Multi-Attribute Decision Making Based on Interval Neutrosophic Trapezoid Linguistic Aggregation Operators

1. Introduction

Smarandache (1998) proposed the neutrosophic set (NS) by adding an independent indeterminacy-membership function. The concept of neutrosophic set is a generalization of classic set, fuzzy set (Zadeh, 1956), intuitionistic fuzzy set (Atanassov, 1989), interval intuitionistic fuzzy set(Atanassov et al., 1989; Atanassov, 1994) and so on. In NS, the indeterminacy is quantified explicitly and truth-membership, indeterminacy membership, and false-membership are completely independent. From scientific or engineering point of view, the neutrosophic set and set- theoretic view, operators need to be specified. Otherwise, it will be difficult to apply in the real applications. Therefore, Wang, et al.(2010) defined a single valued neutrosophic set (SVNS) and then provided the set theoretic operations and various properties of single valued neutrosophic sets. Furthermore, Wang, et al.(2005) proposed the set theoretic operations on an instance of neutrosophic set called interval valued neutrosophic set (IVNS) which is more flexible and practical than NS. The works on neutrosophic set (NS) and interval valued neutrosophic set (IVNS), in theories and application have been progressing rapidly (e.g, Kharal, 2013; Ansaria et al., 2013; Saha et al, 2013; Rabounski et al, 2005 ; Lupiáñez, 2008 ; Wang et al, 2010; Deli et al, 2014 ; Deli et al, 2014a, Ye, 2014 ; Ye, 2014a ; Ye, 2014b ; Ye, 2014c ; Ye, 2014d ; Ye, 2014e ; Ye, 2014f ; Ye, 2014g ; Zeng, 2006; Peide et al. 2014 ; Arora et al, 2011; Arora et al, 2010 ; Chi et al. 2013 ; Liu et al. 2014 ;Biswas et al. 2014 ; Şahin et al . 2014 ; Aggarwal et al, 2010 ; Broumi et al, 2013; Broumi et al, 2013a; Broumi et al, 2013b; Broumi et al, 2013c; Broumi et al, 2014d; Broumi et al, 2013e; Broumi et al, 2014f; Broumi et al, 2014g ; Broumi et al, 2014h, Broumi et al, 2015i ; Broumi et al, 2014j ; Broumi et al, 2015k ; Broumi et al, 2015l ; Broumi et al, 2015m)