A two-sided matching method considering the lowest value of acceptability with regret theory for probabilistic linguisti
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ORIGINAL ARTICLE
A two‑sided matching method considering the lowest value of acceptability with regret theory for probabilistic linguistic term sets Peng Li1 · Nannan Wang1 · Cuiping Wei2,3 · Na Zhang4 Received: 4 March 2020 / Accepted: 20 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In order to solve matching problems for probabilistic linguistic information, a novel two-sided matching decision method for the probabilistic linguistic term sets (PLTSs) based on the regret theory considering the lowest value of acceptability is proposed. First, we propose a new utility function to transform the PLTSs to utility values, which can be conveniently applied to two-sided matching models. Then, to reflect the bounded rationality of expert and make the decision result close to real decision process, we put forward a novel regret-based model to obtain regret-rejoice by setting the lowest value of acceptability based on the utility function. Furthermore, we presented a new type of two-sided matching method considering constraint condition based on the lowest value of acceptability. Finally, we apply our method to a real case and make comparisons with two traditional two-sided methods. Keywords Decision making · Regret theory · Two-sided matching · Probabilistic linguistic term sets
1 Introduction Two-sided matching problems have widely existed in our social life, such as marriage matching [2, 7, 10], matching of buyer and seller [11–12, 14], matching of technological knowledge [3, 9, 27], matching of venture investment [40], matching of person-post [37]. Due to the complexity of two-sided matching problems, in some cases, matching agents cannot use crisp numbers to express their evaluations. To address this issue, numerous scholars have extended two-sided matching methods from crisp numbers to uncertain information, such as fuzzy numbers [12], intuitionistic fuzzy information [32], interval-valued intuitionistic fuzzy information [36], triangular intuitionistic fuzzy information [37], and hesitant fuzzy * Na Zhang [email protected] 1
College of Economics and Management, Jiangsu University of Science and Technology, Zhenjiang 212003, PR China
2
College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, PR China
3
College of Information Science and Engineering, Qufu Normal University, Rizhao 276826, PR China
4
School of Economics and Management, Shihezi University, Shihezi 832000, PR China
information [4]. For the two-sided matching problems, when the criterion to evaluate is subjective, agents usually feel comfortable to use linguistic information to make an evaluation. Furthermore, many decision making problems need more than one expert. Probabilistic linguistic term sets (PLTSs) proposed by Pang et al. [30] can be used to express the evaluation information for many experts. PLTSs can not only effectively describe the uncertainty of expert but also have flexibility to deal with linguistic information [17]. Owing to the advantages of PLTS, a large amount
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