A Study on Bipolar Fuzzy Set and Graph and its Application

Abstract

This thesis introduces the distance between bipolar fuzzy set with four fundamental newlinedistance. The energy and Laplacian energy of bipolar fuzzy graph are examined. The newlineDouble Layered Bipolar Fuzzy Graph (DLBFG) and its related properties. The matrix newlinerepresentation of DLBFG and its properties are analyzed using some tools in Bipolar Fuzzy newlineGraph (BFG) and illustrated with some example. The Basic Core Graph from the DLBFG newlineis analyzed. From DLBFG we establish Balanced Double Layered Bipolar Fuzzy Graph newline(BDLBFG). The matrix representation of DLBFG is verified. Various product of BFG are newlineexamined. A new FG in precise Triple Layered Bipolar Fuzzy Graph (TLBFG) is newlinecharacterized. Two new algorithms are developed to find Triangular Bipolar Fuzzy newlineNumbers (TBFN) and Triangular Fuzzy Numbers (TFN), which gives newlinethe direction for further.