Abstract
This paper proposes the concepts of a neutrosophic number and a trapezoidal neutrosophic number (TNN), the basic operational relations of TNNs, and the score function of TNN. Then, we develop a trapezoidal neutrosophic weighted arithmetic averaging (TNWAA) operator and a trapezoidal neutrosophic weighted geometric averaging (TNWGA) operator to aggregate TNN information and investigate their properties. Furthermore, a multiple attribute decision making method based on the TNWAA and TNWGA operators and the score function of TNN is established under a TNN environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.
Highlights
Fuzzy decision making is an important topic in decision theory
This paper proposed neutrosophic numbers and trapezoidal neutrosophic number (TNN) and the operational relations of TNNs as the extension of IFNs and ITFNs and introduced the score function of a TNN for comparing TNNs
We established a decision making method based on the trapezoidal neutrosophic weighted arithmetic averaging (TNWAA) or trapezoidal neutrosophic weighted geometric averaging (TNWGA) operator and the score function to solve multiple attribute decision making problems with TNN information
Summary
Fuzzy decision making is an important topic in decision theory. Recently, many researchers have proposed various fuzzy decision making methods (Liu and Yu, 2013; Meng and Chen, 2014; Wang and Liu, 2014; Zhou and He, 2014; Wan and Dong, 2014). Ye (2014b) proposed a cross-entropy measure of SVNSs and applied it to multi criteria decision making problems with single valued neutrosophic information. Zhang et al (2014) defined the score, accuracy and certainty functions for interval neutrosophic numbers (INNs) and presented a comparative approach for INNs, and they developed some aggregation operators for INNs and a multi criteria decision-making method by means of the aggregation operators. Ye (2014e) proposed the weighted arithmetic average and weighted geometric average operators of interval neutrosophic linguistic numbers (INLNs) and applied them to multiple attribute decision making problems with interval neutrosophic linguistic information. We can introduce the concepts of neutrosophic numbers and TNNs to extend the discrete domains of SVNSs and INSs to continuous domains of TNNs, which are the further extension of IFNs and ITFNs (Wang and Zhang, 2009).
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