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Fuzzy hierarchical analysis. (English) Zbl 0602.90002
This paper extends hierarchical analysis to the case where the participants are allowed to employ fuzzy ratios in place of exact ratios. If a person considers alternative A more important than alternative B, then the ratio used might be approximately 3 to 1, or between 2 to 1, and 4 to 1, or at most 5 to 1. The pairwise comparison of the issues and the criteria in the hierarchy produce fuzzy positive reciprocal matrices. The geometric mean method is employed to calculate the fuzzy weights for each fuzzy matrix, and these are combined in the usual manner to determine the final fuzzy weights for the alternatives. The final fuzzy weights are used to rank the alternatives from highest to lowest. The highest ranking contains all the undominated issues. The procedures easily extends to the situations where many experts are utilized in the ranking process, or to the case of missing data. Two examples are presented showing the final fuzzy weights and the final ranking.

91B06Decision theory
90B50Management decision making, including multiple objectives
03E72Fuzzy set theory
Full Text: DOI
[1] Aczel, J.; Saaty, T. L.: Procedures for synthesizing ratio judgments. J. math. Psychology 27, 93-102 (1983) · Zbl 0522.92028
[2] Buckley, J. J.: Ranking alternatives using fuzzy numbers. Fuzzy sets and systems 15, 21-31 (1985) · Zbl 0567.90057
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[8] Saaty, T. L.: Exploring the interface between hierarchies, multiple objectives and fuzzy sets. Fuzzy sets and systems 1, 57-68 (1978) · Zbl 0378.94001
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[10] Saaty, T. L.; Vargas, L. G.: Inconsistency and rank preservation. J. math. Psychology 28, 205-214 (1984) · Zbl 0557.62093
[11] Uppuluri, V. R. R.: Logarithmic least-squares approach to saaty’s decision problems. Mathematics and statistics research department progress report, 19-21 (1978)
[12] Uppuluri, V. R. R.: Expert opinion and ranking methods. Oak ridge national laboratory, NRC FIN no. B044 (1983)
[13] Van Laarhoven, P. J. M.; Pedrycz, W.: A fuzzy extension of saaty’s priority theory. Fuzzy sets and systems 11, 229-241 (1983) · Zbl 0528.90054
[14] Wagenknecht, M.; Hartmann, K.: On fuzzy rank-ordering in polyoptimization. Fuzzy sets and systems 11, 253-264 (1983) · Zbl 0528.90079