Group decision making with interval linguistic hesitant fuzzy preference relations.

Highlights • Interval linguistic hesitant fuzzy preference relations are presented. • An additive consistency concept is defined. • Models for judging consistency and determining missing values are constructed. • Two equivalent methods for ranking objects are provided; • An additive consistency and consensus-based algorithm is developed. Abstract This paper introduces a new type of fuzzy sets called interval linguistic hesitant fuzzy sets (ILHFSs), which can address the qualitatively uncertain preferences of decision makers as well as reflect their hesitancy. Such fuzzy sets endow the decision makers with more flexibility: (i) several interval linguistic variables are allowed to represent a judgment, and (ii) the number of interval linguistic variables can be different for different preferences. To show the application of ILHFSs, a group decision-making method with interval linguistic hesitant fuzzy preference relations (ILHFPRs) is introduced. To achieve this goal, an additive consistency concept for ILHFPRs is presented to derive the rational rankings. Following this concept, a programming model for judging the additive consistency of ILHFPRs is constructed. Then, an additive consistency-based programming model is established to ascertain missing values in incomplete ILHFPRs. Subsequently, an approach for calculating the interval linguistic hesitant fuzzy priority weight vector from incomplete and inconsistent ILHFPRs is presented. To measure the agreement degree of the decision makers' judgements, a consensus index is offered, and a method for determining the weights of the decision makers is proposed. Finally, a numerical example about evaluating commodity sales platforms in China is chosen to illustrate the utilization of the new method. The results extend and perfect the application scope of preference relations, which offer the decision makers more choices to express their judgments. [ABSTRACT FROM AUTHOR]