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Preference relations are generally used to cope with multi-attribute group decision making (MAGDM), which express the experts’ preference information through pairwise comparisons. To make decision rationale, one of the vital issues related to preference relations is how to make the preference information logical. The logicality level of preference information is usually described by the consistency of preference relation. Thus, developing methods to check and improve the consistency of preference relations is necessary and significant. In this paper, we give a general description of multiplicative transitivity property for fuzzy preference relation (FPR). Then, based on the new multiplicative transitivity function which can repair some counterintuitive cases of the traditional one, we define the stably multiplicative consistency, the stably mean multiplicative consistency (SMMC), and the acceptable SMMC for interval-valued hesitant FPR (IVHFPR). Additionally, several algorithms are developed to improve the SMMC of IVHFPR. A practical example concerning the respiratory illness diagnosis is given to demonstrate the applicability of IVHFPR with SMMC.

The Stably Multiplicative Consistency of Fuzzy Preference Relation and Interval-Valued Hesitant Fuzzy Preference Relation