The International Arab Journal of Information Technology (IAJIT)

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From Neutrosophic Soft Set to Effective Neutrosophic Soft Set Generalizations and Applications

The Neutrosophic Soft Set (NSS) is an advanced and highly effective expansion of soft sets, specifically designed to handle parameterized values of alternatives. As an enhanced version of fuzzy soft sets, it provides a novel mathematical framework that offers significant advantages in dealing with uncertain information. This model is created by merging soft sets and neutrosophic sets, providing a robust approach to uncertainty management. Various algorithms have been proposed for making neutrosophic decisions using NSSs. However, these algorithms neglect external effective that influence the Decision- Making (DM) process, focusing solely on parameters. To address this issue, the article introduces the concept of Effective Neutrosophic Soft Sets (ENSSs). Additionally, we extend and generalize the innovative concept of Effective Fuzzy Soft Sets (EFSSs) to accommodate three independent membership criteria, aiming to enhance effectiveness and realism. We also introduce operations on ENSSs, including subset, complement, union, intersection, AND, and OR, which are defined along with illustrative examples. Furthermore, we examine some of its properties. Moreover, we present applications of this concept in DM problems and Medical Diagnosis (MD).

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