Journal of Prime Research in Mathematics

# 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

### 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.