Extension of competition graphs under complex fuzzy environment
- PDF / 1,568,443 Bytes
- 20 Pages / 595.276 x 790.866 pts Page_size
- 26 Downloads / 191 Views
ORIGINAL ARTICLE
Extension of competition graphs under complex fuzzy environment Muhammad Akram1 · Aqsa Sattar1 · Faruk Karaaslan2
· Sovan Samanta3
Received: 3 May 2020 / Accepted: 7 October 2020 © The Author(s) 2020
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. Keywords Complex fuzzy set · k-Competition · p-Competition · m-Step competition · Economic competition.
Introduction In 1968, Cohen [6] introduced the conception of competition graphs (CGs) to determine the problems of ecosystem. CGs have many utilizations in distinct areas of life. The analogy of Cohen was based on the fact that there is a competition between two species if both species have a common prey. Many variations of CGs are present in the literature, namely competition common enemy graph of digraph [22], p-competition graphs of digraph [12,13], competition hypergraphs [23] and tolerance competition graphs [4]. Another worthwhile generalization of competition graphs was given by Cho et al. [5] in 2000. All the introduced competi-
B
Faruk Karaaslan [email protected] Muhammad Akram [email protected] Aqsa Sattar [email protected] Sovan Samanta [email protected]
1
Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
2
Department of Mathematics, Faculty of Sciences, Çankiri Karatekin University, 18100, Çankiri, Turkey
3
Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, West Bengal 721636, India
tion graphs are crisp graphs which cannot describe all the real-world competitions. In ecosystem, the species may be vegetarian, non-vegetarian, strong, weak, and similarly the prey may be harmful, digestive, energetic, etc. In 1965, Zadeh [25] developed the conception of fuzzy set to represent the uncertainty of human judgment by initiating the membership function which is restricted to take the values form the unit interval [0,1]. For example, today is sunny, it might be 100% true if there are no clouds, 80% true if there are few clouds, 50% true if it is hazy and 0% true if it rains all day. A graph is an easy way to interpret the information which involve the relationship between objects. Fuzzy graphs are designed
Data Loading...
