84 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO. 1, FEBRUARY 2014
Analytical Hierarchy Process Usi...
LI et al.: ANALYTICAL HIERARCHY PROCESS USING FUZZY INFERENCE TECHNIQUE 85
Within the AHP–OWA approach, the fuzzy linguist...
86 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO. 1, FEBRUARY 2014
Fig. 1. Hierarchical structure o...
LI et al.: ANALYTICAL HIERARCHY PROCESS USING FUZZY INFERENCE TECHNIQUE 87
TABLE I
DEFINITION AND NORMALIZATION OF THE ROU...
88 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO. 1, FEBRUARY 2014
TABLE II
FIRST-STEP FUZZY (IF–TH...
LI et al.: ANALYTICAL HIERARCHY PROCESS USING FUZZY INFERENCE TECHNIQUE 89
After execution of two step fuzzy rules, the we...
90 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO. 1, FEBRUARY 2014
Fig. 3. An empirical illustratio...
LI et al.: ANALYTICAL HIERARCHY PROCESS USING FUZZY INFERENCE TECHNIQUE 91
Fig. 4. The weights of traffic attributes change...
92 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO. 1, FEBRUARY 2014
Fig. 6. Travel time comparison d...
LI et al.: ANALYTICAL HIERARCHY PROCESS USING FUZZY INFERENCE TECHNIQUE 93
V. CONCLUSION
In this paper, an AHP–FUZZY appro...
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Analytical hierarchy process using fuzzy inference technique for real time route guidance system

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Transcript of "Analytical hierarchy process using fuzzy inference technique for real time route guidance system"

  1. 1. 84 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO. 1, FEBRUARY 2014 Analytical Hierarchy Process Using Fuzzy Inference Technique for Real-Time Route Guidance System Caixia Li, Sreenatha Gopalarao Anavatti, and Tapabrata Ray Abstract—This paper focuses on an optimum route search func- tion in the in-vehicle routing guidance system. For a dynamic route guidance system (DRGS), it should provide dynamic routing advice based on real-time traffic information and traffic condi- tions, such as congestion and roadwork. However, considering all these situations in traditional methods makes it very difficult to identify a valid mathematical model. To realize the DRGS, this paper proposes the analytical hierarchy process (AHP) using a fuzzy inference technique based on the real-time traffic informa- tion. This AHP–FUZZY approach is a multicriterion combination system. The nature of the AHP–FUZZY approach is a pairwise comparison, which is expressed by the fuzzy inference techniques, to achieve the weights of the attributes. The hierarchy structure of the AHP–FUZZY approach can greatly simplify the definition of a decision strategy and explicitly represent the multiple criteria, and the fuzzy inference technique can handle the vagueness and uncertainty of the attributes and adaptively generate the weights for the system. Based on the AHP–FUZZY approach, a simulation system is implemented in the route guidance system, and the process is analyzed. Index Terms—Analytical hierarchy process (AHP), fuzzy inference technique, real-time route guidance. I. INTRODUCTION THE ROUTE guidance system is a routing system that provides an optimum route to drivers based on a cost function and a route solution. The cost function is related to the travel time (TT), distance, or the cost of a road segment, etc. Based on the cost function, the route choice mechanism can provide the optimum route for drivers. The route choice mechanism is the key technique of vehicle navigation systems providing path-planning strategy for travelers. Defining suitable mathematical models to represent the route choice mechanism in traditional methods uses numerical techniques where per- ceived traffic attributes are treated as crisp inputs, such as TTs. However, much of human reasoning is based on imprecise, vague, and subjective values. Thus, the traditional methods ignore the presence of vagueness and ambiguity in drivers’ perception, making them difficult to be valid mathematical models. From the human reasoning perspectives, the fuzzy logic and the developed fuzzy model techniques show great advan- tage to model human decision-making process over traditional methods. Teodorovic and Kikuchi [1] first proposed the fuzzy Manuscript received October 4, 2012; revised April 8, 2013 and July 1, 2013; accepted July 3, 2013. Date of publication July 25, 2013; date of current version January 31, 2014. The authors are with the University of New South Wales, Canberra, ACT 2612 Australia (e-mail: caixia.li@student.adfa.edu.au; S.Anavatti@adfa. edu.au; T.Ray@adfa.edu.au). Digital Object Identifier 10.1109/TITS.2013.2272579 logic method in route selection. The drivers’ perceived TTs are treated as fuzzy numbers, and route choices are given by an approximate reasoning model and fuzzy inference. This model consists of rules indicating the degree of preference of each route. However, this model only considers TT attributes, which is also difficult when generalized to multiple routes. Teodorovic and Kalic [2] proposed a route choice model using fuzzy logic in air transportation. This approach, other than TT, considers more attributes, such as travel cost, flight frequency, and the number of stopovers. However, it is limited to two possible routes. Lotan and Koutsopoulos [3] also proposed a modeling route choice framework based on fuzzy set theory and approximate reasoning. This approach extended the perceived traffic at- tributes used in the route choice mechanism. However, this approach work for particular origin/destination (O/D) pair, and it is also difficult to generalize for different O/D pairs. Pang et al. [4] proposed a fuzzy–neural approach. The pro- cedures and membership functions of the fuzzy system can be retrieved from the implementation of the neural network. A special learning algorithm is used to learn and adapt itself to the recent choices of the driver. This approach is not simply minimization of TT, but more attributes are considered in this model. In