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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, $V\left({M}_{1}\ge {M}_{2}\right)=1$ iff ${m}_{1}\ge {m}_{2}$, $V\left({M}_{2}\ge {M}_{1}\right)=\text{hgt}\left({M}_{1}\cap {M}_{2}\right)={\mu }_{{M}_{1}}\left(d\right)$, the vectors of weight with respect to each element under a certain criterion are represented by $d\left({A}_{i}\right)=minV\left({S}_{i}\ge {S}_{k}\right)$, $k=1,2,\cdots ,n$; $k\ne i$. This decision process is demonstrated by an example.

##### MSC:
 91B06 Decision theory 03E72 Fuzzy set theory