In this chapter, some basic definitions and operations on the concepts of fuzzy set, fuzzy number, intuitionistic fuzzy set, single-valued neutrosophic set, single-valued neutrosophic number (SVN-number) are presented. Secondly, two centroid point are called 1. and 2. centroid point for single-valued trapezoidal neutrosophic number (SVTN-number) and single-valued triangular neutrosophic number (SVTrN-number) are presented. Then, some desired properties of 1. and 2. centroid point of SVTN-numbers and SVTrN-numbers studied. Also, based on concept of 1. and 2. centroid point of SVTrN-numbers, a new single-valued neutrosophic multiple-attribute decision-making method is proposed. Moreover, a numerical example is introduced to illustrate the availability and practicability of the proposed method. Finally, since centroid points of normalized SNTN-numbers or SNTrN-numbers are fuzzy values, all definitions and properties of fuzzy graph theory can applied to SNTN-numbers or SNTrN-numbers. For example, definition of fuzzy graph theory based on centroid points of normalized SVTN-numbers and SVTrN-numbers is given.
Top1. Introduction
In practical applications including multi-atttribute decision-making(MADM) problems, many decision makers have different uncertain or ambiguous natural events and their modelling and solution involves the use of mathematical systems. Therefore, a number of theories have been introduced for dealing with such systems in an effective way such as; fuzzy set theory (Zadeh, 1965) intuitionistic fuzzy set theory (Atanassov, 1996), neutrosophic set theory (Smarandache, 1998) and so on. Then, many extended forms of the theories have been studied on fuzzy set theory [(İbrahim, 2004), (Rao & Shankar, 2011), (Wang et al., 2006), (Wang, 2009)], intuitionistic fuzzy set theory [(Dong et al. 2015), (Chan & Kumar, 2007), (Das & Guha, 2013), (Das & Guha, 2016), (Esmailzadeh, 2013), (Gani & Mohamed, 2015), (Gautamet al. 2016), (Hajek & Olej, 2014), (Kumar & Kaur, 2013), (Li, 2010), (Li, 2014), (Li & Yang, 2015), (Liu & Li, 2017), (Nayagam et al. 2016), (Nehi, 2010), (Prakash et al. 2016), (Rezvani, 2013), (Roseline & Amirtharaj, 2015), (Varghese, & Kuriakose, 2012)] and neutrosophic set theory [(Broumi et al., 2014), (Broumi et al., 2014a), (Broumi et al., 2014b), (Deli et al., 2014), (Liu et al.,2014a), (Liu et al.,2014b), (Peng et al., 2014), (Peng et al., 2016), (Wang et al., 2010)].