A Revised Picture Fuzzy Linguistic Aggregation Operator and Its Application to Group Decision-Making
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A Revised Picture Fuzzy Linguistic Aggregation Operator and Its Application to Group Decision-Making Xue-yang Zhang 1,2 & Jing Wang 2 & Jian-qiang Wang 2
&
Jun-hua Hu 2
Received: 28 May 2018 / Accepted: 14 May 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The complexity of decision environments poses challenges for individuals engaged in decision-making proceedings. Picture fuzzy linguistic sets (PFLSs) are an effective tool for depicting the inherent subjective nature of human cognition. Aiming for the promotion of a general theory on PFLSs, we conduct a critical research to identify some limitations of a recent publication in Cognitive Computation [2018, 10(2), 242–259]. This published article is a meaningful and interesting study that initiates the PFLS as well as introduces the corresponding operations and the Archimedean picture fuzzy linguistic weighted arithmetic averaging operator. Unfortunately, we have carefully analyzed these operations and found that they may not be appropriate to all situations within picture fuzzy linguistic environment, which would result in the violation of human cognition. To eliminate this limitation, we explore and suggest novel operational laws and an aggregation operator for PFLSs from a modified version, so as to support further study on picture fuzzy linguistic group decision-making. Furthermore, a comparative and illustrative example is presented to validate the advantages of our modified operations. Towardly, the research outcome will be of significant benefit to promoting the development of picture fuzzy linguistic decision-making theory. Accordingly, our contribution to improving the current research on PFLSs makes their application in solving realistic problems feasible and practical. Keywords Picture fuzzy linguistic set . Limitation . Novel operational law . Aggregation
Introduction The picture fuzzy linguistic set (PFLS) is an emerging tool that opens up an effective way to meet the demand of describing realistic decision problems that relate to cognitive information. To date, there are only a few studies involving decision-making with picture fuzzy linguistic information. From a practical perspective, the fundamental issue in supporting the picture fuzzy linguistic decision-making process is the operational rules on the PFLS. Therefore, the article [1], which introduces the operations and an aggregation operator for PFLS, is a typical epistemological step toward the development of picture fuzzy linguistic decision-making. However, after a careful study, we found that there are some * Jian-qiang Wang [email protected] 1
Institute of Big Data Intelligent Management and Decision, College of Management, Shenzhen University, Shenzhen 518060, People’s Republic of China
2
School of Business, Central South University, Changsha 410083, People’s Republic of China
queries that need to be specified. The existing operations, which are used to aggregate individual opinions and attribute values, are not reasonable to some extent. Moreov
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