. Chanas
et al. (1993) formulated the fuzzy transportation problems in three different situations and proposed
method for solving the formulated fuzzy transportation problems. Chanas and Kuchta (1996) proposed
the concept of the optimal solution for the transportation problem with fuzzy coefficients expressed as
fuzzy numbers, and developed an algorithm for obtaining the optimal solution.
Chanas and Kuchta (1998) developed a new method for solving fuzzy integer transportation problem
by representing the supply and demand parameters as L-R type fuzzy numbers. Saad and Abbas (2003)
proposed an algorithm for solving the transportation problems under fuzzy environment. Liu and Kao
(2004) presented a method for solving fuzzy transportation problems based on extension principle.
Chiang (2005) proposed a method to find the optimal solution of transportation problems with fuzzy
requirements and fuzzy availabilities. Gani and Razak (2006) obtained a fuzzy solution for a two stage
cost minimizing fuzzy transportation problem in which availabilities and requirements are trapezoidal
fuzzy numbers using a parametric approach. Das and Baruah (2007) discussed Vogel’s approximation
method to find the fuzzy initial basic feasible solution of fuzzy transportation problem in which all the
parameters (supply, demand and cost) are represented by triangular fuzzy numbers. Li et al. (2008) pro-
posed a new method based on goal programming approach for solving fuzzy transportation problems
with fuzzy costs.
Chen et al. (2008) proposed the methods for solving transportation problems on a fuzzy network. Lin
(2009) used genetic algorithm for solving transportation problems with fuzzy coefficients. Dinagar and
Palanivel (2009) investigated the transportation problem in fuzzy environment using trapezoidal fuzzy
numbers. De and Yadav (2010) modified the existing method (Kikuchi 2000) by using trapezoidal fuzzy
numbers instead of triangular fuzzy numbers. Pandian et al. (2010) proposed a new algorithm for find-
ing a fuzzy optimal solution for fuzzy transportation problem where all the parameters are trapezoidal
fuzzy numbers. Mohideen and Kumar (2010) did a comparative study on transportation problem in fuzzy
environment. Sudhakar et al. (2011) proposed a different approach for solving two stage fuzzy transpor-
tation problems in which supplies and demands are trapezoidal fuzzy numbers. Hadi Basirzadeh (2011)

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20. 389
PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems

Values of µ Z
c( ) at different values of c can be determined using equations given below:
µ Z
c
for c
c
for c
for c( ) =
≤
−
≤ ≤
≤ ≤
−
0 104
104
64
104 168
1 168 184
248
,
,
,
cc
for c
for c
64
184 248
0 248
,
,
≤ ≤
≥











By using the proposed method a decision maker has the following advantages:
1. The proposed method gives the optimal solution in terms of mixed fuzzy numbers. Moreover, the
proposed method gives the opportunity to the decision maker to solve all the types of FTP;
2. The proposed method is computationally very simple and easy to understand.
7. CONCLUSION
On the basis of the present study, it can be concluded that the type-1, type-2 and type-4 FTP which can
be solved by the existing methods (Pandian and Natarajan (2010), Dinagar and Palanivel (2009), Rani,
Gulathi, and Kumar (2014), Hadi Basirzadeh (2011), Gani and Razak (2006)) can also be solved by
the proposed method. However, it is much easier to apply the proposed method as compared to all the
Figure 1. Graphical representation of type-3 fuzzy transportation cost

21. 390
PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems

existing methods. Also, new method and new multiplication operation on TrFN is proposed to compute
the optimal objective values in terms of trapezoidal fuzzy number which are very simple and easy to
understand and it can be easily applied by decision maker to solve type-1 and type-3 FTP. The proposed
method gives the optimal solution in terms of mixed fuzzy numbers. Hence the proposed method gives
the opportunity to the decision maker to solve all the types of FTP and computationally very simple
when compared to all the existing methods.
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This work was previously published in PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems edited by
Deng-Feng Li, pages 121-146, copyright year 2016 by IGI Publishing (an imprint of IGI Global).

24. 
