Interval linguistic fuzzy decision making in perspective of preference relations

Consistency analysis is a crucial topic for preference relations. This paper studies the consistency of interval linguistic fuzzy preference relations (ILFPRs) using the constrained interval linguistic arithmetic and introduces a new consistency definition. Then, several properties of this definition are researched. Meanwhile, the connection between this concept and a previous one is discussed. Following this concept, programming models for judging the consistency and for deriving consistent ILFPRs are constructed, respectively. Considering the case that incomplete ILFPRs may be obtained, a programming model for obtaining missing judgments following the consistency discussion is built. Afterwards, the consensus for group decision making (GDM) is studied and a model for adjusting individual ILFPRs to reach the consensus threshold is established. Consequently, an interactive procedure for GDM with ILFPRs is presented. A practical problem is provided to illustrate the utilization of the new algorithm and comparative discussion is offered

An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and Fusion: Taxonomy and future directions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The reciprocal preference relation (RPR) is a powerful tool to represent decision makers’ preferences in decision making problems. In recent years, various types of RPRs have been reported and investigated, some of them being the ‘classical’ RPRs, interval-valued RPRs and hesitant RPRs. Additive consistency is one of the most commonly used property to measure the consistency of RPRs, with many methods developed to manage additive consistency of RPRs. To provide a clear perspective on additive consistency issues of RPRs, this paper reviews the consistency measurements of the different types of RPRs. Then, consistency-driven decision making and information fusion methods are also reviewed and classified into four main types: consistency improving methods; consistency-based methods to manage incomplete RPRs; consistency control in consensus decision making methods; and consistency-driven linguistic decision making methods. Finally, with respect to insights gained from prior researches, further directions for the research are proposed