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Multi-criteria analysis: a manual

Studies in Fuzziness and Soft Computing

Aggregation of fuzzy information is a new branch of Atanassov's intuitionistic fuzzy set (AIFS) theory, which has attracted significant interest from researchers in recent years. In this paper, we treat the intuitionistic fuzzy aggregation operators with the help of Einstein operations. We first introduce some new operations of AIFSs, such as Einstein sum, Einstein product, and Einstein scalar multiplication. Then, we develop some intuitionistic fuzzy aggregation operators, such as the intuitionistic fuzzy Einstein weighted averaging operator and the intuitionistic fuzzy Einstein ordered weighted averaging operator, which extend the weighted averaging operator and the ordered weighted averaging operator to aggregate Atanassov's intuitionistic fuzzy values, respectively. We further establish various properties of these operators and analyze the relations between these operators and the existing intuitionistic fuzzy aggregation operators. Moreover, we give some numerical examples to illustrate the developed aggregation operators. Finally, we apply the intuitionistic fuzzy Einstein weighted averaging operator to multiple attribute decision making with intuitionistic fuzzy information.

Intuitionistic Fuzzy Information Aggregation Using Einstein Operations

Evaluation of sustainable supply chain risk management using an integrated fuzzy TOPSIS- CRITIC approach

In the real-world problems, we are likely confronted with some alternatives that eed to be evaluated with respect to multiple conflicting criteria. Multi-criteria ecision-making (MCDM) refers to making decisions in such a situation. There are any methods and techniques available for solving MCDM problems. The evaluation ased on distance from average solution (EDAS) method is an efficient multi-criteria ecision-making method. Because the uncertainty is usually an inevitable part of he MCDM problems, fuzzy MCDM methods can be very useful for dealing with the eal-world decision-making problems. In this study, we extend the EDAS method o handle the MCDM problems in the fuzzy environment. A case study of supplier election is used to show the procedure of the proposed method and applicability of t. Also, we perform a sensitivity analysis by using simulated weights for criteria to xamine the stability and validity of the results of the proposed method. The results f this study show that the extended fuzzy EDAS method is efficient and has good tability for solving MCDM problems.

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Extended EDAS Method for Fuzzy Multi-criteria Decision-making: An Application to Supplier Selection

Since its inception in 1965, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found, for example, in artificial intelligence, computer science, medicine, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, and robotics. Mathematical developments have advanced to a very high standard and are still forthcoming to day. In this review, the basic mathematical framework of fuzzy set theory will be described, as well as the most important applications of this theory to other theories and techniques. Since 1992 fuzzy set theory, the theory of neural nets and the area of evolutionary programming have become known under the name of ‘computational intelligence’ or ‘soft computing’. The relationship between these areas has naturally become particularly close. In this review, however, we will focus primarily on fuzzy set theory. Applications of fuzzy set theory to real problems are abound. Some references will be given. To describe even a part of them would certainly exceed the scope of this review. Copyright © 2010 John Wiley & Sons, Inc.

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H.-J. Zimmermann

Papers

Fuzzy set theory