Index

A
A* 370, 1396-1397, 1399, 1409, 1415, 1420, 1424
Action Refinement 873-874, 883, 887, 902-903
Active AFO 1203, 1205-1206, 1213-1215, 1222,
1231, 1236
Actuator Nonlinearities 487-488, 507, 515
Adaptive Control 75, 115, 456, 488, 501, 509, 511,
515, 1203, 1396-1397, 1420
Adaptive Gateway Discovery 663, 665-666, 678
AdaptiveNeuro-FuzzyInferenceSystem(ANFIS)153-
154, 157, 177, 293, 308, 347, 354, 420, 443-445,
449-450, 456, 573, 594, 835, 837-838, 847, 950,
1183-1184, 1186, 1192, 1197, 1368, 1385, 1390,
1393, 1457, 1542, 1545, 1678
Advisory System 554, 571
AFRAS 1327
Aggregation 298, 420, 430-431, 442, 449, 464, 523,
611, 825, 920, 923-924, 928, 1045-1046, 1049-
1051, 1177, 1328, 1340-1341, 1360, 1426, 1457,
1478-1482, 1530, 1564, 1566, 1630-1631, 1637,
1667, 1677, 1708, 1710-1712, 1718
Agro-Ecological Zone 782-784, 792-793, 801, 806
Analog 628, 630, 633, 639-643, 860, 938-939, 1220
Ant Colony Optimization (ACO) 459-461, 464, 468,
479, 666, 1291
Ant Q System 462, 466
Ant System 461-462, 465-467, 469, 475, 477
Antecedent 32, 36-38, 79, 83-84, 99-100, 241, 285,
296, 298-300, 302, 304, 418, 422, 428, 430-431,
442,461,472,521,611,907-908,923,927,1021,
1043-1044, 1046-1048, 1156, 1158-1159, 1218,
1224, 1226, 1229, 1246, 1248, 1274, 1319, 1322,
1333, 1390, 1407, 1461, 1564-1566, 1601, 1618-
1619, 1671-1672, 1674, 1677, 1688
Arduino 855, 860-861, 863-864, 872
Artificial Earthquake 1183, 1189, 1195-1198
Artificialintelligence(AI)79,130,187,552,684,715,
749, 935, 938, 943, 957, 988-989, 1215, 1217,
1285, 1288, 1367, 1380, 1386, 1388, 1397, 1425,
1450, 1453-1454, 1466, 1470, 1477, 1521, 1525,
1577, 1667-1669, 1673, 1688, 1764
ArtificialNeuralNetworks(ANN)79-80,86,154-155,
171, 180, 218-219, 274, 276, 279, 301, 419-420,
444, 449, 541, 553-554, 557-558, 560-562, 567,
569, 571-572, 682-683, 685-690, 705, 717, 758,
838, 1020, 1074, 1184, 1197, 1204, 1285-1286,
1291-1292, 1294-1295, 1299, 1309, 1367, 1386-
1388, 1398, 1404, 1453, 1477, 1519, 1679, 1759
AVR 235-239, 241-242, 244-246, 860
B
Back Propagation 87, 155, 187, 273-274, 278, 284,
286, 289, 314, 559, 569, 571, 684, 687, 691, 707,
758, 950, 1298-1299, 1309, 1389-1390, 1527,
1542, 1752
Back-Propagation Algorithm (BPA) 74, 594, 1186,
1304, 1527
Backward Chaining 541, 545, 557, 906-907, 913, 917,
919-920, 922, 924, 928, 932, 1245, 1267
Belief Rule Base Systems 932
Betweenness Centrality 233
Bidder Selection 1620-1623, 1628, 1631, 1635, 1637
Bioinformatics 517, 1291, 1518-1522, 1524-1528,
1534-1535, 1537-1538
Bisimulation Relation 888, 890
BMR 766
Brain Computer Interface (BCI) 347
C
Calorie 763-771, 774, 776-779, 781
Calorie burn 763, 765-771, 774, 776-779
CDSS 184-188, 192, 194, 197, 274, 685, 709, 920-
921, 923-925
cEnter simulator 990, 1001
Certainty Factor 420-421, 423-424, 442, 1678
Volume I pp. 1-572; Volume II pp. 573-1149; Volume III 1150-1765
xxii

25. Index
circuit breakers 987-997
CivilEngineering1184-1185,1453-1454,1470-1471,
1477
Classical Approach 967, 1587, 1592-1593
Client Opinion 647
Cloud Computing 459-460, 1314-1315, 1341, 1351,
1362-1364, 1366, 1643
Cluster Head 610, 612-613, 1596-1598, 1603-1605,
1611, 1615, 1618
Clustering Algorithms 624, 839, 1524, 1599, 1601,
1606, 1610-1611, 1614, 1618
coefficient matrix 6, 10, 57-58, 61, 252, 256
Collaborative Filtering 574-576
Computational Intelligence 171, 274, 612, 721, 1072,