addition, it can handle more than two feasible routes and apply to any O/D pair with any number of feasible routes. In particular, its learning algorithm can also learn from the choice selection of the driver. However, it has a high requirement of quality data, and the training procedure is time-consuming. Yager and Kelman [5] introduced an extension of the an- alytical hierarchy (AHP) approach using ordered weighted averaging (OWA) operators, suggesting that the capabilities of AHP as a comprehensive tool for decision-making improved by integration of the fuzzy linguistic OWA operators. OWA is a kind of a multicriterion aggregation procedure, which was developed in the context of fuzzy set theory and is composed of two weights: the weights of criterion importance and order weights. The order weights decide the optimum route choice of road network, whereas the AHP proposed by Saaty in 1980 is based on the additive weighting model. The route choice can be given by a two-step method. First, the AHP decomposes the decision problem into a hierarchy of subproblems composed of several criteria, and the importance of weights is associated with their criteria. Then, the weights can be aggregated with the criteria by the weighted combination methods. This approach is of great importance for spatial decision problems that cannot complete pairwise comparisons of the alternatives [6], [7]. Boroushaki and Malczewski [8] used a quantifier-guided OWA combination with AHP by the fuzzy linguistic quantifiers. 1524-9050 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. W IN G Z TEC H N O LO G IES 9840004562
  2. 2. LI et al.: ANALYTICAL HIERARCHY PROCESS USING FUZZY INFERENCE TECHNIQUE 85 Within the AHP–OWA approach, the fuzzy linguistic quantifier has the capability of capturing qualitative information which the decision-maker may discern the relationship between the differ- ent evaluation criteria. Although this fuzzy linguistic quantifier can enhance the ordered weighted averaging process, due to the vagueness and uncertainty of traffic attributes and route deci- sions, a crisp pairwise comparison of AHP cannot capture the vagueness of traffic attributes. However, it suggests a systematic fuzzy logic inference technique that can be introduced into the AHP structure to compensate for the deficiency of AHP. Arslan [9] proposed using a fuzzy technique and an ana- lytical hierarchy process (AHP–FUZZY) to handle public as- sessments on transportation projects. This approach can capture essential subjective preferences to pairwise among alternatives by AHP. However, this approach can only respond to current O/D pairs, but it cannot react to real-time traffic information to generate a new route. Thus, this paper introduces the fuzzy logic to improve the quantifying process of the AHP approach. In addition, the aforementioned approaches are mainly based on provision of O/D pairs’ routes without considering heavy traffic congestion of some road segments, and the optimum route given by the comparison of the O/D pairs is similar. This paper considers both the traffic density of road segments of each intersection and the overall cost of O/D pairs to generate an entirely different route, which is of great importance to the extension of route choice problems. Numerical simulation results are provided to show the adaptiveness of the route guidance system. This paper is outlined as follows. Section II gives a descrip- tion on the AHP approach, a fuzzy inference technique, and the process of the AHP–FUZZY approach. Section III describes a route selection process based on some important traffic at- tributes and focuses on the implementation procedures applying the AHP–FUZZY approach in the real-time route guidance sys- tem. To demonstrate the process of the AHP–FUZZY approach, an implementation of the simulation and the results analysis are presented in Section IV based on Sydney traffic data. Some conclusions are given in Section V. II. METHODOLOGY A. AHP Approach The AHP approach is a flexible but well-structured method- ology to analyze and solve complex decision problems by structuring them into a hierarchical framework [10]. It can be realized by three steps: 1) development of the AHP hierar- chy; 2) pairwise comparison of elements of the hierarchical structure; and 3) construction of an overall priority rating. For the first step of the AHP procedure, the decision problem is decomposed into a hierarchy, which consists of goal, objectives, attributes and alternatives. The pairwise comparison as the second step of the AHP procedure is the basic measurement mode employed in the AHP procedures, which can greatly reduce the conceptual complexity of a problem since only two components are considered at any given time. The decision hierarchy tree of the AHP can provide the selection and ranking of alternatives by pairwise comparison according to related criteria. The pairwise comparison matrices are based on the alternatives A1, . . . , Am, in terms of each criteria being considered. A pairwise matrix for an expert i with respect to criterion k can be denoted as Ak i = A1 ... Am A1 . . . Am⎡ ⎢ ⎣ ak, i 11 · · · ak, i 1m ... ... ... ak, i m1 · · · ak, i mm ⎤ ⎥ ⎦ . (1) Each aij denotes the strengths of preferences that the user believe alternative i over alternative j. Each pairwise matrix in the form of m × m, whose elements are aij’s, is a square positive reciprocal matrix aij = 1/aji and aii = 1 ∀ i, j = 1, . . . , m. (2) Therefore, the ratio either under or above the principal di- agonal of the matrix are enough to complete the matrix by taking the reciprocals of the given elements. Each aij could be regarded as an estimate of the weight of the alternative i, i.e., wi, to alternative j, i.e., wj, as follows: aij = wi/wj. (3) Then wi = aijwj. (4) After the pairwise comparison matrix is obtained, the next step is to summarize preferences so that each element can be assigned a relative importance. It can be achieved by com- puting