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ARTICLE

Decision Making Algorithmic Approaches Based on Parameterization of Neutrosophic Set under Hypersoft Set Environment with Fuzzy, Intuitionistic Fuzzy and Neutrosophic Settings

Atiqe Ur Rahman^1,*, Muhammad Saeed¹, Sultan S. Alodhaibi², Hamiden Abd El-Wahed Khalifa^3,4

1 Department of Mathematics, University of Management and Technology, Lahore, 54000, Pakistan
2 Department of Mathematics, College of Science and Arts, Qassim University, Al-Rass, 51921, Saudi Arabia
3 Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, 12613, Egypt
4 Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya, 51951, Saudi Arabia

* Corresponding Author: Atiqe Ur Rahman. Email:

(This article belongs to the Special Issue: Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))

Computer Modeling in Engineering & Sciences 2021, 128(2), 743-777. https://doi.org/10.32604/cmes.2021.016736

Received 23 March 2021; Accepted 07 May 2021; Issue published 22 July 2021

Abstract

Hypersoft set is an extension of soft set as it further partitions each attribute into its corresponding attribute-valued set. This structure is more flexible and useful as it addresses the limitation of soft set for dealing with the scenarios having disjoint attribute-valued sets corresponding to distinct attributes. The main purpose of this study is to make the existing literature regarding neutrosophic parameterized soft set in line with the need of multi-attribute approximate function. Firstly, we conceptualize the neutrosophic parameterized hypersoft sets under the settings of fuzzy set, intuitionistic fuzzy set and neutrosophic set along with some of their elementary properties and set theoretic operations. Secondly, we propose decision-making-based algorithms with the help of these theories. Moreover, illustrative examples are presented which depict the structural validity for successful application to the problems involving vagueness and uncertainties. Lastly, the generalization of the proposed structure is discussed.

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