New Similarity Measures for Dual Hesitant Fuzzy Sets and Their Application
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New Similarity Measures for Dual Hesitant Fuzzy Sets and Their Application Ruiping Yuan1 • Fanyong Meng1,2
Received: 7 February 2020 / Revised: 27 April 2020 / Accepted: 17 June 2020 Taiwan Fuzzy Systems Association 2020
Abstract Dual hesitant fuzzy sets (DHFSs) are powerful and efficient to express hesitant preferred and non-preferred information simultaneously. This paper focuses on similarity measures for DHFSs. To do this, it first analyzes the limitations of previous similarity measures for DHFSs. Then, several new dual hesitant fuzzy similarity measures are defined that can avoid the issues of previous ones. To discriminate the importance of decision-making criteria, several weighted similarity measures are further defined in views of additive and 2-additive measures. When the weighting information is not exactly known, optimization methods for determining additive and 2-additive measures are built, respectively. Furthermore, a method for multicriteria decision-making based on new weighted similarity measures is developed. Finally, two numerical examples are provided to show the utilization of the new method and compare with previous methods. Keywords Multi-criteria decision-making DHFS Similarity measure 2-Additive measure Shapley value
1 Introduction To cope with uncertain and fuzzy decision-making information, fuzzy decision-making theory has been developed into a hot researching topic. With the development of & Fanyong Meng [email protected] 1
School of Information, Beijing Wuzi University, Beijing 101149, China
2
School of Business, Central South University, Changsha 410083, China
decision-making theory, scholars noted that Zadeh’s fuzzy sets [1] cannot express the non-preferred or hesitant decision-making information. To address this issue, Atanassov [2] introduced the concept of Atannasov’s intuitionistic fuzzy sets (AIFSs) that employs two real values in [0, 1] to express the preferred and non-preferred judgments, respectively. To further denote the uncertain judgments of the decision-makers (DMs), Atanassov and Gargov [3] defined interval-valued intuitionistic fuzzy sets (IVIFSs) that are composed by two intervals in [0, 1] to separately denote the uncertain preferred and non-preferred judgments of DMs. On the other hand, Torra [4] presented the concept of hesitant fuzzy sets to show the hesitancy of DMs. Taking the advantages of these two types of fuzzy sets, many extending forms are proposed such as intuitionistic multiplicative sets (IMSs) [5], interval-valued intuitionistic multiplicative sets (IVIMSs) [6], linguistic intuitionistic fuzzy sets (LIFVSs) [7], multiplicative linguistic intuitionistic fuzzy sets (MLIFSs) [8], hesitant multiplicative fuzzy sets (HMFSs) [9], interval-valued hesitant fuzzy sets (IVHFSs) [10, 11], hesitant fuzzy linguistic term sets (HFLTSs) [12], multiplicative hesitant fuzzy linguistic sets (MHFLSs) [13], and interval linguistic hesitant fuzzy sets (ILHFSs) [14]. At present, the theory and application of decision-making with such types of fuzzy i
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