Bipolar fuzzy graphs based on the product operator

Abstract

From both theoretical and experimental perspectives, bipolar fuzzy set theory serves as a foundation for bipolar cognitive modeling and multi-agent decision analysis, where the product operator may be preferred over the min operator in some scenarios. In this paper, we discuss the basic properties of operations on product bipolar fuzzy graphs (PBFGs)(bipolar fuzzy graphs based on the product operator) such as direct product, Cartesian product, strong product, lexicographic product, union, ring sum and join. Also we define the notion of complement of PBFGs and investigate its properties. Moreover, application of PBFG theory is presented in multi-agent decision making.