Abstract
Bipolar fuzzy sets are used to describe the positive and negative of the uncertainty of objects, and the bipolar fuzzy graphs are used to characterize the structural relationship between uncertain concepts in which the vertices and edges are assigned positive and negative membership function values to feature the opposite uncertainty elevation. The dominating set is the control set of vertices in the graph structure and it occupies a critical position in graph analysis. This paper mainly contributes to extending the concept of domination in the fuzzy graph to the bipolar frameworks and obtaining the related expanded concepts of a variety of bipolar fuzzy graphs. Meanwhile, the approaches to obtain the specific dominating sets are presented. Finally, a numeral example on city data in Yunnan Province is presented to explain the computing of domination in bipolar fuzzy graph in the specific application.
Highlights
Fuzzy sets are used to describe the uncertainty of things, and are widely used in fuzzy reasoning, fuzzy intelligent decision-making systems and other fields, and have received widespread attention
A bipolar intuitionistic fuzzy set on universal set V is denoted by where the positive membership degree expresses the satisfaction degree of element v to the property corresponding to a bipolar intuitionistic fuzzy set
Sankar and Ezhilmaran [44] introduced more concepts on bipolar intuitionistic fuzzy graphs, and Alnaser et al [45] defined the concepts of incidence intuitionistic bipolar fuzzy matrix and line intuitionistic bipolar fuzzy graph
Summary
Fuzzy sets are used to describe the uncertainty of things, and are widely used in fuzzy reasoning, fuzzy intelligent decision-making systems and other fields, and have received widespread attention (see Bera and Pal [1] and [2], Islam and Pal [3], Samanta et al [4], Amanathulla et al [5], Pal et al [6], Prabakaran et al [7], Bagherinia et al [8], Gonzalez et al [9], and Maldonado et al [10]). Graphs are an effective tool to describe the structured data. Edges are used to measure the hierarchical and subordinate relationships between concepts, and the entire data set can be stored as graphs.
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