the weights and priorities, w = [w1, w2, . . . , wp] for p objectives and w(q) = [w1(q), w2(q), . . . , wI(q)] for attributes associated with the qth objective. The weights can be achieved by normalizing the eigenvec- tor with respect to the maximum eigenvalue of the pairwise comparison matrix. The normalized eigenvector consists of an iterative process; first matrix A is calculated by normalizing the columns of A, i.e., ˆA = a∗ qt p×p (5) where a∗ qt = aqt/ p q=1 aqt, for all t = 1, 2, . . . , n. The vector of w can be given by wq = ˆa∗ qt(z) ∀ q = 1, 2, . . . , p. (6) By the simple rule, the attribute weights can be calculated as follows: a∗ kh(q) = akh(q) l k=1 akh(q) ∀ h = 1, 2, . . . , l (7) wk(q) = ˆa∗ kh(q) ∀ k = 1, 2, . . . l. (8) Finally, the weights can be given by aggregating the relative weights of objectives and attribute levels, which can be done by a sequence of multiplication of the matrices of relative weights at each level of hierarchy. The global weights of each criterion wg j are calculated as follows: wg j = wq × wk(q). (9) W IN G Z TEC H N O LO G IES 9840004562
  3. 3. 86 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO. 1, FEBRUARY 2014 Fig. 1. Hierarchical structure of the AHP–FUZZY system. For the overall evaluation results, Ri of the ith alternative is calculated as follows: Ri = n j=1 wg j xij (10) where xij is associated with a set of standardized criterion values, i.e., X = [xij]m×n, for xij ∈ [0, 1], j = 1, 2, . . . , n. B. Fuzzy Approach A fuzzy logic system [11] is a process of mapping an input space onto an output space using membership functions and linguistically specified rules. The process of fuzzy inference in- volves membership functions, logical operations, and IF–THEN rules. In terms of the AHP approach, the estimation of pairwise comparison depends on subjective perception or experience of relative significance of factors. However, the decision-maker cannot determine the relative significant weights with any certainty between any certain values, such as between scales of 1 to 9. They can only linguistically describe the factors A method that can determine weights of pairwise comparison corresponding to the degree of importance described by the decision-maker will be greatly useful. Therefore, fuzzy logic theory representing the inference procedure explicitly by a set of fuzzy IF–THEN rules, which can offer a high degree of transparency into the system being modeled and can deal with the ambiguity of the judgment process, can compensate the disadvantage of the AHP approach. With the inputs and output defined, it needs to specify a set of rules to define the model. The rules of approximate reasoning, which can be used to describe the route choice, are IF–THEN rules. After the inputs are fuzzified and the degree of each part of the antecedent is satisfied for each rule, the logical operations can help the logical verbal rules. Finally, the defuzzification process can help resolve the output value from the set. C. AHP–FUZZY Model An AHP—FUZZY model is proposed in this paper, which uses a FUZZY model to replace the crisp ratios to present the weights of pairwise comparison and to distinguish the relative significance of all factors. In the proposed model, a three-level hierarchical structure is constructed to present the relationship between a module and a component, as shown in Fig. 1. The AHP–FUZZY structure also consists of goal, objectives, attributes, and alternatives. To adaptively realize the route guidance system for the whole day, this AHP–FUZZY model employs a two-step system. For the first step, it is used to adaptively choose route planning objectives based on traffic density; for the second step, it generates the weights of attributes considering both the overall cost of O/D pairs and traffic on road segments of each intersection. Thus, the spatial decision problem here involves a set of geographically defined alternatives and a set of evaluation criteria and its associated weights. Consider directed graph G = (V, E) with origin point o ∈ V and destination d ∈ V . “A” denotes the set of all acyclic routes from the origin point o to destination point d on G = (V, E). For each road segment of the road network, e ∈ E criteria are defined; then, the multicriterion structure is imposed on the road network. As aforementioned, the purpose of this paper is to give the route decision with the least cost, considering both the traffic density of road segments of each intersection and the overall cost of O/D pairs. Suppose that there are a set of m alternatives, i.e., m adjacency road segments for each node, which can be denoted by Ai for i = 1, 2, . . . , m. The al- ternatives are to be evaluated by a set of p objectives Oq, where q = 1, 2, . . . , p. The objectives are measured in terms of the underlying attributes. Thus, a set of n attributes as- sociated with the p objectives can be denoted by Cj, where j = 1, 2, . . . , n, whereas a subset of attributes associated with the qth objective is denoted by Ck(q) for k = 1, 2, . . . , l, l ≤ n. There are two sets of weights, i.e., w = [w1, w2, . . . , wp] and w(q) = [w1(q), w2(q), . . . , wI(q)], and they are assigned to the objectives and attributes, respectively. The weights have the following properties: wq ∈ [0, 1], p q=1 wq = 1, and wk(q) ∈ [0, 1], I k=1 wk(q) = 1. Based on the basic knowledge of the AHP approach, the fuzzy logic approach is employed to improve its performance. For the weights of the objectives and weights, they are no longer constant values but will be decided by the fuzzy logic rules. Combining with the given weights, the global weights of each criterion wg j are calculated as wg j = wq × wk(q), whereas the performance of alternatives Ai with respect to attributes Cj represented by a set of standardized criterion values X = [xij]m×n for xij ∈ [0, 1], j = 1, 2, . . . , n. The final evaluation results of the ith alternative can be also W IN G Z TEC H N O LO G IES 9840004562
