Deriving fuzzy weights of criteria from inconsistent fuzzy comparison matrices by using goal programming method

Article type: Research Article

Authors: Izadikhah, Mohammad

Affiliations: Department of Mathematics, Islamic Azad University, Arak-Branch, Arak, Iran

Note: [] Corresponding author. Mohammad Izadikhah, Department of Mathematics, Islamic Azad University, Arak-Branch, Arak, Iran. Tel.: +98 861 3663041; P.O. Box 38135/567; E-mail: m-izadikhah@iau-arak.ac.ir; m_izadikhah@yahoo.com (M. Izadikhah).

Abstract: In this paper, deriving the fuzzy weights of criteria from the fuzzy pair-wise comparison matrix with triangular fuzzy elements is investigated. In the proposed method we first use the ranking function to convert the triangular fuzzy data into crisp one. Then by using the goal programming method we derive the fuzzy weights of criteria. We propose two new methods, and it is shown that these methods are able to derive the weights of criteria in the case of crisp elements. We compare the results of the presented method with some of the existing methods. The approach is illustrated by some numerical examples.

Keywords: Triangular fuzzy number, Fuzzy pair-wise comparison matrix, Goal programming, Fuzzy weight, Ranking function

DOI: 10.3233/IFS-2012-0615

Journal: Journal of Intelligent & Fuzzy Systems, vol. 25, no. 1, pp. 69-80, 2013