Next Article in Journal
Endomorphism Spectra of Double Fan Graphs
Next Article in Special Issue
Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra
Previous Article in Journal
A New Machine Learning Algorithm Based on Optimization Method for Regression and Classification Problems
Previous Article in Special Issue
Applying Fixed Point Techniques to Stability Problems in Intuitionistic Fuzzy Banach Spaces

## Printed Edition

A printed edition of this Special Issue is available at MDPI Books....
Article

# An Extension of Fuzzy Competition Graph and Its Uses in Manufacturing Industries

by 2,*,†, 2,† and
1
Department of Mathematics, Khanpur Gangche High School, Paschim Medinipur 721201, India
2
Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
3
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, Inida
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(6), 1008; https://doi.org/10.3390/math8061008
Received: 11 May 2020 / Revised: 5 June 2020 / Accepted: 10 June 2020 / Published: 19 June 2020
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2020)
Competition graph is a graph which constitutes from a directed graph (digraph) with an edge between two vertices if they have some common preys in the digraph. Moreover, Fuzzy competition graph (briefly, FCG) is the higher extension of the crisp competition graph by assigning fuzzy value to each vertex and edge. Also, Interval-valued FCG (briefly, IVFCG) is another higher extension of fuzzy competition graph by taking each fuzzy value as a sub-interval of the interval $[ 0 , 1 ]$ . This graph arises in many real world systems; one of them is discussed as follows: Each and every species in nature basically needs ecological balance to survive. The existing species depends on one another for food. If there happens any extinction of any species, there must be a crisis of food among those species which depend on that extinct species. The height of food crisis among those species varies according to their ecological status, environment and encompassing atmosphere. So, the prey to prey relationship among the species cannot be assessed exactly. Therefore, the assessment of competition of species is vague or shadowy. Motivated from this idea, in this paper IVFCG is introduced and several properties of IVFCG and its two variants interval-valued fuzzy k-competition graphs (briefly, IVFKCG) and interval-valued fuzzy m-step competition graphs (briefly, IVFMCG) are presented. The work is helpful to assess the strength of competition among competitors in the field of competitive network system. Furthermore, homomorphic and isomorphic properties of IVFCG are also discussed. Finally, an appropriate application of IVFCG in the competition among the production companies in market is presented to highlight the relevance of IVFCG. View Full-Text
Show Figures

Figure 1

MDPI and ACS Style

Pramanik, T.; Muhiuddin, G.; Alanazi, A.M.; Pal, M. An Extension of Fuzzy Competition Graph and Its Uses in Manufacturing Industries. Mathematics 2020, 8, 1008. https://doi.org/10.3390/math8061008

AMA Style

Pramanik T, Muhiuddin G, Alanazi AM, Pal M. An Extension of Fuzzy Competition Graph and Its Uses in Manufacturing Industries. Mathematics. 2020; 8(6):1008. https://doi.org/10.3390/math8061008

Chicago/Turabian Style

Pramanik, Tarasankar, G. Muhiuddin, Abdulaziz M. Alanazi, and Madhumangal Pal. 2020. "An Extension of Fuzzy Competition Graph and Its Uses in Manufacturing Industries" Mathematics 8, no. 6: 1008. https://doi.org/10.3390/math8061008

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

1