Year: 2019
Type: article
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.
Source: Mathematics
DOI: 10.3390/math7050470
Authors: Cen Zuo, Anita Pal, Arindam Dey
Language: English
Topic: Fuzzy and Soft Set Theory
Field: Decision Sciences
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $1,216
OpenAlex ID: W2944910080