Generation of maximal fuzzy cliques of fuzzy permutation graph and applications

Abstract

Fuzzy permutation graph (FPG) plays a significant role in solving real-life problems where the scope and application of crisp permutation graph get limited due to the fuzziness involved in real situations. In this article an algorithm is designed to find out all maximal fuzzy cliques of a FPG. A similar algorithm is developed at the same time to find out all maximal fuzzy independent sets of the said graph. The inter-relationship between FPG and its two types of complements is presented based on the facts and theories established on fuzzy cliques and fuzzy independent sets. The importance of fuzzy cliques of FPG is discussed through an application on a daily-life problem. The unique property of a FPG having two types of complement graphs help us to solve many useful problems. Here, we have shown how this property of FPG helps us to overcome a hazardous situation occurred due to disrupted scheduling of trains on a foggy day.