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Keywords = neutrosophic cubic soft expert system

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26 pages, 404 KiB  
Article
A Generalized Approach towards Soft Expert Sets via Neutrosophic Cubic Sets with Applications in Games
by Muhammad Gulistan and Nasruddin Hassan
Symmetry 2019, 11(2), 289; https://doi.org/10.3390/sym11020289 - 22 Feb 2019
Cited by 10 | Viewed by 3405
Abstract
Games are considered to be the most attractive and healthy event between nations and peoples. Soft expert sets are helpful for capturing uncertain and vague information. By contrast, neutrosophic set is a tri-component logic set, thus it can deal with uncertain, indeterminate, and [...] Read more.
Games are considered to be the most attractive and healthy event between nations and peoples. Soft expert sets are helpful for capturing uncertain and vague information. By contrast, neutrosophic set is a tri-component logic set, thus it can deal with uncertain, indeterminate, and incompatible information where the indeterminacy is quantified explicitly and truth membership, indeterminacy membership, and falsity membership independent of each other. Subsequently, we develop a combined approach and extend this concept further to introduce the notion of the neutrosophic cubic soft expert sets (NCSESs) by using the concept of neutrosophic cubic soft sets, which is a powerful tool for handling uncertain information in many problems and especially in games. Then we define and analyze the properties of internal neutrosophic cubic soft expert sets (INCSESs) and external neutrosophic cubic soft expert sets (ENCSESs), P-order, P-union, P-intersection, P-AND, P-OR and R-order, R-union, R-intersection, R-AND, and R-OR of NCSESs. The NCSESs satisfy the laws of commutativity, associativity, De Morgan, distributivity, idempotentency, and absorption. We derive some conditions for P-union and P-intersection of two INCSESs to be an INCSES. It is shown that P-union and P-intersection of ENCSESs need not be an ENCSES. The R-union and R-intersection of the INCSESs (resp., ENCSESs) need not be an INCSES (resp. ENCSES). Necessary conditions for the P-union, R-union and R-intersection of two ENCSESs to be an ENCSES are obtained. We also study the conditions for R-intersection and P-intersection of two NCSESs to be an INCSES and ENCSES. Finally, for its applications in games, we use the developed procedure to analyze the cricket series between Pakistan and India. It is shown that the proposed method is suitable to be used for decision-making, and as good as or better when compared to existing models. Full article
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