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Extensions of the TOPSIS for group decision-making under fuzzy environment. (English) Zbl 0963.91030
Summary: The aim of this paper is to extend the TOPSIS to the fuzzy environment. Owing to vague concepts frequently represented in decision data, the crisp value are inadequate to model real-life situations. In this paper, the rating of each alternative and the weight of each criterion are described by linguistic terms which can be expressed in triangular fuzzy numbers. Then, a vertex method is proposed to calculate the distance between two triangular fuzzy numbers. According to the concept of the TOPSIS, a closeness coefficient is defined to determine the ranking order of all alternatives by calculating the distances to both the fuzzy positive-ideal solution and fuzzy negative-ideal solution simultaneously. Finally, an example is shovm to highlight the procedure of the proposed method at the end of this paper.

91B06Decision theory
03E72Fuzzy set theory
Full Text: DOI
[1] Bellman, R. E.; Zadeh, L. A.: Decision-making in a fuzzy environment. Management sci. 17, No. 4, 141-164 (1970) · Zbl 0224.90032
[2] Buckley, J. J.: Fuzzy hierarchical analysis. Fuzzy sets and systems 17, 233-247 (1985) · Zbl 0602.90002
[3] C.T. Chen, A new decision approach for solving plant location selection problem, Int. J. Prod. Econom. (1997), submitted.
[4] Delgado, M.; Verdegay, J. L.; Vila, M. A.: Linguistic decision-making models. Int. J. Intelligent system 7, 479-492 (1992) · Zbl 0756.90001
[5] Dyer, J. S.; Fishburn, P. C.; Steuer, R. E.; Wallenius, J.; Zionts, S.: Multiple criteria decision making, multiattribute utility theory: the next ten years. Management sci. 38, No. 5, 645-654 (1992) · Zbl 0825.90620
[6] Herrera, F.; Herrera-Viedma, E.; Verdegay, J. L.: A model of consensus in group decision making under linguistic assessments. Fuzzy sets and systems 78, 73-87 (1996) · Zbl 0870.90007
[7] Hsu, H. M.; Chen, C. T.: Fuzzy hierarchical weight analysis model for multicriteria decision problem. J. chinese inst. Industrial eng. 11, No. 3, 129-136 (1994)
[8] Hsu, H. M.; Chen, C. T.: Aggregation of fuzzy opinions under group decision making. Fuzzy sets and systems 79, 279-285 (1996)
[9] Hsu, H. M.; Chen, C. T.: Fuzzy credibility relation method for multiple criteria decision-making problems. Inform. sci. 96, 79-91 (1997) · Zbl 0917.90210
[10] Hwang, C. L.; Yoon, K.: Multiple attributes decision making methods and applications. (1981) · Zbl 0453.90002
[11] Kaufmann, A.; Gupta, M. M.: Introduction to fuzzy arithmetic: theory and applications. (1985) · Zbl 0588.94023
[12] D.S. Negi, Fuzzy analysis and optimization, Ph.D. Thesis, Department of Industrial Engineering, Kansas State University, 1989.
[13] J. Teghem, Jr., C. Delhaye, P.L. Kunsch, An interactive decision support system (IDSS) for multicriteria decision aid, Math. Comput. Modeling 12:10/11 (1989) 1311--1320.
[14] Zadeh, L. A.: Fuzzy sets. Inform. and control 8, 338-353 (1965) · Zbl 0139.24606
[15] L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Inform. Sci. 8 (1975) 199--249(I), 301--357(II). · Zbl 0397.68071
[16] Zimmermann, H. J.: Fuzzy set theory and its applications. (1991) · Zbl 0719.04002
[17] Zwick, R.; Carlstein, E.; Budescu, D. V.: Measures of similarity among fuzzy concepts: A comparative analysis. Int. J. Approximate reasoning 1, 221-242 (1987)