1285, 1369, 1520, 1756
Computer Algorithm 807, 820
Concrete Technology 1453-1454, 1462, 1470-1471,
1477
Coronary Artery Disease (CAD) 184-185, 685, 1367-
1369
Correlation coefficient 275-276, 574, 578, 580-582,
596, 606, 717, 1110-1113, 1115-1116, 1118-
1119, 1122-1123, 1127-1130, 1132, 1134, 1136,
1145-1147, 1387, 1478-1480, 1501-1503, 1510-
1511, 1513, 1711-1713, 1717-1718, 1721, 1725,
1727-1730, 1733
CPU Scheduler 321-322, 324-325, 327
Crisp Values 376, 431, 442, 556, 565, 571, 615, 633,
686, 723-724, 793, 829, 856, 1003-1004, 1017,
1094, 1111, 1245, 1255, 1262, 1331, 1458, 1462,
1633, 1649, 1667, 1674
Critical Path Method 369, 1690-1691, 1693-1695,
1698, 1701, 1703
Currency Volatility 132
Cyber Intelligence 1150-1151, 1174, 1177-1179
Cycloconverter 740-741, 762
D
Data Acquisition 292, 821, 826, 988-989, 1001, 1203,
1220-1221, 1226, 1230-1231, 1544-1545, 1753
Data Availability 516-517, 533
Data Grid 516-517, 519, 530, 536
Data Mining 178, 184-185, 187-188, 190, 195, 202,
219-220, 226, 233, 419, 422, 435, 684, 686, 716,
720, 735, 1264, 1291, 1309, 1369, 1425, 1522,
1525, 1534, 1580, 1708-1709, 1711-1713, 1733,
1740, 1755-1757, 1759-1760, 1762, 1764
dead-zone 488, 493, 1396-1397
DecisionMaking31,209-210,224,369,418-419,421,
449, 461, 476, 479, 520, 552-553, 555-557, 559-
560, 573-574, 610, 625, 647-652, 658, 684, 735,
791, 820, 828, 858, 893, 906, 924, 936, 957, 969,
978, 987, 1012, 1020, 1073, 1112, 1146, 1150-
1154, 1157, 1162-1165, 1174, 1177, 1179, 1204,
1218-1220, 1236-1237, 1253, 1309, 1330, 1350,
1354-1355, 1426, 1450, 1454, 1478-1479, 1495,
1520, 1553, 1582, 1597, 1620-1622, 1659, 1661,
1663, 1667-1670, 1673, 1681, 1693, 1708, 1710-
1713, 1718, 1720-1721, 1723, 1733-1734, 1757
Decision Support Systems 184, 682, 717, 1111, 1150,
1264, 1367, 1627, 1708, 1711, 1713
Decision Trees 188, 190, 197, 218, 222, 274, 687,
1525, 1713, 1756-1757
Deductive reasoning 1285
Defuzzification 83-84, 86, 98, 189, 192, 194, 239,
241, 284-285, 296, 329, 418, 420, 424, 430-431,
435, 442, 449, 451-452, 473, 523, 556, 571, 632,
721, 724, 752, 769, 773-774, 785, 787-788, 798,
820-821,824-825,829,947,950,962,1003-1006,
1012, 1015-1018, 1024, 1045-1046, 1049-1051,
1061, 1108, 1158-1160, 1185, 1217-1220, 1226,
1229, 1231, 1243, 1245, 1274, 1322, 1325, 1360,
1374, 1376, 1404, 1457-1458, 1529, 1564-1567,
1576, 1585, 1592, 1594, 1600-1601, 1611, 1619,
1667, 1677, 1679-1680, 1696, 1752
Defuzzification Techniques 556, 571
Degree of Membership 78, 173, 233, 325-326, 328,
368,420,472,493,521,611,635,819,979,1004,
1033, 1036, 1043, 1047, 1243, 1375, 1454, 1562,
1582, 1603, 1671-1672, 1688, 1716, 1752
Direct Matrix Converter 742-744, 762
Discernibility Matrix 1371, 1426-1427, 1437, 1450
Distance Protection 836
distribution network 989, 997
DNA Sequence 1519, 1522, 1524, 1528, 1530, 1534,
1536
DTD 1237-1238, 1240, 1247, 1249, 1251, 1263, 1267
Dynamic Data Replication 520
Dynamic Load Balancing 1643, 1663
Dynamic Performance 1397, 1420
E
E-Commerce 573-574, 969-971, 982
Electroencephalogram (EEG) Signals 347-352, 355
Elitist Ant System 461, 466, 469, 475
Employee Engagement 647-649, 658
xxiii

26. Index
Entropy 191, 273-275, 279-280, 283-284, 286, 289
Evidential Reasoning Approach 920, 932
Evolutionary Algorithm (EA) 1108
EWS 203, 207, 209, 212-214, 216, 227, 233
Expert System 184, 192, 195, 197, 202, 221-222, 224,
