Branch Mathematics and Statistics Faculty and Staff Publications

Document Type

Article

Publication Date

2017

Abstract

Double Refined Indeterminacy Neutrosophic Set (DRINS) is an inclusive case of the refined neutrosophic set, defined by Smarandache [1], which provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world.

More precision is provided in handling indeterminacy; by classifying indeterminacy (I) into two, based on membership; as indeterminacy leaning towards truth membership (IT ) and indeterminacy leaning towards false membership (IF ). This kind of classification of indeterminacy is not feasible with the existing Single Valued Neutrosophic Set (SVNS), but it is a particular case of the refined neutrosophic set (where each T , I , F can be refined into T1 , T2, …; I 1 , I2, …; F1 , F2, …).

DRINS is better equipped at dealing indeterminate and inconsistent information, with more accuracy than SVNS, which fuzzy sets and Intuitionistic Fuzzy Sets (IFS) are incapable of. Based on the cross entropy of neutrosophic sets, the cross entropy of DRINSs, known as double refined Indeterminacy neutrosophic cross entropy, is proposed in this paper.

This proposed cross entropy is used for a multicriteria decision-making problem, where the criteria values for alternatives are considered under a DRINS environment. Similarly, an indeterminacy based cross entropy using DRINS is also proposed.

The double refined Indeterminacy neutrosophic weighted cross entropy and indeterminacy based cross entropy between the ideal alternative and an alternative is obtained and utilized to rank the alternatives corresponding to the cross entropy values. The most desirable one(s) in decision making process is selected.

An illustrative example is provided to demonstrate the application of the proposed method. A brief comparison of the proposed method with the existing methods is carried out

Publisher

Trans Tech Publications, Switzerland

Publication Title

Applied Mechanics and Materials

ISSN

1662-7482

Volume

859, pp 129-143

Language (ISO)

English

Keywords

Double Refined Indeterminacy, n-Refined Indeterminacy, Refined Neutrosophic Set, entropy, decision making

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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