  4. 4. LI et al.: ANALYTICAL HIERARCHY PROCESS USING FUZZY INFERENCE TECHNIQUE 87 TABLE I DEFINITION AND NORMALIZATION OF THE ROUTE CHOICE CRITERIA calculated as Ri = n j=1 wg j xij, where xij is associated with the standardized attribute value. III. IMPLEMENTATION OF AHP–FUZZY APPROACH The framework of the AHP–FUZZY model can be divided into four parts: 1) the construction of a hierarchical structure, as shown in Fig. 1; 2) the implementation of the AHP; 3) the fuzzy arithmetic operation; and 4) the establishment of the priority of relative importance. A. Traffic Attributes Traditionally, the movements of vehicles are considered as isolated moving units in the route guidance system. However, a car driving on the road is influenced by the whole road network, including static and dynamic information. Van Vuren and Van Vliet [8] assumed that distance or time minimization is the only criterion for drivers’ route choice. Further study done by Bovy and Stern [9] showed that more factors could influence route choice, such as TT, travel distance (TD), width of the road, delays, road safety, traffic density, etc. Generally, distance and TT are usually considered as the main factors to decide the route selection in current onboard route guidance system usually inducing the shortest distance or the least time route based on the road distance information or history traffic flow information. However, the route guidance system based on the shortest route without considering traffic conditions and traffic congestion, can easily cause traffic congestion, energy waste, and environmental pollution. In this paper, we focus on the travelers whose purpose of travel is working. For workers, they always want to get to their destination with the least cost, such as with the shortest distance or at the least time. In this paper, distance and TT are also considered. When workers travel on nonpeak hours, the shortest distance or the least time paths are more favorable. However, when workers make a route choice during peak hours, they also want to get to their destination with less time delay and less congestion, which are all related to traffic density on the route. Thus, the objective attributes considered in this paper mainly include three attributes, i.e., TD, TT, and traffic density, and the weights of objective attributes are also decided by traffic density and volume delays (VYs). The focus of this paper is on the route choice to reduce traffic congestion on the roads and enhance travel efficiency of drivers. Thus, TD, TT, and travel density (TS) are the three main criteria considered in this route guidance system for k routes given by the route search algorithm. The definition and normalization of route choice criteria are shown in Table I. Fig. 2. Membership functions of linguistic variables. B. Fuzzy Rules for Pairwise Comparison In the pairwise comparison matrices, the crisp ratio of aij are replaced by fuzzy numbers with its membership function, such as that shown in Fig. 2. The fuzzy number represents importance on linguistic variables. The arithmetic of triangular fuzzy numbers is decided by the degree of confidence level. In this AHP–FUZZY model, a triangular membership func- tion is used. As to membership functions, it can change their intervals to modify the membership functions, such as the triplet fuzzy model (al, am, au), whose membership function μ(x) is defined as follows: μA(x) = ⎧ ⎪⎨ ⎪⎩ 0, x < al (x − al)/(am − al), al ≤ x ≤ am (au − x)/(au − am), am ≤ x ≤ au 0, x > au. (11) It can use the interval of confidence at a given level of con- fidence coefficient β to change the intervals of the membership function, and the triangular fuzzy number Aβ has the following characteristics: ∀ β ∈ [0, 1] Aβ = aβ l , aβ u =[(am −al)∗β+al, −(au −am)∗β+au] . (12) Thus, the intervals of the membership functions can be changed by various β levels (0 < β ≤ 1). As in Section II, this model uses a fuzzy model to replace the crisp ratios to present the weights of pairwise comparison and to distinguish the relative significance of all factors. There are two weights that are to be determined: the weights of objective attributes and the weights of alternative attributes. To determine these two weights, this AHP–FUZZY model employs a two-step system. For the first step, it presents the weights of objectives based on traffic density; for the second step, it generates the weights of attributes considering both the W IN G Z TEC H N O LO G IES 9840004562
  5. 5. 88 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO. 1, FEBRUARY 2014 TABLE II FIRST-STEP FUZZY (IF–THEN) RULES FOR THE WEIGHTS OF OBJECTIVE ATTRIBUTES overall cost of O/D pairs and traffic on road segments of each intersection. For the first-step rule, the weights of the objectives are deter- mined by the traffic density and VYs. Thus, traffic density and VYs of fuzzy rules consist of the antecedent and consequent of fuzzy rules that are composed of objective attributes. The linguistic descriptions of fuzzy inputs are labeled as “much more” (MM), “more” (ME), “medium” (M), “less” (L) and “much less” (ML), and the fuzzy outputs are labeled as “high” (H), “medium” (M), and “low” (L). The weights of the objective attributes are determined by the first-step rule, as shown in Table II. The IF–THEN rule can be described by the antecedent and consequent, such as, if TS is much less (ML), then the weight of traffic distance is high (H). Pairwise comparisons are the key technology of the AHP approach, which can be implemented by comparing three traffic attributes: TD, TT and traffic congestion for differ- ent routes based on a fuzzy rule system. As to the value of the objective weights, it can be generated by the fuzzy membership function and by the defuzzification process. For the criterion weight wk(q), it is generated by the second fuzzy rule. For the second step, it generates the weights of attributes considering both the overall cost between current origin and destination pairs