226, 233, 275, 418-422, 424-425, 427, 430-431,
435-436, 442, 445, 540-541, 543, 545-546,
548-549, 551-554, 684-688, 717, 721, 908-911,
919-920, 928, 933, 936, 939, 943-944, 947-948,
950-952, 954, 956-957, 967, 979, 987-993, 997,
1001, 1020, 1022, 1052, 1060, 1066, 1068, 1074,
1204, 1237-1239, 1248-1252, 1263-1264, 1273,
1285, 1368, 1600, 1667-1674, 1678-1681, 1688
F
Fair Share Scheduler 321-324
Fault Detection 393-395, 405, 416, 682, 987, 989,
991, 997, 1001
Fault Isolation 416, 1184
Feature Selection 274, 280, 283-284, 286, 347, 349-
351, 353-355, 359, 361, 363, 1369
finite element 1-3, 14-15, 20, 250-252, 258-261, 264,
267, 269, 1540-1542, 1545
Finite Element Analysis 3, 15, 1540
FIS 154-155, 173-176, 179, 181-182, 189, 195, 293,
295-296, 298, 302, 305, 314-315, 422, 531, 573-
574, 582, 601, 604, 607, 611, 613-614, 616, 632-
633, 639, 641, 643, 647, 650, 652-653, 655, 722,
724, 752, 821, 947, 950-951, 1046, 1049, 1053,
1055, 1390-1392, 1457-1458, 1460-1463, 1529,
1569, 1653, 1658, 1675, 1752-1754
Fitness Function 286, 1021, 1109, 1535, 1600
FLC 312-313, 317-318, 807, 809, 818-823, 825-826,
1203-1205, 1215, 1217-1219, 1221-1222, 1228-
1229, 1231
Flexible Alternating Current Transmission Systems
(FACTS) 130
FNN 78, 685-687, 707, 731, 751, 1396-1397, 1399-
1401, 1405, 1407, 1409, 1411-1412, 1414-1415,
1420, 1424
Foot Print of Uncertainty 130
Forward Chaining 557, 907, 910, 913-914, 917, 919-
920, 922-924, 932, 1267
fully fuzzy 1, 3-4, 9-10, 18, 25, 55-56, 61-62, 65, 252,
256-257, 373-375, 379-382, 385
Fully fuzzy system 1, 3-4, 9-10, 18, 25, 252, 257
Fuzzification 86, 188-189, 192, 239-241, 295, 328-
330, 418, 420, 424-425, 430, 435, 442, 447, 452,
615, 631, 721-722, 752, 769-770, 785, 793, 809,
819, 822, 827-828, 939, 947-948, 958, 1024,
1046-1047, 1051, 1074, 1108-1109, 1217-1219,
1243, 1245, 1367, 1374, 1376, 1403-1405, 1408,
1529, 1564-1565, 1576, 1584, 1600, 1667, 1674,
1677, 1680, 1752
Fuzzy Ant Colony Optimization 459, 461, 468, 479
fuzzy arithmetic 2, 56, 134, 251-253, 256, 1073-1074,
1673
Fuzzy Associative Memory 1045, 1157, 1454
Fuzzy Concept 55, 421, 523, 1061, 1404
Fuzzy Control 78, 235, 240-242, 246, 312-313, 487-
488, 515, 528, 758, 818, 820, 822, 827, 830, 938-
939, 1003, 1017-1018, 1061, 1184, 1204, 1217-
1219, 1273, 1400, 1403-1406, 1411-1413, 1669
FuzzyControlSystem758,938-939,1003,1017-1018,
1184, 1400, 1403-1404, 1412
Fuzzy Correlation coefficient 1122, 1712, 1721, 1725,
1728
Fuzzy Correlation Rule Mining 1708, 1713
Fuzzy eigenvalue problem 1, 4, 11, 20, 25
Fuzzy Expert Systems 219-220, 222-224, 226, 419,
425,442,909,935,938,943,946,950,967,1045,
1454, 1673, 1681
Fuzzy Implication 862, 1203, 1218-1220, 1229, 1236,
1644, 1649, 1672
Fuzzy Inference System 98, 132, 134, 136-137, 144-
146, 154-155, 157, 171, 173, 175, 177, 189, 192,
241, 274, 293, 295, 301, 308, 314, 324, 327, 329,
347, 354, 431, 443, 454, 523, 525-527, 531, 533,
536, 545, 547, 573, 579, 582, 594, 601-602, 604,
611, 616, 630, 633, 635, 639, 647, 650, 652-653,
655-656, 665-666, 671-672, 685, 722-724, 752,
758, 769-770, 773, 779, 781, 806, 835, 837-
838, 847, 863-864, 950-951, 1021, 1045, 1051,
1184-1186, 1356-1360, 1368, 1380, 1385, 1390,
1392-1393, 1458, 1460, 1462, 1529, 1553, 1568-
1569, 1600, 1652-1653, 1672, 1674, 1678-1679,
1681, 1752
Fuzzy Knowledge Base 194, 240, 984
fuzzy linear equations 252, 258, 261
