Solving generalised intuitionistic fuzzy 1-median problem on tree networks with a new ranking method (Q2247446)

Summary: The 1-median location problem on a tree \(T\) is to find a vertex \(\upsilon^\ast\) on \(T\) that minimise the sum of the weighted distances from all vertices to the vertex \(\upsilon^\ast\). In this paper, we investigate the 1-median location problem on tree networks with generalised intuitionistic fuzzy weights. We first present a new method for comparing generalised fuzzy numbers and then develop it for generalised intuitionistic fuzzy numbers. The proposed method for ranking generalised fuzzy numbers can also effectively rank real numbers. These methods are able to rank the generalised trapezoidal fuzzy numbers and generalised trapezoidal intuitionistic fuzzy numbers in linear times. Then numerical examples are given to compare the proposed methods with other existing methods. Finally, we apply our ranking method to solve the 1-median location problem on a tree network with generalised trapezoidal intuitionistic fuzzy vertex weights and then we show that the problem is solvable in linear time.