Ctotal and traffic cost on current road segments Csegment of each intersection, which decides which route will be favorable. Their linguistic importance of antecedent is also described as “much more” (MM), “more” (ME), “medium” (M), “less” (L), and “much less” (ML), and the consequent is also described as “high” (H), “medium” (M) and “low” (L). The fuzzy rules for a pairwise comparison of alternatives are described in Table III. After defining the fuzzy inputs and fuzzy rules, the aggrega- tion of all outputs s is given by s = max y∈Y min (μA(y), μB(y)) (13) TABLE III SECOND-STEP FUZZY (IF–THEN) RULES FOR THE ALTERNATIVES ATTRIBUTES where y is the universe of discourse, and μA(y) and μB(y) are the membership functions of the inputs relating to the state of the alternatives A and B. As in most fuzzy systems, a center-of-gravity-based defuzzi- fication is used. The centroid zk corresponding to the alternative k is given by zk = N i=1 αiOi(k)Si(k) N i=1 αiSi(k) (14) where αi is the degree to which the kth rule is fired, Oi(k) is the centroid of the fuzzy set corresponding to the right- hand-side entry of rule i with respect to alternative k, and Si(k) is the area of this set. (If N i=1 αiSi(k) = 0, then zk is equal to 0). Based on the fuzzy rules and the membership functions of fuzzy sets, the criterion weights wk(q) are generated by the defuzzification process. The final evaluation results of the ith al- ternative can be also calculated as follows: Ri = n j=1 wg j xij, where xij is associated with the attributes value. W IN G Z TEC H N O LO G IES 9840004562
  6. 6. LI et al.: ANALYTICAL HIERARCHY PROCESS USING FUZZY INFERENCE TECHNIQUE 89 After execution of two step fuzzy rules, the weight objec- tives wq and alternatives wk(q) can be given. Then, the final evaluation results can be given by the establishment of priority of relative importance. C. Consistency Test of Judgment Matrix To measure the consistency degree in terms of the pairwise comparison matrix A, the consistency index (CI) can be ob- tained by CI = λmax − n n − 1 (15) where n is the number of variables compared and the eigenvalue of λmax is the biggest eigenvalue obtained in terms of the eigenvector. The consistency ratio (CR) of CI is defined as follows: CR = CI/RI (16) where RI is associated with the random CI generated by the pairwise comparison matrix. If CR < 0.1, it indicates a reason- able degree of consistency; otherwise, the CR is not considered to be suitable, and it needs to be revised through the pairwise comparison until it reaches the consistency level. D. Calibration of Fuzzy Rules and Membership Functions The overall objective of the AHP–FUZZY model is to pro- vide reasonable and plausible route to drivers that can alleviate traffic congestion. Once the basic framework of rules is es- tablished, the calibration of the model can be further improve for future choices. To calibrate the model, the actual observed choices are compared with predicted routes. Since each choice can be viewed as a collection of rules that contributed to it, the following rating index Ri can be used to generate the ranking of rule i for given L observed choices: Ri = L l=1 αl i ∗ δ(l) − L l=1 αl i ∗ (1 − δ(l)) L l=1 Fi(l) for i = 1, . . . , N (17) where δ(l) = 1, if correct choice is made for the observation l 0, otherwise (18) Fi(l) = 1, if αl i > 0 0, otherwise (19) and αl i is the degree of ith rule fired for the observed choice l. Note that if L l=1 Fi(l) = 0, then the ith rule needs to be deleted from the rule sets. Therefore, if the right choice is made, each rule i contributes αl i to the rating of rule I, and negative αl i if otherwise. Effective average (given by dividing by the number of cases in which each rule is actually fired to some degree) is used since some “good” rules are rarely fired (such as rules in dealing with some special events or incidents). Rules with lower weights indicate some problems, possibly in the rule itself, the relevant membership functions, or any combination of the above. This heuristic method is sequentially executed by picking rules with low ratings and improving them to make sure some bad rules are picked. The implementation process of the AHP–FUZZY system is as follows. 1) For the hierarchical structure of the AHP–FUZZY sys- tem, the goal is to achieve optimum route choices for drivers. The map layers contain the attributes values assigned to road segment, and the standardized criterion values are denoted as follows: X = [xij]m×n for xij ∈ [0, 1], j = 1, 2, . . . , m. 2) In the pairwise comparison matrices, the ratio aij is replaced by fuzzy numbers. The attributes associated with the objective are distance, TT, and density, and their weights can be determined by the first rule system. The second fuzzy-rule-based pairwise comparison system de- termines the road segments’ weight wk(q). Combining with the given weights, the global weights of each cri- terion wg j can be given by wg j = wq × wk(q). 3) The final evaluation cost of the ith alternative can be also calculated as follows: Ri = n j=1 wg j xij, where xij is associated with the attributes value. After determining all the cost of routes, optimum routes are given by ranking the cost of routes. 4) The consistency test of the pairwise matrix is as follows. For each pairwise matrix, it needs to judge if the CR is in the reasonable level; if not, it needs to modify the pairwise comparison until the consistency level is CR < 0.1. 