Abstract
The objective of the paper is to introduce a new cross entropy measure in a neutrosophic cubic set (NCS) environment, which we call NC-cross entropy measure. We prove its basic properties. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision-making (MADM) strategy based on a weighted NC-cross entropy measure. To show the feasibility and applicability of the proposed multi attribute decision-making strategy, we solve an illustrative example of the multi attribute decision-making problem.
Highlights
In 1998, Smarandache [1] introduced the neutrosophic set by considering membership, indeterminacy, non-membership functions as independent components to uncertain, inconsistent and incomplete information
We have introduced NC-cross entropy measure in neutrosophic cubic set (NCS) environments
We have proved the basic properties of the proposed NC-cross entropy measure
Summary
In 1998, Smarandache [1] introduced the neutrosophic set by considering membership (truth), indeterminacy, non-membership (falsity) functions as independent components to uncertain, inconsistent and incomplete information. Biswas et al [24,25,26] presented several MADM strategies in single valued neutrosophic environments such as technique for order of preference by similarity to ideal solution (TOPSIS) [24], grey relational analysis [25], and entropy based MADM [26]. Pramanik and Mondal [46] extended the single valued neutrosophic grey relational analysis method to interval neutrosophic environments and applied it to an MADM problem. For multi attribute group decision-making (MAGDM), Pramanik et al [66] defined a similarity measure for NCSs and proved some of its basic properties and developed a new MAGDM strategy with linguistic variables in NCS environments. Pramanik et al [88] developed two new MADM strategies based on cross entropy measures in bipolar neutrosophic set (BNS) and interval BNS environments
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