An inconsistency index of interval additive reciprocal matrices with application to group decision making

Abstract

Inconsistency measure and aggregation of decision information are two important issues in group decision making. In this study, interval additive reciprocal matrices are used to express the opinions of decision makers within the framework of fuzzy analytic hierarchy process (FAHP). Some existing consistency indexes of interval additive reciprocal matrices are reviewed and the existing shortcomings are shown. By considering the randomness experienced by decision makers in comparing alternatives, a novel inconsistency index named as the weak-consistency index is introduced. Some properties of the proposed weak-consistency index are studied in detail. Consistent additive reciprocal matrices are most useful for the ideal cases, while interval-valued matrices are their softened versions. In order to aggregate individual interval additive reciprocal matrices, a new aggregation operator based on the novel consistency index is proposed. The properties of the collective interval additive reciprocal matrix are further addressed. Numerical results are reported to illustrate the proposed weak-consistency index and group decision making model. Comparisons with some existing consistency indexes and group decision making models reveal that the known shortcomings are overcome.