5) Finally, calibrate the fuzzy rules and membership func- tions to further improve the routes provided to the driver, which are reasonable and plausible. IV. EMPIRICAL ILLUSTRATION The case study involves the traffic road network in Sydney. The road network contains 287 nodes and 592 directed edges. This study only considers the weekday traffic conditions be- cause it has similar traffic characters; in addition, this paper only focuses on the “work” activity, and the travel mode is “car.” Four-week traffic volume data were collected on the main roads in Sydney in 2005. For the data process, to simulate the real-time route guidance system, the real-time traffic in- formation and traffic prediction data for the succeeding period are needed. For the real-time traffic prediction, a hybrid traffic prediction model combining artificial neural networks and the autoregressive integrated moving average method [12] is used to realize the real-time traffic prediction for the whole periods of day, which can overcome the extremely overprediction and underprediction phenomena for some specific periods. First, this paper used the former three-week traffic volume data to be the training data or historical data to get the real-time traffic prediction model. Second, it uses the fourth-week traffic data to compare with the predicted data. A comparative study shows that the hybrid traffic prediction model can represent the traffic W IN G Z TEC H N O LO G IES 9840004562
  7. 7. 90 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO. 1, FEBRUARY 2014 Fig. 3. An empirical illustration of the AHP-FUZZY approach. flow more accurately, and the results gained from this hybrid model are found to outperform traditional individual methods modeling the real urban traffic. To demonstrate the process of the AHP–FUZZY approach, an example is given in Fig. 3. The objectives are measured in terms of three criteria: 1) distance; 2) time; 3) density. When the route selection is implemented, there are a number of routes given for selection. In this illustration example, we just consider the top 3 reasonable routes for analysis. The demonstration of the process of the AHP-FUZZY ap- proach is described as follows: 1) Firstly, the hierarchical structure of AHP-FUZZY is established. 2) This AHP-FUZZY model also has customized character- istic. When the driver makes the route planning, he can determine the route condition he wants. For example, if the driver wants the economic way to get the destination, he can choose less travel distance and travel time to minimize the traffic cost on the road. If the driver wants to increase the sense of comfort, he can choose less traffic density on the road. That is, the driver can choose the degree of importance of traffic attributes (travel distance, travel time and traffic density). There are three degrees of importance for each attribute for decision-makers to choose, such as: “less”, “medium” and “more”, and the weights are gained from the degree of importance corre- sponding to attributes. In addition, the traffic conditions vary intensively from different time periods of day. For the peak hours, the traffic cost on this road segment with high traffic density is higher than usual during non-peak hours. Thus, based on the average traffic density of routes and volume delays, the weights of attributes can be given by the first fuzzy rule as shown in Table II. Combing the weights given by drivers and weights based on the average traffic density of routes and volume delays, the weights of attributes can be finally determined. Based on TABLE IV PAIR-WISE COMPARISON MATRIX OF THE OBJECTIVE ATTRIBUTES TABLE V PAIR-WISE COMPARISON MATRIX OF ALTERNATIVES CORRESPONDING TO THE DISTANCE the three attributes, there are three optimum routes for case study. Table IV shows the pair-wise comparison of objective attributes. 3) After determining the weights of the objective, the second step is to get the weights of alternative attributes in terms of the route information. It can also be obtained from the pair-wise comparison of route information based on the second as shown in Table III. Table V shows the pair-wise comparison of alternatives corresponding to distance. 4) Combining with the above weights, the global weights of each criterion, wg j can be given by wg j = wq × wk(q). Finally, the overall priority rating can be given based on the ranking function: Ri = n j=1 wg j xij, where xij is associated with the attributes value. After determining all the cost of routes, optimum routes are given by ranking the cost of routes. In order to validate the AHP-FUZZY model providing op- timum path during the whole time of day, we choose one of the O/D pairs (from A to B). The objective of this paper to automatically generate optimum routes based on drivers’ requirements. For this purpose, this AHP-FUZZY model must adaptively adjust the attributes weights to get the optimum route for the whole time periods of day. Fig. 4 shows the weights of W IN G Z TEC H N O LO G IES 9840004562
  8. 8. LI et al.: ANALYTICAL HIERARCHY PROCESS USING FUZZY INFERENCE TECHNIQUE 91 Fig. 4. The weights of traffic attributes change during the whole day. traffic attributes in terms of least cost route changing during the whole day. In addition, it also shows that the weights change less during off-peak hours, while it shows great variability during peak hours. It is suggesting the weights of the traffic attributes change greatly with the traffic flow variation, that is, the route choice changes with traffic flow variation. In order to further validate the proposed approach, it was compared with current simulation approaches, such as Multi- Agent Transport Simulation (MATSim) [13], Intelligent Trans- portation System for Urban Mobility (ITSUMO) [14] and MITSIMLab [15] which was developed at MIT Intelligent Transportation Systems Program. The first simulation practice (MATSim) has strength on the planning side. The route plan- ning approach used in MATSim is time-dependent Dijkstra algorithm, which calculates link travel time from the output of the traffic flow simulation. The link travel times are encoded in 15 minutes time bins, thus, they can be used as the weights of the links in the network graph. It also uses iteration cycle to run the traffic flow simulation with specific plans for the agents, and the uses the planning modules to update plans. Then, the updated plans are applied into traffic flow simulation, etc., until consistency is reached. However, it can not