Automatic Iterative Algorithm with Local Revised Strategies to Improve the Consistency of Hesitant Fuzzy Linguistic Preference Relations

Abstract

Hesitant fuzzy linguistic term set (HFLTS) provides a new and useful tool for expressing decision makers (DMs)’s qualitative views and ideas since it allows DMs to hesitate about several possible linguistic terms. Consistency is the fundamental research in decision-making process under hesitant fuzzy linguistic preference relations (HFLPRs) decision-making environment and the distance measure is utilized as a technology to measure the consistency level of HFLPRs. However, traditional distance measures were developed based on an assumption that the number of linguistic terms in the corresponding HFLTSs is the same. Some optimization models to improve consistency level of HFLPRs did not give DMs strong sense of participation and a sense of respect for their preferences. To solve the above issues, in this paper, a new distance measure of HFLTSs is defined, and some desirable properties are discussed. After that, in line with the distance measure, we propose a consistency index of HFLPRs by computing the deviation between the normalized hesitant fuzzy linguistic preference relation (N-HFLPR) and its expected hesitant fuzzy linguistic preference relation (E-HFLPR). Furthermore, for unacceptable consistent HFLPRs, some local revised strategies provided by an automatic iterative algorithm are used to modify original HFLPRs until it satisfies acceptable consistency. Finally, some comparisons between the existing methods and our proposed approaches are to demonstrate the feasibility of the proposed approaches by utilizing several illustrative examples.