The multiple judge,multiple criteria ranking problem: A fuzzy set approach

This paper investigates the problem of selecting, from a set of issues, those which best satisfy a collection of criteria. A group of judges have fuzzy sets defined over the issues, for each criterion, whose values lie in a finite linearly ordered set $\text{L}$. These judges also have fuzzy sets defined over the set of criteria. The paper discusses methods of aggregating all the fuzzy sets into one fuzzy set μ, defined on the issues, so that μA?L gives the final ranking for issue A.     

A hybrid neuro-fuzzy analytical approach to mode choice of global logistics management

This paper presents a hybrid neuro-fuzzy methodology to identify appropriate global logistics (GL) operational modes used for global supply chain management. The proposed methodological framework includes three main developmental phases: (1) establishment of a GL strategic hierarchy, (2) formulation of GL-mode identification rules, and (3) development of a GL-mode choice model. By integrating advanced multi-criteria decision-making (MCDM) techniques including fuzzy analytical hierarchy process (Fuzzy-AHP), Fuzzy-MCDM, and the technique for order preference by similarity to an ideal solution (TOPSIS), six types of global logistics and operational modes coupled with corresponding fuzzy-based multi-criteria decision-making rules are specified in the second phase. Using the specified fuzzy decision-making rules as the input database, an adaptive neuro-fuzzy inference system (ANFIS) is then developed in the third phase to identify proper GL modes for the implementation of global supply chain management. A numerical study with a questionnaire survey database aimed at the information technology (IT) industries of Taiwan is conducted to illustrate the applicability of the proposed method.     

Comparison of first aggregation and last aggregation in fuzzy group TOPSIS

The Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS), one of the major multi attribute decision making (MADM) techniques, ranks the alternatives according to their distances from the ideal and the negative ideal solution. In real evaluation and decision making problems, it is vital to involve several people and experts from different functional areas in decision making process. Also under many conditions, crisp data are inadequate to model real-life situations, since human judgments including preferences are often vague and cannot estimate his preference with an exact numerical value. Therefore aggregation of fuzzy concept, group decision making and TOPSIS methods that we denote “fuzzy group TOPSIS” is more practical than original TOPSIS.     

A QFD-based fuzzy MCDM approach for supplier selection

Supplier selection is a highly important multi-criteria group decision making problem, which requires a trade-off between multiple criteria exhibiting vagueness and imprecision with the involvement of a group of experts. In this paper, a fuzzy multi-criteria group decision making approach that makes use of the quality function deployment (QFD) concept is developed for supplier selection process. The proposed methodology initially identifies the features that the purchased product should possess in order to satisfy the company’s needs, and then it seeks to establish the relevant supplier assessment criteria. Moreover, the proposed algorithm enables to consider the impacts of inner dependence among supplier assessment criteria. The upper and the lower bounds of the weights of supplier assessment criteria and ratings of suppliers are computed by using the fuzzy weighted average (FWA) method. The FWA method allows for the fusion of imprecise and subjective information expressed as linguistic variables or fuzzy numbers. The method produces less imprecise and more realistic overall desirability levels, and thus it rectifies the problem of loss of information. A fuzzy number ranking method that is based on area measurement is used to obtain the final ranking of suppliers. The computational procedure of the proposed framework is illustrated through a supplier selection problem reported in an earlier study.     

A new method for ranking fuzzy numbers and its application to group decision making

In this paper, a new method for comparing fuzzy numbers based on a fuzzy probabilistic preference relation is introduced. The ranking order of fuzzy numbers with the weighted confidence level is derived from the pairwise comparison matrix based on 0.5-transitivity of the fuzzy probabilistic preference relation. The main difference between the proposed method and existing ones is that the comparison result between two fuzzy numbers is expressed as a fuzzy set instead of a crisp one. As such, the ranking order of n fuzzy numbers provides more information on the uncertainty level of the comparison. Illustrated by comparative examples, the proposed method overcomes certain unreasonable (due to the violation of the inequality properties) and indiscriminative problems exhibited by some existing methods. More importantly, the proposed method is able to provide decision makers with the probability of making errors when a crisp ranking order is obtained. The proposed method is also able to provide a probability-based explanation for conflicts among the comparison results provided by some existing methods using a proper ranking order, which ensures that ties of alternatives can be broken.     

A novel two-phase group decision making approach for construction project selection in a fuzzy environment

This paper considers a construction project problem under multiple criteria in a fuzzy environment and proposes a new two-phase group decision making (GDM) approach. This approach integrates a modified analytic network process (ANP) and an improved compromise ranking method, known as VIKOR. To take uncertainty and risk into account, a new decision making approach is presented with multiple fuzzy information by a group of experts, and a risk attitude for each expert is incorporated that can be expressed linguistically. First, a modified fuzzy ANP method is introduced to address the problem of dependence as well as feedback among conflicting criteria and to determine their relative importance. Then, a fuzzy VIKOR method is extended to rank potential projects on the basis of their overall performance. An illustrative example from the literature is provided for the construction project problem to demonstrate the effectiveness and feasibility of the proposed approach. The computational results show that the proposed two-phase GDM approach is suitable to cope with imprecision and subjectivity for the complicated decision making problem. Finally, the associated results of the proposed approach with risk attitudes and without risk attitudes are compared with the results reported by Cheng and Li [1], and the merits are highlighted.     

A chi-square method for obtaining a priority vector from multiplicative and fuzzy preference relations

Decision makers (DMs)’ preferences on decision alternatives are often characterized by multiplicative or fuzzy preference relations. This paper proposes a chi-square method (CSM) for obtaining a priority vector from multiplicative and fuzzy preference relations. The proposed CSM can be used to obtain a priority vector from either a multiplicative preference relation (i.e. a pairwise comparison matrix) or a fuzzy preference relation or a group of multiplicative preference relations or a group of fuzzy preference relations or their mixtures. Theorems and algorithm about the CSM are developed. Three numerical examples are examined to illustrate the applications of the CSM and its advantages.     

A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment

The purpose of this paper is to design a new extension of the ELECTRE, known as the elimination and choice translating reality method, for multi-criteria group decision-making problems based on intuitionistic fuzzy sets. This method is widely utilized when a set of alternatives should be identified and evaluated with respect to a set of conflicting criteria by reflecting decision makers’ (DMs’) preferences. However, handling the exact data and numerical measure is difficult to be precisely focused because the DMs’ judgments are often vague in real-life decision problems and applications. A more realistic and practical approach can be to use linguistic variables expressed in intuitionistic fuzzy numbers instead of numerical data to model DMs’ judgments and to describe the inputs in the ELECTRE method. The proposed intuitionsitic fuzzy ELECTRE utilizes the truth-membership function and non-truth-membership function to indicate the degrees of satisfiability and non-satisfiability of each alternative with respect to each criterion and the relative importance of each criterion, respectively. Then, a new discordance intuitionistic index is introduced, which is extended from the concept of the fuzzy distance measure. Outranking relations are defined by pairwise comparisons and a decision graph is depicted to determine which alternative is preferable, incomparable or indifferent in the intuitionistic fuzzy environment. Finally, a comprehensive sensitivity analysis is employed to further study regarding the impact of threshold values on the final evaluation, and a comparative analysis is demonstrated with an application example in flexible manufacturing systems between the proposed ELECTRE method and the existing intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method.