Abstract
In each hesitant fuzzy linguistic preference relation, experts may express their opinions through comparison linguistic information combined with a discrete fuzzy number. In this paper, a hesitant fuzzy linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is proposed, which enriches the flexibility of group decision-making. First, some main concepts related to discrete fuzzy numbers and an aggregation function of individual subjective linguistic preference relations are introduced. Then, a consistency measure is presented to check and improve the consistency in a given matrix. Further, in order to achieve the predefined degree of consensus and to arrive at the final result, a consensus-reaching process based on the interactive feedback mechanism is defined. Meanwhile, a revised formula is introduced to calculate the consistency and the degree of consensus in a preference relation matrix. Besides, an illustrative example and comparative analysis are conducted through the proposed calculation process and the optimization algorithm. Finally, the analysis on the threshold values is made to help the decision-maker determine critical consensus level. The proposed method can address both consistency and consensus, and the results confirmed the effectiveness of the proposed method and its potential use in the qualitative decision-making problems.
Highlights
With the development of science and information technology, many decision problems in social and economic life become more and more complicated
We aggregate the hesitant fuzzy linguistic preference relations (HFLPRs) in each subgroup, which can be obtained from Algorithm 2
With the help of the HFLPR model based on the discrete fuzzy number, decision-makers have more flexibility when expressing their preference in pairwise comparisons
Summary
With the development of science and information technology, many decision problems in social and economic life become more and more complicated. Various linguistic models have been proposed, such as the 2-tuple linguistic model [2, 3], the type-2-fuzzy-set-based model [4, 5], the granular method [6, 7], and symbolic linguistic models [8, 9]. These models have been popular; they have proved to be inadequate when facing more complex subjective information. Rodriguez et al [10] propose the concept of the hesitant fuzzy linguistic term set (HFLTS) which increases the flexibility and richness of linguistic elicitation in hesitant situations under qualitative settings
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