New Concepts of Picture Fuzzy Graphs with Application

Cen Zuo, Anita Pal and Arindam Dey
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Cen Zuo: Artificial Intelligence and Big Data College, Chongqing College of Electronic Engineering, Chongqing 401331, China
Anita Pal: Department of Mathematics, National Institute of Technology, Durgapur 713209, India
Arindam Dey: Department of Computer Science and Engineering, Saroj Mohan Institute of Technology, Hooghly 712512, India

Mathematics, 2019, vol. 7, issue 5, 1-18

Abstract: The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, in which a intuitionistic fuzzy set may fail to reveal satisfactory results. Picture fuzzy set is an extension of the classical fuzzy set and intuitionistic fuzzy set. It can work very efficiently in uncertain scenarios which involve more answers to these type: yes, no, abstain and refusal. In this paper, we introduce the idea of the picture fuzzy graph based on the picture fuzzy relation. Some types of picture fuzzy graph such as a regular picture fuzzy graph, strong picture fuzzy graph, complete picture fuzzy graph, and complement picture fuzzy graph are introduced and some properties are also described. The idea of an isomorphic picture fuzzy graph is also introduced in this paper. We also define six operations such as Cartesian product, composition, join, direct product, lexicographic and strong product on picture fuzzy graph. Finally, we describe the utility of the picture fuzzy graph and its application in a social network.

Keywords: fuzzy graph; picture fuzzy graph; social network; direct product; lexicographic product; strong product (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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