Fuzzy relational equations in analytical hierarchy process

This article introduces a procedure for solving an analytic hierarchy process (AHP) problem under fuzzy environment. In this method the attributes are considered as inputs and the outputs to the AHP hierarchy levels. The concept of fuzzy relational equation has been used to model the AHP problem and to articulate the inherent input-output relations among the attributes. This model of AHP gives the solutions corresponding to the various combination operators of the fuzzy relations. This leads to the ranking of the attributes (at each hierarchy level) in the AHP problem.