fuzzy Logic Control 751, 807, 809, 818, 820, 1004,
1204, 1403, 1600
Fuzzy Logic Controller 239, 241, 308, 312, 314, 574,
739, 751-752, 825, 1203, 1217, 1220, 1236
xxiv

27. Index
Fuzzy Logic Technique 738-739, 759, 762
Fuzzy Membership function 192, 556, 561, 564-565,
947, 995, 1074, 1077, 1243-1244, 1262, 1375,
1673
Fuzzy Method 650, 653, 657-658, 791
Fuzzymin-maxneuralnetwork688,692-693,705,707
Fuzzy Model 32, 133-134, 138, 146, 192, 278, 292,
295, 398-399, 419, 450, 653, 656, 658, 715,
952, 1003-1004, 1185-1186, 1374, 1390, 1596,
1598, 1600-1601, 1604, 1606, 1609, 1618-1619,
1676-1678
fuzzy numbers 2, 4-6, 14, 20, 25, 50, 55-57, 61, 134,
251-253, 255-257, 269, 367-369, 371, 373-374,
376, 380, 390, 418, 422, 425, 427-428, 435,
652, 1004, 1012, 1016-1017, 1075-1077, 1085,
1111, 1121-1122, 1139, 1478, 1480-1483, 1488,
1495-1496, 1501-1502, 1511, 1513, 1623-1624,
1631-1632, 1637, 1690-1691, 1693-1697, 1702,
1712, 1723, 1733, 1752
Fuzzy Rule Interpolation 31-33, 35, 37, 50
Fuzzyrules41,86-87,98,132,134-135,137,143-148,
155, 188, 192, 194, 197, 241, 274, 278, 284-285,
312-314, 354, 418, 420-421, 424, 428, 430, 435,
442, 461, 468, 476, 479, 493, 509, 545-546, 556,
561, 564, 574, 614, 616, 619, 631, 650, 685-686,
752, 758, 765, 769-771, 781, 785, 788, 819-820,
828, 838, 957-958, 979-981, 984, 1000, 1003-
1004, 1024, 1156-1159, 1170, 1175, 1178-1179,
1184-1186, 1231, 1242, 1244, 1246, 1248, 1262,
1273-1274, 1303, 1319-1320, 1322, 1333, 1361,
1367-1368, 1374, 1376, 1407, 1411-1412, 1457,
1529-1530, 1565-1567, 1580, 1601, 1611-1613,
1652, 1669, 1671-1674, 1676-1677, 1688
Fuzzy Set Theory 44, 80-81, 134, 155, 171, 192, 321,
324-325, 368, 421, 521, 540, 572, 938, 941-942,
989, 1003, 1045, 1073, 1075, 1085, 1156, 1184,
1270, 1342, 1398, 1425, 1427, 1454, 1457, 1479,
1597, 1622-1623, 1637, 1668-1669, 1678, 1688-
1689, 1691, 1694, 1696, 1702, 1709
Fuzzy Test System 1228, 1236
Fuzzy Theory 1-2, 420, 809, 1073, 1109, 1396, 1398,
1424, 1695-1696
Fuzzy Universal Approximation Theorem 515
FuzzyVariable427,442,461,1226,1228,1236,1332,
1562, 1565-1566, 1671, 1688
FuzzyXML1237-1239,1242,1246-1249,1251,1253,
1262-1264, 1267
FuzzyTrust 1339-1340
G
Gait Analysis 1203, 1231, 1236
Gait Cycle 1205, 1208-1209, 1222-1224, 1236
Game Mechanics 765, 781
Gamification 763-765, 767-768, 778-779, 781
Gateway Periodicity 666
GenericArchitecture554,562,1237-1239,1251-1252
Generic model 1553, 1555, 1559, 1561, 1567-1568,
1573
Genetic Algorithm 34, 132, 134, 136, 236, 273-274,
277, 282, 287, 289, 293, 350, 368, 419, 460-462,
612,688,751,1020-1021,1070,1072,1079-1080,
1091, 1287, 1386, 1453, 1471, 1518, 1527, 1535-
1537, 1541, 1600, 1680
GeneticProgramming275,933,1287,1291,1535-1536
GradientDescent34,76,97,130,284,571,1286,1298
H
Harvard Classification 540, 543, 545-546
Hedge 1319-1320, 1688
Hemiparesis 1205, 1210-1211, 1236
Hesitant Decision System 1426, 1431, 1437
Hesitant Information System 1426, 1431, 1434
Hierarchical Fuzzy Inference System 1356-1360
Hierarchical Fuzzy System 32-34, 42
HMI Evaluation 633, 642-643
homogeneous reactor 264, 269
Homomorphisms 1425, 1439
Homotopy perturbation method 3-4, 20, 25
Hotels Location Selection (HLS) 31, 45
Human Machine Interface 628, 630
Hybrid Intelligent System 443-445, 686, 1518-1519,
1521
Hybrid Renewable Energy System 815-816
Hybridization 86, 171, 177, 180, 444, 553-554, 560-
561, 572, 1518-1520, 1527, 1536-1538
