A Novel Preference Measure for Multi-Granularity Probabilistic Linguistic Term Sets and its Applications in Large-Scale
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A Novel Preference Measure for Multi-Granularity Probabilistic Linguistic Term Sets and its Applications in Large-Scale Group Decision-Making Baoli Wang1 • Jiye Liang2
Received: 23 January 2020 / Revised: 6 May 2020 / Accepted: 9 May 2020 Taiwan Fuzzy Systems Association 2020
Abstract Comparing probabilistic linguistic term sets (PLTSs) is quite essential in solving PLTS-expressed multi-attribute group decision-making problems (PLTSMAGDM). Researchers have designed various comparison measures to obtain the rank of PLTSs. However, most of the existing PLTS comparison measures need additional tedious adjustments before conducting a specific computation. Besides, these measures do not adequately consider the effects of the semantics of the basic linguistic term set and the probabilistic distributions. This paper proposes a new preference degree for g-granularity probabilistic term sets (g-GPLTSs) to overcome the two shortcomings simultaneously by integrating the effect from basic linguistic terms and probabilistic distributions without any adjustment. Moreover, the g-GPLTS preference degree also shows the extended adaptability for comparing PLTSs with unbalanced semantics. Based on the newly proposed preference degree, we construct a useful min-conflict model to solve PLTS-MAGDM with a large number of experts expressing the three-way primary grading. Finally, an illustrative example concerning software supplier selections, followed by the comparative analysis, is presented to verify the feasibility and effectiveness of the proposed method.
& Baoli Wang [email protected] Jiye Liang [email protected] 1
School of Mathematics and Information Technology, Yuncheng University, Yuncheng 044000, Shanxi, China
2
Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan 030006, Shanxi, China
Keywords Preference degrees Probabilistic linguistic term sets Min-conflict model Multi-attribute group decision-making Three-way primary gradings
1 Introduction Multi-attribute group decision-making (MAGDM) is a situation that selects an optimal scheme from a set of possible alternatives, which are evaluated under a set of attributes by a group of experts [1, 2]. Nowadays, numerous decision situations significantly impact public interest, which leads to an increasing need for experts from varying professional backgrounds to take part in MAGDM processes [3, 4]. Under those circumstances, the multi-attribute large-scale group decision-making problem (MALSGDM) has been a focus in different fields, such as the selection of suppliers in a large enterprise, the location of landfill sites, and the adjustment of subway fares in social management [5]. Among the MAGDM problems, some attributes cannot be measured quantitatively with real numbers but accessed by some qualitative information. To describe these qualitative attributes in decision-making, researchers have proposed a series of linguistic models to explicit the evaluation information [6–13]. The exp
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