Preference programming approach for solving intuitionistic fuzzy AHP

Abstract

The aim of this paper is to present a novel approach for deriving weights of the decision criteria or alternatives in multi-attribute decision making (MADM) under intuitionistic fuzzy (IF) environment. In order to tackle the uncertainty and imprecision of the practical situations, decision makers’ pair-wise comparison judgments are represented by intuitionistic fuzzy numbers (IFNs). The assessment of the priorities from these IF pair-wise comparison judgments is formulated as an IF decision making problem where goals are described in intuitionistic fuzzy sense. Then by resolving hesitancy via a parameter, IF goals are transformed into fuzzy goals. Finally, aggregation of fuzzy goals and application of the max - min principle lead us to a nonlinear optimization problem whose solution gives the desired crisp priorities. Unlike the other prioritization methods, the proposed approach generates crisp priorities from IF pair-wise comparison matrix. Thus, the proposed approach eliminates the additional requirement of arithmetic operations of IFNs for aggregation and also avoids the ranking process of IFNs to compare the final IF priorities, which may produce ambiguous results. Finally, examples are given to illustrate the proposed process with an application to MADM problem.

Keywords

• AHP
• Intuitionistic fuzzy numbers
• Decision making