hyperboxes689,692-693,696-698,701-703,705,707
I
if-then rules 83, 155, 171, 175, 177-181, 187, 241,
289, 398-399, 428, 449, 492, 515, 521, 546, 611,
639, 650, 758, 769, 838, 862, 907, 941, 954, 979,
1043-1045, 1157, 1218, 1319, 1361, 1455, 1669,
1672, 1681
Image processing 154, 165, 274, 517, 687, 735, 957
xxv

28. Index
imprecise knowledge 170-175, 177, 181-183, 325,
419, 1673
incremental learning 689, 692, 695, 707
Indirect Matrix Converter 742-743, 762
Induction Motor 78, 738-739, 741-742, 749, 751-753,
755, 757-760, 762
Inference Engine 83, 85, 99, 192, 241, 329-330, 492,
523, 543, 556-557, 686, 721, 798, 819-820, 838,
862,920,925,933,1017,1217,1229,1251,1267,
1356, 1360, 1376, 1600-1601, 1668, 1688, 1752
Information Retrieval 445, 1239, 1241
Intelligence Analysis 209, 1151, 1154, 1175, 1178
IntelligentControl1203-1204,1215,1236,1399,1404
Intelligent Decision Making 969, 1668
IntelligentTechniques732,735,1285,1385,1518,1537
Interval Analysis 2, 394-395, 411, 416
Intuitionistic Fuzzy Based Fair Share Scheduler 321,
324
Intuitionistic Fuzzy Inference System 327, 329
Intuitionistic Fuzzy Set 321, 324-326, 1709
Iterative methods 55, 59, 61
J
JXTA-Overlay 1268-1272, 1275, 1277, 1280-1283
K
k-Nearest Neighbors 1757
Knowledge-based Systems 187, 611, 920
L
LEACH 609-615, 619-624, 1596-1597, 1604, 1608-
1610
Leader-Follower 1400-1402, 1414, 1424
linear equations 1, 3-4, 6-7, 9-10, 18, 25, 55-56, 252,
257-258, 261, 1185, 1189
Linguistic Variable 83, 142, 222, 226, 240, 442, 556,
565, 631, 762, 821, 824, 908, 941, 979, 1004,
1047, 1051, 1156, 1242-1243, 1245, 1262, 1273,
1407, 1671
Load Balancing 517, 663-666, 672-674, 678, 1643-
1644, 1649, 1652, 1657-1659, 1661, 1663-1664
Longitudinal wave velocity 1385-1387, 1392-1393
Low Frequency Oscillations 119, 130
Lyapunov approach 487-488
Lyapunov’s (Second) Approach 515
M
Machine Learning 171, 274, 288, 292-293, 295, 298,
301, 305, 419, 424, 445, 572, 703, 716, 1190,
1285, 1302, 1306, 1309, 1367-1368, 1521-1522,
1579, 1679, 1757, 1764
MADM 652, 1110, 1112, 1146, 1710-1712
MAGDM 1478-1480, 1495, 1510, 1513, 1708, 1711-
1712, 1732-1733
Mamdani Inference System 189, 308, 604, 801, 806
Mammography 687, 707, 1023, 1061
MANET 663-666, 678
Matrix (SDU) Decomposition 515
matrix decomposition 487, 500
Max-Min Ant System 475
mechanical properties 176-177, 179, 181, 1454, 1458,
1471
Medical Applications 705, 708, 957, 1020, 1268,
1270, 1281
Medical Diagnostic 194, 968
Metastasis 1020, 1024, 1028, 1061
microstructural features 172, 174-175, 177, 181-182
Military Decision Making 1150-1153
Mobile Communications 859
Molecular Biology 1518, 1524-1525, 1537
Multi-Agent Systems (MAS) 873, 1327, 1330, 1366
Multi-Input–Multi-Output System (MIMO) 515
multilayer perceptron neural network 686-691, 699-
700, 702, 705, 707, 709
MultipleAttributeGroupDecisionMaking(MAGDM)
1478, 1495, 1708, 1711, 1720
Multiple Model Approach 393, 398-399, 411, 416
Multi-Robot System 1401, 1424
multivariable nonlinear systems 487-488
Mutual Information (MI) 347, 349, 353
N
Natural Frequency 2, 24-25, 1540-1541
Neural Networks 79, 86-87, 154, 187-188, 218-219,
274, 276, 278, 282, 314, 319, 420, 444, 541, 571,
682-690, 692, 699, 703, 705, 707, 719, 808, 819,
830, 937, 963, 1184, 1186, 1198, 1291, 1295,
1298-1299, 1303, 1305, 1309, 1367, 1386, 1388,
1453-1454, 1477, 1518, 1520-1521, 1524, 1526-
