Intuitionistic fuzzy inverse 1-median location problem on tree networks with value at risk objective

Abstract

The inverse p-median location problem on networks is to modify the parameters of the original problem at minimum total cost with respect to given modification bounds such that a prespecified set of p vertices becomes a p-median with respect to new parameters. Therefore, the inverse p-median location problem is a decision-making problem in which decision-makers’ knowledge of the modification costs may be vague and imprecise. In this paper, we investigate the inverse 1-median location problem on tree networks with intuitionistic fuzzy weight modification costs. We first propose the new concepts of the credibilistic value at risk and conditional value at risk metrics in an intuitionistic fuzzy environment. Then we prove that these metrics satisfy in the harmonious risk metric properties. Finally, we solve the inverse 1-median location problem with intuitionistic fuzzy weight modification costs on tree networks and obtain its value at risk function in $O(n^2 \log n)$ time.