In this study, the authors develop a new decision-making method on single-valued trapezoidal neutrosophic numbers (SVTN-Numbers) where all the decision information take the form of SVTN-Numbers. To construct the method, some new similarity measures between two SVTN-Numbers are presented. Then, concept of impact value on SVTN-Numbers by using the cut sets of SVTN-Numbers is proposed, and the corresponding properties are discussed. Finally, a real example is introduced and compared with different methods to show the applicability and feasibility of the proposed multi-attribute decision-making method.
Top1 Introduction
In real decision making to select the best alternative from all the feasible set of alternatives, multi-attribute decision making problems and solution methods are the important branches of modern decision sciences to deal with incomplete, indeterminate and inconsistent information. To modeling the multi-attribute decision making problems, theory of fuzzy sets initiated by (Zadeh, 1965) is an effective theory to describe uncertain information. Since the theory only has a membership and cannot express non-membership, (Atanassov, 1999) defined theory of intuitionistic fuzzy sets which has both membership and non-membership such that 0 ≤membership value +non-membership≤ 1 where 0 ≤membership value≤ 1 and 0 ≤non-membership≤ 1. The fuzzy sets and intuitionistic fuzzy sets, have been studied and applied in different fields in decision making problems including multi-attribute decision making(MADM) problems in (Ban, 2008; Chen & Li, 2011; Li, 2014; Li, 2010; Peng et al. 2014; Pramanik et al., 2015; Wang & Zhang, 2009).
Sometimes the theories can not handle incomplete information indeterminate information and inconsistent information. To handle this type of information, Smarandache (Smarandache, 1998; Smarandache, 2005) gave theory of neutrosophic sets which contains truth-membership function, indeterminacy membership function and false-membership function are completely independent. After Smarandache, (Wang et al., 2010) gave the theory of single-valued neutrosophic sets which is a particular case of the neutrosophic set which presents more reasonable mathematical tools to deal with indeterminate data. The theories have studied in various areas such as (Cao et al. 2016; Deli & Broumi, 2015; Farhadinia & Ban, 2013; Ji et al. 2018; Hayat et al., 2018; Karaaslan & Hayat, 2018; Karaaslan 2018; Karaaslan 2019; Kumar & Kaur, 2013; Li, 2014; Li et al., 2010; Liu et al.,2002; Liang et al., 2018; Liang et al.,2017; Liu et al.,2012; Liu et al.,2011; Li et al., 2016; Liu et al.,2016; Liu & Liu, 2014; Liu & Shi, 2015; Peng et al., 2016; Peng et al., 2014; Shenify & Mazarbhuiya, 2015; Tian et al., 2016a; Tian et al., 2016b; Tian et al., 2016c; Wu et al., 2016; Wang & Wang, 2016; Ye, 2010; Ye, 2012; Ye, 2014a; Ye, 2014b).