Fuzzy shortest path in an interval-valued fuzzy hypergraph using similarity measures

Abstract

In this paper, a new approach is introduced to find the shortest path between two given vertices on interval-valued fuzzy hypergraphs. When only crisp numbers are not sufficient to measure a real world parameter, fuzzy numbers are considered. But, there are many types of fuzzy numbers available in literature. Most useful fuzzy number is trapezoidal fuzzy numbers. Throughout this paper the interval-valued trapezoidal fuzzy number is used as the arc length of the interval-valued fuzzy hypergraph. We have measured similarity between two interval-valued fuzzy numbers to find the shortest path. An algorithm is also designed to find all possible hyperpaths in a hypergraph and calculated its time complexity.