Fuzzy Linear Programming Method for Deriving Priorities in the Fuzzy Analytic Hierarchy Process

Authors

1 School of Mathematics and Computer Sciences, Damghan University, P.O. Box 36715{364, Damghan, Iran.

2 Department of Applied Mathematics, Payame Noor University, Tehran, Iran.

Abstract

There are various methods for obtaining the preference vector of pair-wise comparison matrix factors. These methods can be employed when the elements of pair-wise comparison matrix are crisp while they are inefficient for fuzzy elements of pair-wise comparison matrix. In this paper, a method is proposed by which the preference vector of pair-wise comparison matrix elements can be obtained even if these elements are fuzzy. First we describe the method for the case of crisp pair-wise comparison matrix and then extend it to the case in which the pair-wise comparison matrix elements are fuzzy, finally, conclusion will be provided.

Keywords


1. A. Chu, R. Kalaba, and K. Springam, A comparison of two methods for determining the weights of belonging to fuzzy sets, J. Opt. Theory and Appl., 27, 531-541 (1979).

2. G. Crawford, and C. Williams, A note on the analysis of subjective judgement matrices, J. Math. Psych., 29, 387-405 (1985).

3. L. Mikhailov, A fuzzy programming method for deriving priorities in the analytic hierarchy process, Journal of the Operational Research Society, 51(3), 341-349 (2000).

4. T.L. Saaty, Axiomatic foundations of the analytic hierarchy process, Management Science, 32, 841-855 (1986).