Abstract
Objectives: The main objective of this study is to define Plithogenic product fuzzy graphs (PPFGs), and introduce its properties. Method: PPFGs is newly introduced as a new graphical model where P-vertices are characterized by four or more attributes and the attribute values of P-edges are computed using the product operator. Findings: Theoretical discussions and results related to PPFGs, and subgraphs, paths, cycles, trees, bridge and cut vertex in PPFGs are demonstrated with examples. A social network model based on the notion of PPFGs has been presented and analyzed to show the utility and the advantage of Plithogenic product fuzzy graph model. Novelty: Strong and weak P-vertices, and highly strong, strong and weak P-edges are identified to analyze the strength of connectivity between different units. P-order, P-size, P-vertex range, P-edge range, degree, total degree, and average P-weight of P-vertices are computed to examine proximity, significance and centrality of units. Keywords: Plithogenic fuzzy sets; Fuzzy graphs; Plithogenic fuzzy graphs; Plithogenic product fuzzy graphs; Social networks
Highlights
Fuzzy sets and fuzzy relations were formulated by L.A
Since the single values of membership degree given to vertices and edges from [0,1] in Fuzzy graphs (FGs) provide limited knowledge and perception regarding any real-life problem under consideration, Intuitionistic fuzzy sets and fuzzy logic, and Intuitionistic fuzzy graphs (IFGs) were introduced by Atanassov in 1986 [4], and Karunambigai and Parvathi in 2006 [5] respectively
Plithogenic product fuzzy graphs (PPFGs) has been defined
Summary
Fuzzy sets and fuzzy relations were formulated by L.A. Zadeh in 1965 [1]. The introduction to Fuzzy graphs (FGs) was done by Kaufmann in 1973 [2]. It was further developed by Azriel Rosenfeld in 1975 [3]. Since the single values of membership degree given to vertices and edges from [0,1] in FGs provide limited knowledge and perception regarding any real-life problem under consideration, Intuitionistic fuzzy sets and fuzzy logic, and Intuitionistic fuzzy graphs (IFGs) were introduced by Atanassov in 1986 [4], and Karunambigai and Parvathi in 2006 [5] respectively. In IFGs, membership and nonmembership degrees from [0,1] are given to each element with the condition that the sum of membership and non-membership degrees is less than or equal to one. There are many real-life situations where the concept of neutrality degree is existent.
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