Extension of competition graphs under complex fuzzy environment

Abstract

A complex fuzzy set (CFS) is a remarkable generalization of the fuzzy set in which membership function is restricted to take the values from the unit circle in the complex plane. A CFS is an efficient model to deal with uncertainties of human judgement in more comprehensive and logical way due to the presence of phase term. In this research article, we introduce the concept of competition graphs under complex fuzzy environment. Further, we present complex fuzzy k-competition graphs and p-competition complex fuzzy graphs. Moreover, we consider m-step complex fuzzy competition graphs, complex fuzzy neighborhood graphs (CFNGs), complex fuzzy economic competition graphs (CFECGs) and m-step complex fuzzy economic competition graphs with interesting properties. In addition, we describe an application in ecosystem of our proposed model. We also provide comparison of proposed competition graphs with existing graphs.

Types of Complex Fuzzy Relations with Applications in Future Commission Market

“…Complex fuzzy logic can also be used to solve those forms of issues more easily and reliably than fuzzy logic. Akram et al [14] introduced the concept of competition graphs under a complex fuzzy environment. ey described an application in the ecosystem.…”

Picture fuzzy tolerance graphs with application

“…Next, Karaaslan [24] exhibited structure of hesitant FGs with their applications in decision making. Recently, Akram et al [3] proposed the concept of CGs under complex fuzzy environment and designed an application of it in ecology.…”

“…22 We consider three PFIs {I i : i = 1, 2, 3} on R L along with corresponding PFTs {T i : i = 1, 2, 3}. Let the support of these PFIs are,respectively,[1.5, 7.5], [3.5, 9.5], [6, 14.5] and also the cores are,respectively, [3,6], [5,8], Then h(I 1 ∩I 2 ) = (1, 0, 0), h(I 1 ∩I 3 ) = (0.33, 0.07, 0.6), h(I 2 ∩ I 3 ) = (0.77, 0.01, 0.22). Therefore,the TMS, AMS and FMS of the edges (r 1 , r 2 ), (r 1 , r 3 ) and (r 2 , r 3 ) are, respectively,(0.37, 0, 0), (0, 0, 1) and (0.11, 0.001, 0.03).…”

Decision-making methods based on fuzzy soft competition hypergraphs

“…The idea of fuzzy competition graphs was initiated by Samanta and Pal [25] with some generalizations including fuzzy k-competition graphs and pcompetition fuzzy graphs. The researchers have extended the notion of fuzzy competition graphs to intuitionistic fuzzy competition graphs [26], m-step fuzzy competition graphs [27], q-rung orthopair fuzzy competition graphs [28], and complex fuzzy competition graphs [29]. Sarwar et al [30] proposed the idea of fuzzy competition hypergraphs and discussed its certain invariants with decision-making problems.…”