MEASUREMENT OF PLANARITY IN PRODUCT BIPOLAR FUZZY GRAPHS

SUMERA NAZ1, SAMINA ASHRAF2, HOSSEIN RASHMANLOU3

[PDF]

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.