1529, 1534, 1538, 1541-1542, 1545, 1548-1549,
1567, 1678, 1756-1757, 1759
xxvi

29. Index
Neuro-Fuzzy Inference 153, 177-178, 293, 420, 443-
445, 449-450, 456, 594, 950, 1183-1184, 1192,
1197, 1390, 1457, 1542, 1545, 1740, 1752
Neuro-Fuzzy Models 155
Neuro-Fuzzy System 99, 154, 165, 179-181, 274, 445,
561-562, 569, 572, 1303, 1518, 1531, 1538, 1580
Neurological Signs 935, 951-952, 956, 968, 1680
Neuron 80, 87, 276, 450-452, 558, 690-691, 700, 707,
839, 1207-1208, 1291-1293, 1295, 1404-1405,
1408-1409, 1526-1527, 1546, 1548, 1759
neutron diffusion 252, 264, 267, 269
Nondestructive Test 1549
Nonlinear System 393, 398, 403-404, 407, 411, 416,
507, 509, 1183, 1185
Nuclear Power Plants 394, 628-629, 633, 639, 641
Number of Clusters 609-612, 614, 621, 625, 839,
1598-1600, 1606-1610, 1618
Nutrient Requirements 551, 553, 561-562
O
Opinion Mining 1578
Optimal Solution 277, 279, 367-369, 375-376, 379-
380, 382, 384, 387, 390, 405, 472, 1072, 1291,
1304, 1621, 1747, 1749
OWA Operator 1481-1482
P
P2P Systems 1269, 1271, 1366
Path Planning 1396-1399, 1401, 1411-1412, 1414-
1416, 1420, 1422, 1424
Peer Reliability 1268-1270, 1277-1278, 1281-1283
Petroleum 715-721, 723, 726-730, 732, 735, 815-816,
860
Phase Backup Protection 835-836, 852
Photometry 540, 543, 545
Physical Activity 763-764, 768, 778-779, 781
Physical Fitness 763-764, 774, 781
Physiographic 782, 791-793, 801, 806
physiographic characteristics 782, 801
porosity 717, 1386
power network 840, 988, 990, 997, 1001
Power Prediction 821, 825
Power System Stability 130, 235-237, 239, 244, 246
Power Systems 74-75, 77-78, 87, 235-237, 239, 242,
293-294, 840, 988-990
Principal Component Analysis (PCA) 1183-1184,
1187, 1197, 1678
Prioritization 280, 647, 651-653, 658, 1176-1178
Production Rule 442, 1672
ProjectEvaluationandReviewTechnique(PERT)1691
Prostate Cancer 935, 946, 957, 962-963, 968, 1309,
1668
protective relays 987, 990-993, 996-997, 1000
PSK Method 367, 369-370, 378-380, 382
PSO195,236,292,301-302,304-305,319,350,1070,
1072, 1074, 1079-1080, 1084, 1091-1092, 1099,
1291, 1532-1533, 1542
PSS 235-239, 241-242, 244-246, 1743
Public Procurement 1620-1622, 1627-1630, 1632,
1635, 1637-1638
PV Panels 809, 816, 829-830
PV Power 809, 816-817, 820-826, 829-830
Q
Quality of Experience 1739, 1741, 1761, 1765
Quality of Service 856, 1739, 1761, 1765
R
Regression Model 187, 715, 719, 724, 727-728, 735,
1388, 1746, 1765
Regression Models 715-716, 1462, 1746-1747
REGRET 1326-1327
Relative Core 1425, 1427, 1437
Relative Reduct 1372-1373, 1425, 1427, 1437
Replica Preserving Value 516, 518, 522-524, 527,
529-531, 533, 536
Replica Replacement Algorithm 516, 518-520, 522,
529-530, 536
Risk Analysis 969, 971-972, 974-975, 977, 1703
Robust Optimization 1740, 1746-1747, 1749-1750,
1765
Rotor 76, 89, 97, 117, 130, 236, 760, 762, 814, 817,
828, 1541-1542, 1544
Rough Set 171, 188, 325, 652, 1367, 1369, 1426,
1518-1519, 1534, 1538
Rough Set Theory 171, 188, 652, 1367, 1369, 1426,
1518, 1534, 1538
RoutingProtocols1596-1598,1600,1608,1614-1615,
1618
RuleBasedSystem911,919-920,928,933,1021,1600
S
SaaS 460, 1364, 1643-1644
Search Engines 443-445
sector nonlinearity 493
xxvii

30. Index
Sensor Faults 394-395, 411, 416
SentiWordNet 1576-1577, 1579, 1581-1585, 1587-
1589, 1592-1594
Service Selection 1354, 1356
Set Theory 44, 78, 80-81, 134, 155, 171, 188, 192,
