Analytic hierarchy process based on fuzzy analysis

Analytic Hierarchical Process(AHP) is proposed to give the priority weight with respect to many items. The priority weights are obtained from the pairwise comparison matrix whose elements are given by a decision maker as crisp values. We extend the crisp pairwise comparisons to fuzzy ones based on uncertainty of human judgement. To give uncertain information as a fuzzy value is more rational than as a crisp value. We assume that the item's weight is a fuzzy value, since the comparisons are based on human intuition so that they must be inconsistent each other. We propose a new AHP, where the item's weight is given as a fuzzy value, in order to deal with inconsistency in the given matrix. The purpose is to obtain fuzzy weights so as to include all the given fuzzy pairwise comparisons, in the similar way to the upper approximation in interval regression analysis.