Decision making with MABAC method under probabilistic single-valued neutrosophic hesitant fuzzy environment
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ORIGINAL RESEARCH
Decision making with MABAC method under probabilistic singlevalued neutrosophic hesitant fuzzy environment Rıdvan S¸ahin1
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Fatma Altun1
Received: 18 August 2019 / Accepted: 5 January 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Recently, there has been great interest on single valued neutrosophic hesitant fuzzy set theory. When compared single valued neutrosophic set, it is more convenient for real life situations. But even in this case, there is still missing data for some decision problems. Probabilistic single valued neutrosophic hesitant fuzzy sets (PSVNHFSs) are defined to solve this problem. Even though it contains more information, it needs some improvements. In this paper, the modified PSVNHFS is defined and some improvements in the theory of PSVNHFS are proposed. Also, we improve some algebraic properties of this set theory and define a distance operator for PSVNHFSs. Then we introduce two aggregation operators called probabilistic single valued neutrosophic hesitant fuzzy weighted arithmetic average (PSVNHFWA) operator and probabilistic single valued neutrosophic hesitant fuzzy weighted geometric average (PSVNHFWG) operator related to algebraic properties presented in this paper. Also, we extend the MABAC method under the probabilistic single valued neutrosophic hesitant fuzzy set theory. Finally, we give an illustrative example to demonstrate the stability and reliability of the proposed theory. Keywords Probabilistic single valued neutrosophic hesitant fuzzy set Decision making MABAC method
1 Introduction To model information with uncertain, incomplete information, Zadeh (1965) defined the concept of fuzzy set (FS) which is characterized by a membership function. Many generalizations of fuzzy sets have been studied such as interval valued fuzzy set (IVFS) (Turksen 1986), hesitant fuzzy set (HFS) (Torra 2010), intuitionistic fuzzy set (IFS) (Atanassov 1986), interval valued intuitionistic fuzzy set (IVIFS) (Atanassov 1999), and so on. One of the fields in which these sets are utilized as a model is multi-criteria decision making (MCDM) problems. Recently, there has been great interest in modeling MCDM problems with these sets since it is more suitable to model uncertainty. There are & Rıdvan S¸ ahin [email protected] Fatma Altun [email protected] 1
Department of Mathematical Engineering, Faculty of Natural Sciences and Engineering, Gumushane University, Gumushane, Turkey
many papers on using these sets as a model in the decision process (Xu 1990, 1998; Zandieh and Aslani 2019; Viriyasitavat 2016). However, there are different types of uncertainty. In such case, it is insufficient to model problems with these sets and a new modeling technique is necessary. For this reason, Smarandache (1998) developed neutrosophic logic and neutrosophic sets (NSs). NSs are characterized with three membership called truth membership, indeterminacy membership and falsity membership. Here the membership degrees take values in non-standard unit interval
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