Fuzzy intersection graph: a geometrical approach

Abstract

The aim of fuzzy intersection graph is twofold: to work with objects with continuum grades of membership and to acknowledge their inter-relationships. Its working elements are fuzzy logic and reasoning with the objective of providing accessible representation of objects and relationships having a blurry backdrop. This article embarked a comprehensive study of fuzzy intersection graph using fuzzy geometry by defining fuzzy graph and fuzzy intersection region with the help of fuzzy points and fuzzy line segments. The main motive behind revamping fuzzy graphs using fuzzy geometry is to represent the linguistic variables and their inter-dependencies as an exact reflection of human thinking. We have interpreted a detailed study on parallel fuzzy lines and intersecting fuzzy lines and deduced a mathematical relation between the measure of parallelness and degree of intersection of fuzzy lines. Fuzzy intersection region, depending on the types of intersecting fuzzy sets, plays an important role. We have defined few of the most important and useful classes of fuzzy intersection graph from fuzzy geometric view point that will be helpful in expressing human thoughts and communication of information as has been demonstrated through an application on supplier–purchaser relationship in any business. The present study on fuzzy interval graph in detail, ensued in obtainment of results that nullified previously obtained results arising the question—are fuzzy interval graphs always strong intersection graphs?