The minimum regret path problem on stochastic fuzzy time-varying networks

Abstract

In this paper, we introduce a stochastic fuzzy time-varying minimum regret path problem (SFTMRP), which combines the characteristics of the min-max regret path and maximum probability path as a variant of the stochastic fuzzy time-varying shortest path problem, and its purpose is to find a path with the minimum regret degree in a given stochastic fuzzy time-varying network. To address this problem, we propose a random fuzzy delay neural network (RFDNN) based on novel random fuzzy delay neurons and without any training requirements. The random fuzzy delay neuron consists of six layers: an input layer, receiving layer, status layer, generation layer, sending layer, and output layer. Among them, the input and output layers are the ports of communication between neurons, and the receiving layer, status layer, generate layer, and sending layer are the information processing units of neurons. The information exchange between neurons is characterized by two kinds of signals: the shortest path signal and the maximum probability solution signal. The theoretical analysis of the proposed algorithm is carried out with respect to time-complexity and correctness. The numerical example and experimental results on 25 randomly generated stochastic fuzzy time-varying road networks with different numbers of 1000-5000 nodes show that the performance of the proposed algorithm is significantly better than that of existing algorithms.

Keywords: Random fuzzy delay neural network; Stochastic fuzzy time-varying minimum regret path; Stochastic fuzzy time-varying network; Stochastic fuzzy time-varying shortest path.