Journal of Prime Research in Mathematics
Vol. 17 (2021), Issue 2, pp. 122 – 137
ISSN: 1817-3462E (Online) 1818-5495 (Print)
ISSN: 1817-3462E (Online) 1818-5495 (Print)
A Conceptual Framework of Convex and Concave Sets under Refined Intuitionistic Fuzzy Set Environment.
Atiqe Ur Rahman \(^{a,*}\), Muhammad Arshad \(^{a}\), Muhammad Saeed \(^{b,}\)
\(^a\) Department of Mathematics, University of Management and Technology, Lahore, Pakistan.
\(^b\) Department of Mathematics, University of Management and Technology, Lahore, Pakistan.
Correspondence should be addressed to: aurkhb@gmail.com
Copyright © 2021 Atiqe Ur Rahman, Muhammad Arshad, Muhammad Saeed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: Received: 09 Feburary 2021; Accepted: 29 July 2021; Published Online: 2 August 2021.
Abstract
Intuitionistic fuzzy set deals with membership and non-membership of a certain element of universe of discourse whereas these are further partitioned into their sub-membership degrees in refined intuitionistic fuzzy set. This study aims to introduce the notions of convex and concave refined intuitionistic fuzzy sets. Moreover, some of its important properties e.g. complement, union, intersection etc. and results are discussed.
Keywords:
Ortho-convexity, Ortho-Concavity, Sub-membership degree, Sub non-membership degree,Infimum projection, Supremum projection.