Applications of the extent analysis method on fuzzy AHP. (English) Zbl 0926.91008

Chang, Dayong

Eur. J. Oper. Res. 95, No. 3, 649-655 (1996).

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.

Keywords:

fuzzy AHP; triangular fuzzy numbers; extent analysis; comparison of fuzzy numbers

References:

[1]	Chang, D.-Y., (Extent Analysis and Synthetic Decision, Optimization Techniques and Applications, Volume 1 (1992), World Scientific: World Scientific Singapore), 352
[2]	Dubois, D.; Prade, H., Decision-making under fuzziness, (Gupta, M. M.; Pagade, R. K.; Yager, R. R., Advances in Fuzzy Set Theory and Applications (1979), North-Holland: North-Holland Amsterdam), 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: McGraw-Hill New York · Zbl 1176.90315