321, 324-326, 368, 421, 521, 540, 572, 652,
888, 938, 941-942, 989, 1003, 1045, 1073, 1075,
1085, 1109, 1156, 1184, 1270, 1342, 1367, 1369,
1398, 1425-1427, 1454, 1457, 1479, 1518, 1534,
1538, 1597, 1622-1623, 1637, 1668-1669, 1678,
1688-1689, 1691, 1694, 1696, 1702, 1709, 1712
SGML 1239-1240, 1267
SHRM 648, 653, 658
Singular Value Decomposition 1189, 1302
Situational Understanding 1151-1154, 1162, 1166,
1170-1175, 1177-1178
Slope of the Land 782, 784, 792-794, 801, 806
SNA 202, 209, 216-221, 233
Social Network Bridge 233
Social Network Centrality 233
Social Network Distance 234
Social Network Tie Strength 234
Softcomputing154,171,274,444,569,682-684,688,
707, 715-716, 739, 749, 762, 779, 855, 957, 963,
1020, 1060, 1150, 1157, 1386-1387, 1454, 1520
Soft Computing Techniques 171, 444, 682-684, 688,
707, 715, 739, 749, 762, 779, 1150, 1454
SPORAS 1325-1327
Stars Classification 540, 543, 548
Starting theory 1553-1555, 1559, 1561
stiffness matrices 252, 259-260, 266-267, 1544
Stock-and-flow diagram 1557-1558, 1562-1563
Structural Equation Model 132-133
Structural Holes 217, 234
Style Sheet 1240, 1267
Sugeno 44, 155, 157, 177, 308, 350, 354, 398, 450,
545-546, 548, 632, 650, 752, 758, 769-770, 781,
787, 1184-1185, 1270, 1273, 1390, 1457, 1532,
1598, 1601, 1619, 1674, 1676-1677, 1753
Supervised Learning 155, 274, 558-559, 562, 572,
684,687,692,760,1298,1579,1594,1757,1759
Swam Intelligence 1518, 1538
Swarm Intelligence 1080, 1285-1286, 1288-1289,
1519-1520
Switching State 751, 762
SWOT 647-654, 656-658
System dynamics 936, 1553, 1555-1556, 1567, 1573
System Identification 298, 300, 1183-1184, 1190,
1197, 1309
T
TAKAGI–SUGENO Model 1601, 1619
Temporal Logic 968
Test Case 235, 237-238, 641, 716, 719, 724, 726-729,
955
Time Series 134, 715-717, 719, 724, 730-732, 735,
950, 1185, 1190-1191, 1524, 1678
TMFC 1342, 1347
Tomosynthesis 1023, 1061
TOPSIS 1110-1112, 1123, 1129-1130, 1138-1139,
1141, 1143, 1145-1147, 1479, 1628, 1712
Training Set 187, 572, 687, 692, 695, 705, 758, 1191,
1312, 1376, 1526, 1532, 1537
Trust Calculation 1314, 1325, 1341, 1362-1364
Trust Fuzzy Comprehensive Evaluation 1348
TTL 665, 669, 673
Tweet 1588, 1591-1593
Type-1 Fuzzy Transportation Problem 374
Type-3 Fuzzy Transportation Problem 367, 369, 374
U
Uncertain Parameter 395, 416
Unified Medical Language System (UMLS) 921, 933
Union 81, 83, 85, 134-135, 553, 611, 695, 824, 995,
1005, 1042, 1317-1318, 1428, 1564, 1671, 1689
Universe of Discourse 80, 83, 135, 325-326, 442, 471,
556,616,619,908,1036-1037,1047,1112,1218-
1219, 1317, 1332, 1334, 1345, 1564, 1671-1672,
1676, 1689, 1709, 1716
Urinary Incontinence 935, 943, 968
V
Vague Data 287, 560, 657, 1074, 1114, 1709
Vague sets 1110-1115, 1118-1119, 1123, 1146, 1709,
1712
Value of Information 1151-1152, 1178
Variable Structure System 515
variable-structure control 494, 497
Venturini Algorithm 739, 743, 755
Verification of Expert System 933
VIKOR 1350-1354, 1356
Virtual Machine Placement 459-462, 464, 468-469,
473, 475-476, 479, 482
Voltage Regulation 75, 237, 239, 246
Voltage Source Converter 89, 739-740, 762
xxviii

31. Index
W
Weighted Averaging Operator 1482
Wind Power 807, 810, 813-814, 827-829
Wind Turbine 809, 813-815, 826-828, 830
Wireless Sensor Networks (WSN) 79, 609-611, 624,
855, 857, 1596, 1598, 1604, 1619
X
XML 865, 1237-1242, 1245-1249, 1251-1253, 1262-
1264, 1267, 1714
xxix