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Applications of the extent analysis method on fuzzy AHP. (English) Zbl 0926.91008
Summary: A new approach for handling fuzzy AHP is introduced, with the use of triangular fuzzy numbers for pairwise comparison scale of fuzzy AHP, and the use of the extent analysis method for the synthetic extent value $$S_i$$ of the pairwise comparison. By applying the principle of the comparison of fuzzy numbers, that is, $$V(M_1\geq M_2)= 1$$ iff $$m_1\geq m_2$$, $$V(M_2\geq M_1)= \text{hgt}(M_1\cap M_2)= \mu_{M_1}(d)$$, the vectors of weight with respect to each element under a certain criterion are represented by $$d(A_i)= \min V(S_i\geq S_k)$$, $$k= 1,2,\dots, n$$; $$k\neq i$$. This decision process is demonstrated by an example.

##### MSC:
 91B06 Decision theory 03E72 Theory of fuzzy sets, etc.
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##### References:
 [1] Chang, D.-Y., (), 352 [2] Dubois, D.; Prade, H., Decision-making under fuzziness, (), 279-302 [3] van Laarhoven, P.J.M.; Pedrycs, W., A fuzzy extension of Saaty’s priority theory, Fuzzy sets and systems, 11, 229-241, (1983) · Zbl 0528.90054 [4] Saaty, T.L., The analytic hierarchy process, (1980), McGraw-Hill New York · Zbl 1176.90315
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