A maximum flow network interdiction model in fuzzy stochastic hybrid uncertainty environments

Abstract

Uncertainty is an inherent characteristic of a decision-making process. Occasionally, historical data may be insufficient to accurately estimate the probability distribution suitable for an unknown variable. In these situations, we deal with fuzzy stochastic variables in solving a problem. As a result, decision-makers, particularly those in the military, are confronted with numerous issues. This article discusses the maximum network flow interdiction under fuzzy stochastic hybrid conditions. The capacity of arcs has been treated as a fuzzy stochastic variable in this problem. The primary objective of this paper is to propose a model to the decision-maker that can be used to manage unknown factors in the network. Since this topic is explored concurrently in a stochastic and fuzzy environment, it is impossible to solve it directly. Consequently, three probability-possibility, probability-necessity, and probability-credibility techniques are utilized to transform it into a deterministic state. Eventually, the proposed model’s efficacy is demonstrated by presenting a numerical example.

Keywords

• network interdiction
• fuzzy stochastic programming
• probability-possibility approach
• possibility measure
• probability measure