consider fine control measures such as instance and the presence of the traffic lights in the network. The second simulation (ITSUMO) which focuses on short time control by means of agents in charge of optimization of signal plans just provides basic tools for the definition of routes and plans for drivers. In fact, the drivers are no more than particles that have no a priori routes and they are re-routed at each intersection according to macroscopic rules, because the ITSUMO is based on cellular automata model. Thus, more sophisticated driver behaviors such as those based on route planning or en-route decision are more difficult to implement in ITSUMO. Currently, the ITSUMO provides a GUI to define a route for drivers, that is, “floating cars”, but the process is time consuming. The MAISim has strength on planning without fine control measures, while the TISUMO has fine control strategy with basic definition of routes. For this, Kai Nagel [16] proposed to integrate the MATSim with the ITSUMO to overcome the shortcomings. That is, once the MATSim generates the plans, the ITSUMO read them and executes them with some control carried out. In this paper, we only focus on the route selection activity, thus, Fig. 5. Travel distance comparison during the whole day among MITSIMLab, MATSIM and AHP-FUZZY model. the route plans generated by the MATSim are compared with AHP-FUZZY approach without considering too much control measures by ITSUMO. The MITSIMLab simulation is a mi- croscopic traffic simulation system which can represent a wide range of traffic management systems and model the response of drivers to real-time traffic information and control. It can enable the MITSIMLab to simulate the dynamic interaction be- tween traffic management systems and drivers. The route choice model implemented in MITSIMLab uses habitual path travel times as explanatory variables, which requires an iterative day- to-day perception updating model to improve initial travel time estimates obtained from planning studies. For each iteration of this process, representing a day, habitual travel times were updated as follows: TTk+1 it = λk ttk it + (1 − λk )TTk it (20) where TTk it and ttk it are the habitual and experienced travel times on link i, time period t on day k, respectively, and λk is a weight parameter (0 < λk < 1). In this study, a convex combinations approach is used to and a constant λk = λ is implemented. Comparing with the above mentioned three simulations, the AHP-FUZZY approach is also a time-dependent route planning approach, which can generate routes for drivers based on real time traffic information and the routes selected also feed into the traffic flow simulation for next iteration, and it is also a customized model which allows the drivers to define their route attributes as the reference for the route selection model. Except the common characteristics, the AHP-FUZZY approach can greatly simplify the definition of decision strategy and represent the multiple criteria explicitly, thus, the model can be easily extended to deal with a variety of traffic attributes, and the fuzzy inference technique can handle the vagueness and uncertainty of the attributes and adaptively generate the weights for the system. In addition, this proposed approach considers both the traffic density of road segments and the overall cost of O/D pairs to generate an entirely different route, which is of great importance to the extension of route choice problems and alleviate traffic congestion. In order to validate the performance of the AHP-FUZZY model, firstly, the travel distance and travel time of a random W IN G Z TEC H N O LO G IES 9840004562
  9. 9. 92 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO. 1, FEBRUARY 2014 Fig. 6. Travel time comparison during the whole day among MITSIMLab, MATSIM and AHP-FUZZY model. TABLE VI PAIR-WISE COMPARISON MATRIX OF THE OBJECTIVE ATTRIBUTES route are compared with the MITSIMLab and MATSIM model. The travel distance and travel time comparison results are shown in Figs. 5 and 6. Fig. 6 shows that the MAISIM model always choose the least travel time. Because the route plan- ning approach used in MATSim is a time-dependent Dijkstra algorithm, which calculates link travel time from the output of the traffic flow simulation. While the route choice model implemented in MITSIMLab iteratively uses updated habitual path travel times and experienced travel time. That is, the driver usually chooses the habitual routes with the updated travel time. Fig. 5 shows that the MITSIMLab model usually provide moderate distance routes which seldom deviate from the habitual route. Comparing these three models during peak- hours and non-peak hours, it can be seen that these three models choose similar routes during non-peak hours, because there is less traffic during non-peak hours and drivers usually travel by least cost path. However, during peak hours, the routes provided by these three models are totally different. The MATSIM model focuses on the travel time which always get the least travel time sacrificing distance, while the MITSIMLab model usually chooses the habitual routes which are usually with less travel distance sacrificing travel time during peak hours. Comparing with MATSIM and MITSIMLab model, the routes generated by the AHP-FUZZY model usually have more distance than the habitual routes, while have less distance than routes provided by MATSIM model as shown in Table VI. In order to further investigate the performance of AHP- FUZZY model during peak hours, secondly, the routes are further compared as shown in Fig. 7. All of routes are not suggested to travel on Southern Cross Drive, because there is higher traffic volume than the average traffic volume on other road segments during peak hours as shown in Fig. 8. Although the route provided by the MATSIM has the least travel time, the route takes a part of M4 Western Distributor Freeway as Fig. 7. Route comparison at 8: 10am among MITSIMLab, MATSIM and AHP-FUZZY model. Fig. 8. Traffic forecast on Southern Cross Drive. Fig. 9. Traffic forecast on M4 Western Distributor Freeway. shown in Fig. 9, which easily cause traffic congestion and it is not reasonable in practice. It seems the route generated by the MITSIMLab model is most plausible, because it has least travel distance with less travel time. However, when it gets to the intersection, which has similar traffic as Southern Cross Drive during peak hours, the route by the AHP-FUZZY approach changes the route before getting to the intersection to avoid the traffic congestion. It is reasonable to avoid the high traffic congestion during peak hours even it may take more travel distance and travel time. W IN G Z TEC H N O LO G IES 9840004562
