Maximum Lower Bound Estimation of Fuzzy Priority Weights from a Crisp Comparison Matrix

In Interval AHP, our uncertain judgments are denoted as interval weights by assuming a comparison as a ratio of the real values in the corresponding interval weights. Based on the same concept as Interval AHP, this study denotes uncertain judgments as fuzzy weights which are the extensions of the interval weights. In order to obtain the interval weight for estimating a fuzzy weight, Interval AHP is modified by focusing on the lower bounds of the interval weights similarly to the viewpoint of belief function in evidence theory. It is reasonable to maximize the lower bound since it represents the weight surely assigned to one of the alternatives. The sum of the lower bounds of all alternatives is considered as a membership value and then the fuzzy weight is estimated. The more consistent comparisons are given as a result of the higher-level sets of fuzzy weights in a decision maker’s mind.