Managing incomplete preferences and consistency improvement in hesitant fuzzy linguistic preference relations with applications in group decision making

Abstract

Incomplete hesitant fuzzy linguistic preference relations (IHFLPRs) are useful in decision making which combine advantages of hesitant fuzzy linguistic term sets and incomplete fuzzy preference relations. The existing researches on IHFLPRs pay little attention to missing elements, and the consistency improvement processes change original information greatly. Inspired by the worst and the best consistency indexes of hesitant fuzzy linguistic preference relations, this paper constructs several optimization models to calculate the missing elements of IHFLPRs. As a result, a complete hesitant fuzzy linguistic preference relation is obtained. Furthermore, an algorithm is introduced to improve the additive consistency of the hesitant fuzzy linguistic preference relation to an acceptable level. Finally a group decision making model based on IHFLPRs is introduced and an example is presented.