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International Journal of Neutrosophic Science
Volume 18 , Issue 2, PP: 227-242 , 2022 | Cite this article as | XML | Html |PDF

Title

Introduction to Restricted Neutrosophic Set and Its Application

Authors Names :   Somen Debnath   1 *  

1  Affiliation :  Department of Mathematics, Umakanta Academy, Agartala-799001, Tripura, India

    Email :  somen008@rediffmail.com



Doi   :   https://doi.org/10.54216/IJNS.180206

Received: November 16, 2021 Accepted: March 21, 2022

Abstract :

This paper is devoted to introduce a novel concept known as restricted neutrosophic set (RNS) as another subclass of neutrosophic set (NS). The purpose of introducing the notion of RNS is to give a new mathematical theory that is more promising and purposeful than the existing fuzzy-centric theories to solve the uncertainty based real-world problems in a lucid manner. From decision-makers point of view, the new mathematical tool can be viewed as a direct extension of Pythagorean neutrosophic set (PNS). The PNS has its own inherent limitation for which the decision-makers can’t answer a certain type of problem. For example, in a certain problem, if we consider the degree of truth-membership =0.8, degree of indeterminate-membership , and the degree of falsity-membership =0.8, then it gives an absurd result under PNS. To remove such kind of absurdity, there is a demand to introduce another superior set-theoretical concept that provides more information for the decision-makers. This gives rise to the introduction of RNS. In RNS, we choose any value belongs to for the three membership degrees so that their product always limited to 1. So, the beauty of RNS is that it can accommodate more information within small range with relaxed membership values i.e under RNS we can consider the maximum membership triplet as . Undoubtedly the RNS gives more compact set-theoretical model to describe imprecise knowledge with ease. Finally, a decision-making approach based algorithm is introduced and applied to solve medical diagnosis problem.

Keywords :

Neutrosophic set; Pythagorean neutrosophic set; Restricted neutrosophic set; Decision-making

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Cite this Article as :
Somen Debnath, Introduction to Restricted Neutrosophic Set and Its Application, International Journal of Neutrosophic Science, Vol. 18 , No. 2 , (2022) : 227-242 (Doi   :  https://doi.org/10.54216/IJNS.180206)