MEASUREMENT OF PLANARITY IN PRODUCT BIPOLAR FUZZY GRAPHS

Abstract

Bipolar fuzzy set theory provides a basis for bipolar cognitive modeling and multiagent decision analysis, where in some situations, the product operator may be preferred to the min operator, from theoretical and experimental aspects. In this paper, the denition of product bipolar fuzzy graphs PBFGs in [16] is modied. The concepts of product bipolar fuzzy multigraphs PBFMGs , product bipolar fuzzy planar graphs PBFPGs and product bipolar fuzzy dual graphs PBFDGs are introduced and their properties are investigated. Meanwhile, the product bipolar fuzzy planarity value of PBFPG is introduced. The relation between PBFPG and PBFDG is also established. Finally, an application of the proposed concepts is provided.

Keywords

• Product bipolar fuzzy graph,product bipolar fuzzy multigraph,product bipolar fuzzy planar graph,product bipolar fuzzy dual graph.

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