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Priority Weighted Neutrosophic Refined Soft Set: A Multi-Criteria Decision-Making Approach

Priority Weighted Neutrosophic Refined Soft Set: A Multi-Criteria Decision-Making Approach

C. Antony Crispin Sweety (Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, India), Sumathi I. R. (Department of Mathematics, Amrita School of Engineering, Coimbatore, India), and Aishwaryapriyadharshini G. (Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, India)
Copyright: © 2022 |Pages: 37
DOI: 10.4018/978-1-7998-7979-4.ch035
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Abstract

This chapter devises a new concept of priority weighted neutrosophic refined soft set (PWNRSS) by combining neutrosophic refined sets and soft sets implemented with prioritized universal elements and weightage-imposed parameters. The concepts of PWNRS subset, PWNRS null set, and PWNRS universal set are defined. Based on the definitions of n-norm and n-co-norm, the theoretical operations of PWNRS sets such as union, intersection, and complement are defined. AND-product and OR-product between two priority-weighted neutrosophic refined soft sets are introduced. Furthermore, priority weights neutrosophic refined soft set is expanded to MCDM technique to handle decision-making issues. TOPSIS has been examined more thoroughly for the PWNRSS decision-making issue. This proposed method might be extremely valuable in large-scale decision-making situations. Numerical examples are also provided to demonstrate the methodologies' dependability and applicability.
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Background

Lotfi L. A. Zadeh (1965) created fuzzy set and it is a collection of items with a grade of membership that ranges from zero to one. Krassimir Atanassov (1986) introduced the intuitionistic fuzzy set as an elaborate version of fuzzy set and that considered the non-membership degree along with membership grade. Both the works advanced the conventional notion of a classical set. Smarandache (1998) discussed on neutrosophy, neutrosophic probability, Set and logic and (2005), (2006), (2010) he proposed the neutrosophic set methodology, a mathematical strategy for dealing with concerns comprising imprecise, indeterminate and incompatible data. In neutrosophic representation membership, indeterminacy, and non-membership values are modeled by the neutrosophic considerations T,I,F within ‑]0,1[+, the non-standard unit interval.

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