ENERGY OF A BIPOLAR FUZZY GRAPH AND ITS APPLICATION IN DECISION MAKING

Abstract

In many domains of information processing, bipolarity is a core feature to be considered: positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false.  If the information is moreover endowed with vagueness and imprecision, then bipolar fuzzy sets (BFSs) constitute an appropriate knowledge representation framework.  In this paper, we introduce the novel concepts of energy of a graph in the context of a bipolar fuzzy environment and investigate some of their properties.  We show that if \(\mathcal{G}\) is a bipolar fuzzy graph (BFG) on n vertices, then E(\(\mathcal{G}\)) ≤ \(\frac{n}{2}\) (1 + \(\sqrt{n}\)) must hold.  Moreover, we introduce the concept of energy of bipolar fuzzy digraphs (BFDGs) along with its application in decision making problem.