Consistency- and Consensus-Based Group Decision-Making Method With Incomplete Probabilistic Linguistic Preference Relations

The use of incomplete probabilistic linguistic term sets (InPLTSs) can enrich the flexibility of qualitative decision-making information expression, especially in decision-making situations with high time pressure and insufficient knowledge. In this article, we develop a method for group decision-ma...

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Published in:	IEEE transactions on fuzzy systems Vol. 29; no. 9; pp. 2565 - 2579
Main Authors:	Liu, Peide, Wang, Peng, Pedrycz, Witold
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.09.2021 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Consensus Consistency Decision making expected multiplicative consistency group decision-making (GDM) incomplete probabilistic linguistic preference relation (InPLPRs) Indexes induced ordered weighted geometric operator Linguistics Mathematical analysis Mathematical model Mathematical programming mathematical programming model Optimization Probabilistic logic Reliability
ISSN:	1063-6706, 1941-0034
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Abstract	The use of incomplete probabilistic linguistic term sets (InPLTSs) can enrich the flexibility of qualitative decision-making information expression, especially in decision-making situations with high time pressure and insufficient knowledge. In this article, we develop a method for group decision-making (GDM) with incomplete probabilistic linguistic preference relations (InPLPRs), considering consistency and consensus simultaneously. First, to fully explore the ability of InPLTSs to express uncertain information, InPLTSs are specifically classified. Then, an expected multiplicative consistency of InPLPRs is introduced, which is conducive to estimating the missing information more accurately and effectively. Subsequently, considering the consensus of GDM problems, a consensus index, which considers the principle of majority and minority, is developed to measure the agreement degree among multiple individuals. Because individual InPLPRs may not all meet acceptable consistency after reaching consensus, a consistency- and consensus-improving mathematical programming model considering information distortion is presented. Then, to aggregate all individual preference relations into a collective one, a reliability-induced ordered weighted geometric operator is introduced, whose induced variable reliability is determined by the confidence degree and consistency index of individual preference relations. Furthermore, a multiphase algorithm with InPLPRs is developed to solve GDM problems. Finally, a numerical example of fire emergency decisions is presented to illustrate the applicability of the proposed method, and a detailed validity test and comparative analysis are conducted to highlight the advantages of the proposed method.
AbstractList	The use of incomplete probabilistic linguistic term sets (InPLTSs) can enrich the flexibility of qualitative decision-making information expression, especially in decision-making situations with high time pressure and insufficient knowledge. In this article, we develop a method for group decision-making (GDM) with incomplete probabilistic linguistic preference relations (InPLPRs), considering consistency and consensus simultaneously. First, to fully explore the ability of InPLTSs to express uncertain information, InPLTSs are specifically classified. Then, an expected multiplicative consistency of InPLPRs is introduced, which is conducive to estimating the missing information more accurately and effectively. Subsequently, considering the consensus of GDM problems, a consensus index, which considers the principle of majority and minority, is developed to measure the agreement degree among multiple individuals. Because individual InPLPRs may not all meet acceptable consistency after reaching consensus, a consistency- and consensus-improving mathematical programming model considering information distortion is presented. Then, to aggregate all individual preference relations into a collective one, a reliability-induced ordered weighted geometric operator is introduced, whose induced variable reliability is determined by the confidence degree and consistency index of individual preference relations. Furthermore, a multiphase algorithm with InPLPRs is developed to solve GDM problems. Finally, a numerical example of fire emergency decisions is presented to illustrate the applicability of the proposed method, and a detailed validity test and comparative analysis are conducted to highlight the advantages of the proposed method.
Author	Pedrycz, Witold Wang, Peng Liu, Peide
Author_xml	– sequence: 1 givenname: Peide orcidid: 0000-0001-5048-8145 surname: Liu fullname: Liu, Peide email: Peide.liu@gmail.com organization: School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, China – sequence: 2 givenname: Peng orcidid: 0000-0003-1880-5440 surname: Wang fullname: Wang, Peng email: wangpeng@mail.sdufe.edu.cn organization: School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, China – sequence: 3 givenname: Witold orcidid: 0000-0002-9335-9930 surname: Pedrycz fullname: Pedrycz, Witold email: wpedrycz@ualberta.ca organization: Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada
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SubjectTerms	Algorithms Consensus Consistency Decision making expected multiplicative consistency group decision-making (GDM) incomplete probabilistic linguistic preference relation (InPLPRs) Indexes induced ordered weighted geometric operator Linguistics Mathematical analysis Mathematical model Mathematical programming mathematical programming model Optimization Probabilistic logic Reliability
Title	Consistency- and Consensus-Based Group Decision-Making Method With Incomplete Probabilistic Linguistic Preference Relations
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