A Hybrid Kruskal’s Algorithm Based on Intuitionistic Fuzzy with Hamacher Aggregation Operator for Road Planning

Abstract

This paper proposes a new approach by applying Kruskal’s algorithm on undirected road graph under intuitionistic fuzzy environment. The new hybrid algorithm consists of two phases. The first one is to determine fuzzy weights of undirected graph by intuitionistic fuzzy multi-criteria decision-making method with Hamacher aggregation operator. The edges between vertices are weighted by the determined criteria, and intuitionistic fuzzy expressions of decision makers are aggregated with Hamacher operator. The second phase is to find minimum spanning tree of intuitionistic fuzzy weighted graph. The Kruskal’s algorithm is adapted to intuitionistic fuzzy set and the pseudocode of fuzzy Kruskal’s algorithm is given. The contribution of this study to the literature is to combine existing algorithms with fuzzy multi-criteria decision-making methods to solve minimum spanning tree problems in real life. This approach is illustrated on a road planning problem of a campus with a large area, which aims to find the shortest distance that connects all buildings.