Overview of Hesitant Linguistic Preference Relations for Representing Cognitive Complex Information: Where We Stand and What Is Next

Hesitant fuzzy linguistic preference relations (HFLPRs) can be used to represent cognitive complex information in a situation in which people hesitate among several possible linguistic terms for the preference degrees of pairwise comparisons over alternatives. HFLPRs have attracted growing attention owing to their efficiency in dealing with increasingly cognitive complex decision-making problems. Due to the emergence of various studies on HFLPRs, it is necessary to make a comprehensive overview of the theory of HFLPRs and their applications. In this paper, we first review different types of linguistic representation models, including the hesitant fuzzy linguistic term set, hesitant 2-tuple fuzzy linguistic term set, probabilistic linguistic term set, and double-hierarchy hesitant fuzzy linguistic term set. The reasons for proposing these models are discussed in detail. Then, the hesitant linguistic preference relation models associated with the aforementioned linguistic representation models are addressed one by one. An overview is then provided in terms of their consistency properties, inconsistency-repairing processes, priority vector derivation methods, consensus measures, applications, and future directions. Basically, we try to answer to two questions: where we stand and what is next? The preference relations and consistency properties are discussed in detail. The inconsistency-repairing processes for those preference relations that are not acceptably consistent are summarized. Methods to derive the priorities from the HFLPRs and their extensions are further reviewed. The consensus measures and consensus-reaching processes for group decision making with HFLPRs and their extensions are discussed. The applications of HFLPRs and their extensions in different areas are highlighted. The future research directions regarding HFLPRs are given from different perspectives. This paper provides a comprehensive overview of the development and research status of HFLPRs for representing cognitive complex information. It can help researchers to identify the frontier of cognitive complex preference relation theory in the realm of decision analysis. Since the research on HFLPRs is still at its initial stage, this review has guiding significance for the later stage of study on this topic. Furthermore, this paper can engage further research or extend the research interests of scholars.

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