Abstract
The normal distribution is a usual one of various distributions in the real world. A normal neutrosophic set (NNS) is composed of both a normal fuzzy number and a neutrosophic number, which a significant tool for describing the incompleteness, indeterminacy, and inconsistency of the decision-making information. In this paper, we propose two correlation coefficients between NNSs based on the score functions of normal neutrosophic numbers (NNNs) (basic elements in NNSs) and investigate their properties. Then, we develop a multiple attribute decision-making (MADM) method with NNSs under normal neutrosophic environments, where, by correlation coefficient values between each alternative (each evaluated NNS) and the ideal alternative (the ideal NNS), the ranking order of alternatives and the best one are given in the normal neutrosophic decision-making process. Finally, an illustrative example about the selection problem of investment alternatives is provided to demonstrate the application and feasibility of the developed decision-making method. Compared to the existing MADM approaches based on aggregation operators of NNNs, the proposed MADM method based on the correlation coefficients of NNSs shows the advantage of its simple decision-making process.
Highlights
IntroductionIn probability theory [1], the normal (or Gaussian) distribution is a very common continuous probability distribution
In probability theory [1], the normal distribution is a very common continuous probability distribution
Motivated by the decision-making methods [18,19,20], this study firstly proposes two correlation coefficients of normal neutrosophic sets (NNSs) based on the score functions of normal neutrosophic numbers (NNNs) and develops an multiple attribute decision-making (MADM) method using the correlation coefficients of NNSs to simplify the decision-making process under normal neutrosophic environments
Summary
In probability theory [1], the normal (or Gaussian) distribution is a very common continuous probability distribution. Liu and Teng [18] presented a normal neutrosophic number (NNN) as an extension of NIFN and its generalized weighted power averaging operator, and applied it to multiple attribute decision-making (MADM) problems with normal neutrosophic information. Motivated by the decision-making methods [18,19,20], this study firstly proposes two correlation coefficients of normal neutrosophic sets (NNSs) based on the score functions of NNNs and develops an MADM method using the correlation coefficients of NNSs to simplify the decision-making process under normal neutrosophic environments.
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