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 definition of product bipolar fuzzy graphs (PBFGs) in [16] is modified. 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.