An Additive-Consistency- and Consensus-Based Approach for Uncertain Group Decision Making With Linguistic Preference Relations

Jing-Feng Tian · Zhiming Zhang · Ming-Hu Ha

47 citations0/0 files storedIEEE Transactions on Fuzzy Systems

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Multi-Criteria Decision Making Game Theory and Voting Systems Optimization and Mathematical Programming

Abstract

Linguistic preference relations (LPRs) can indicate the decision makers (DMs)' qualitative pairwise judgments regarding a set of alternatives in uncertain multicriteria decision-making problems. This paper examines several goal programming models for managing the additive consistency and consensus of LPRs and then develops an additive-consistency- and consensus-based method for group decision making (GDM) with LPRs. First, this paper offers a consistency index to quantify the consistency level for LPRs and define acceptable consistent LPRs. For an LPR that is unacceptably additive consistent, several additive-consistency-based programming models are developed to address the inconsistency and to establish an acceptably consistent LPR. Then, an additive-consistency-based procedure to generate the priority weight vector from the LPR is offered. An additive-consistency-based algorithm for decision making with an LPR is presented. Subsequently, considering the consensus in GDM, a consensus index is proposed for gauging the agreement degree among individual LPRs. Regarding individual LPRs that do not exhibit acceptably additive consistency or acceptable consensus, several goal programming models to derive new LPRs with acceptable consistency and consensus are provided. Afterward, the DMs' weights are determined objectively, and individual LPRs are integrated into a collective LPR. An additive-consistency- and consensus-based GDM method with a group of LPRs is developed. Finally, two practical numerical examples are offered, and a comparative analysis is presented.

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References

1994Analytical hierarchy process 2000Linguistic decision analysis: steps for solving decision problems under linguistic information 1978Decision-making with a fuzzy preference relation 1984Fuzzy preference orderings in group decision making 1996A model of consensus in group decision making under linguistic assessments 2003A method based on linguistic aggregation operators for group decision making with linguistic preference relations*1 2004Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment 2004Deviation measures of linguistic preference relations in group decision making

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2019Group decision making based on multiplicative consistency and consensus of fuzzy linguistic preference relations 2021Multiplicative consistency analysis of linguistic preference relation with self‐confidence level and self‐doubting level and its application in a group decision making 2023Large-scale group consensus hybrid strategies with three-dimensional clustering optimisation based on normal cloud models 2019Optimizing consistency and consensus improvement process for hesitant fuzzy linguistic preference relations and the application in group decision making

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