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Computer Science
Artificial Intelligence

Extension of competition graphs under complex fuzzy environment

Profile image of Dr. Sovan SamantaDr. Sovan Samanta

Complex & Intelligent Systems

https://doi.org/10.1007/S40747-020-00217-5
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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.

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The q-rung orthopair fuzzy set is a powerful tool for depicting fuzziness and uncertainty, as compared to the Pythagorean fuzzy model. The aim of this paper is to present q-rung orthopair fuzzy competition graphs (q-ROFCGs) and their generalizations, including q-rung orthopair fuzzy k-competition graphs, p-competition q-rung orthopair fuzzy graphs and m-step q-rung orthopair fuzzy competition graphs with several important properties. The study proposes the novel concepts of q-rung orthopair fuzzy cliques and triangulated q-rung orthopair fuzzy graphs with real-life characterizations. In particular, the present work evolves the notion of competition number and m-step competition number of q-rung picture fuzzy graphs with algorithms and explores their bounds in connection with the size of the smallest q-rung orthopair fuzzy edge clique cover. In addition, an application is illustrated in the soil ecosystem with an algorithm to highlight the contributions of this research article in pr...

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Fuzzy Competition Graphs
Dr. Sovan Samanta

2020

In 1968, Cohen [4] first introduced competition graph while working on a problem in ecology. Competition graph (CompG) is one kind of intersection graph and it is originally used for modeling ecological problems. Though this graph can be used to model various types of problems in the real world, Cohen used the crisp competition graph to model the ecological problem and hence the vertices and edges of such graphs were precisely defined. Since the real world is full of uncertainty, so it is better to model such competitions by using the concept of fuzzy graphs. For example, in ecology, species have different characteristics such as non-vegetarian, vegetarian, weak, strong, small, large, etc. Also, the preys may or may not be digestive, tasty, harmful, etc. There are no specific measures for the terms tasty, digestible, harmful, etc. these are linguistic terms and these terms may be formulated mathematically with the help of fuzzy sets. Thus, preys and interrelationship between the species and preys can be modeled using a FG. In ecology, the food web is a very important ecological system for investigation of the ecological balance. So, motivated from the concept of food web and uncertainty involved in the ecological system, fuzzy competition graphs were defined. These graphs were also generalized to model other kinds of problems involved in the real world. Such generalizations are fuzzy k-competition graphs, p-competition fuzzy graphs, and m-step fuzzy competition graphs. The concept of fuzzy neighborhood graphs has also been incorporated. The contribution of this chapter is from the papers [6, 8, 8-10, 15]. For more results on competition graphs, readers may consult with [1-3, 5, 7, 11, 17, 18]. 4.1 Types of Fuzzy Competition Graphs The concept of competition graphs (CompG) is extended to fuzzy competition graphs (FCompG) by incorporating the uncertainty in the vertices and edges. The contents of this section are from [12]. First of all, the fuzzy out-neighborhood (out-nbd) and fuzzy in-neighborhood (in-nbd) of a vertex are defined.

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