Probabilistic Linguistic Preference Relation-Based Decision Framework for Multi-Attribute Group Decision Making

Abstract

With trending competition in decision-making process, linguistic decision-making is gaining attractive attention. Previous studies on linguistic decision-making have neglected the occurring probability (relative importance) of each linguistic term which causes unreasonable ranking of objects. Further, decision-makers' (DMs) often face difficulties in providing apt preference information for evaluation. Motivated by these challenges, in this paper, we set our proposal on probabilistic linguistic preference relation (PLPR)-based decision framework. The framework consists of two phases viz., (a) missing value entry phase and (b) ranking phase. In phase (a), the missing values of PLPR are filled using a newly proposed automatic procedure and consistency of PLPR is ensured using a consistency check and repair mechanism. Following this, in phase (b), objects are ranked using newly proposed analytic hierarchy process (AHP) method under PLPR context. The practicality of the proposal is validated by using two numerical examples viz., green supplier selection problem for healthcare and the automobile industry. Finally, the strength and weakness of the proposal are discussed by comparing with similar methods. Symmetry 2019, 11, 2 2 of 18 weighted geometric aggregation operator for a linguistic domain. Further, He et al. [8] put forward a new entropy measure for linguistic-based group decision-making.Though linguistic decision-making is an attractive concept, DMs still face difficulties in rationally rating the objects. The main reason for this difficulty is the cognitive behavior of the human mind, which encourages pair-wise comparative analysis rather than a standalone rating [9]. Motivated by the power of pair-wise comparison and linguistic term set (LTS), Herrera et al. [10,11] proposed the linguistic preference relation (LPR) concept for group decision-making and investigated some choice functions for the same. Following this, Xu [12] put forward some deviation measures for decision-making process under LPR context. Recently, Molinera et al. [13] developed new fuzzy ontologies for linguistic preference information and applied the same for decision-making. Wang and Xu [14] put forward an interactive algorithm for filling the missing LPR values using consistency measures and repaired the consistency of the same using the repairing mechanism.Inspired by the power of linguistic information and its substantial use in decision-making, Rodriguez [15] proposed the hesitant fuzzy linguistic term set (HFLTS) which is an extension to LTS under hesitant fuzzy environment [16]. The HFLTS allowed DMs to give different choices of preference for the same instance, which managed uncertainty to some extent. Motivated by the power of HFLTS, Zhu and Xu [17] put forward the hesitant fuzzy linguistic preference relation (HFLPR), which is an extension to preference relation under HFLTS context. They also investigated some consistency measures for the same. Following this, Wang and Xu [18] presented the concept of extended hesitant fuzzy prefe...

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