  10. 10. LI et al.: ANALYTICAL HIERARCHY PROCESS USING FUZZY INFERENCE TECHNIQUE 93 V. CONCLUSION In this paper, an AHP–FUZZY approach for route guidance system has been proposed in which the fuzzy-rule-based system are introduced to generate the weights of attributes instead of the tradition pairwise comparison. Fuzzy logic theory repre- senting the inference procedure explicitly by a set of fuzzy IF–THEN rules, which can offer a high degree of transparency into the system being modeled and deal with the ambiguity of the judgment process, can compensate the disadvantage of the AHP approach. Compared with the traditional route choice approaches simulated in MATSim and MITSIMLab, this proposed paper can provide reasonable and plausible optimal route choice based on the combination of road segments’ cost and the overall O/D cost, rather than the route selection among a number of known routes. Considering the specific road segment information can greatly reduce traffic congestion. 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Fuzzy Syst., vol. 7, no. 4, pp. 401– 417, Dec. 1999. [6] T.vanVurenand D.vanVliet, RouteChoiceandSignalControl. Avebury, U. K.: ITS Institute for Transport Studies: Ashgate, 1992. [7] P. H. Bovy and E. Stein, Route Choice: Wayfinding in Transport Networks. Norwell, MA, USA: Kluwer, 1990. [8] S. Boroushaki and J. Malczewski, “Implementing an extension of the ana- lytical hierarchy process using ordered weighted averaging operators with fuzzy quantifiers in ArcGIS,” Comput. Geosci., vol. 34, no. 4, pp. 399– 410, Apr. 2008. [9] T. Arslan, “A hybrid model of fuzzy and AHP for handling public assessments on transportation projects,” Transportation, vol. 36, no. 1, pp. 97–112, Jan. 2009. [10] T. L. Saaty, Multicriteria Decision Making: The Analytic Hierarchy Pro- cess: Planning, Priority Setting, Resource Allocation. Pittsburgh, PA, USA: RWS, 1990. [11] H. J. Zimmermann, Fuzzy Set Theory and its Applications. Boston, MA, USA: Kluwer, 1991. [12] C. Li, S. Anavatti, and T. Ray, “Short-term traffic prediction using dif- ferent techniques,” in Proc. IEEE Ind. Electron. Soc., Melbourne, VIC, Australia, 2011, pp. 2423–2428. [13] K. Wang and Z. Shen, “A GPU-based parallel genetic algorithm for gener- ating daily activity plans,” IEEE Trans. Intell. Transp. Syst., vol. 13, no. 3, pp. 1474–1480, Sep. 2012. [14] B. Chen and H. H. Cheng, “A review of the applications of agent tech- nology in traffic and transportation systems,” IEEE Trans. Intell. Transp. Syst., vol. 11, no. 2, pp. 485–497, Jun. 2010. [15] K.-T. Seow and D.-H. Lee, “Performance of multiagent taxi dispatch on extended-runtime taxi availability: A simulation study,” IEEE Trans. Intell. Transp. Syst., vol. 11, no. 1, pp. 231–236, Mar. 2010. [16] A. L. C. Bazzan, K. Nagel, and F. Klügl, “Integrating MATSim and ITSUMO for daily replanning under congestion,” in Proc. 35th CLEI, Pelotas, Brazil, Sep. 2009, [Online]. Available: www.inf.ufrgs.br/maslab/ pergamus/pubs/Bazzan+2009.pdf.zip Caixia Li received the B.E. degree in commu- nication engineering from Changchun University, Changchun, China, and the M.Sc. degree in civil en- gineering and transportation control in South China University of Technology, Guangzhou, China. She is currently working toward the Ph.D. degree with the University of New South Wales, Canberra, Australia. Her research interests include cooperative trans- portation management and route guidance systems under provision of real-time traffic information. Sreenatha Gopalarao Anavatti received the B.E. degree in mechanical engineering from the Univer- sity of Mysore, Mysore, India, and the Ph.D. degree in aerospace engineering from the Indian Institute of Science, Bangalore, India. From 1991 to 1997, he was an Assistant Professor with the Indian Institute of Technology, Mumbai, India. From 1997 to 1998, he was an Associate Professor with the Indian Institute of Technology, Mumbai. He is currently a Senior Lecturer with the University of New South Wales, Canberra, Australia. His research interests include dynamic guidance, active vibration control, and applications of fuzzy and neural networks for practical applications. Tapabrata Ray received the B.E. and Ph.D. degrees from the Indian Institute of Technology, Kharagpur, India. From 1996 to 1997, he was a member of the tech- nical staff with the Information Technology Institute, Singapore. From 1997 to 1999, he was a Lecturer with Singapore Polytechnic, Singapore. From 1991 to 2001, he was a Fellow with the Institute of High Performance Computing, Singapore. From 2001 to 2004, he was a Senior Research Scientist with the National University of Singapore, Singapore. He is currently a Senior Lecturer and an Australian Research Council Future Fellow with the School of Engineering and Information Technology, University of New South Wales, Canberra, Australia, where he leads the Multidisciplinary Design Optimization Group. His research interests include multiobjective op- timization, constrained optimization, robust design and constrained robust de- sign, dynamic multiobjective optimization, and realistic transportation models. W IN G Z TEC H N O LO G IES 9840004562

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