Shortest Path Problem with Subnormal Gaussian Fuzzy Costs
2026-05-26 • Cryptography and Security
Cryptography and SecurityNetworking and Internet Architecture
AI summaryⓘ
The authors study how to find the shortest path in a network when the travel costs are uncertain and described by fuzzy numbers with Gaussian shapes. They introduce a way to measure and combine the reliability of these fuzzy costs, and use a ranking system that considers average cost, reliability, and variability to pick the best route efficiently. To check how stable their method is, they run simulations that sample different confidence levels and find the results remain consistent. Finally, they test their approach on a large air traffic network, showing it works well with real data and balances cost with reliability.
fuzzy shortest pathdirected graphsgeneralized fuzzy numbersGaussian membership functionsweighted geometric meanreliability-aware rankingalpha-cutMonte Carlo samplingDijkstra algorithmair traffic network
Authors
Murat Moran, Hande Günay Akdemir
Abstract
This paper addresses the fuzzy shortest path problem in directed graphs, where edge costs are modeled as generalized fuzzy numbers with Gaussian membership functions. We interpret height as an indicator of information reliability. Based on this view, we introduce a weighted geometric mean to aggregate heights during the addition of generalized Gaussian fuzzy numbers. We employ a reliability-aware ranking that jointly considers the core, height, and standard deviation of fuzzy edge costs to determine the shortest path, thereby capturing their central tendency, reliability, and variability while keeping Dijkstra-level complexity per relaxation. The method yields routes that are not only cost-efficient but also supported by highly reliable information. To assess robustness, we construct a crisp baseline from the ranking and conduct Monte Carlo alpha-cut sampling--drawing membership levels uniformly and then sampling within the induced intervals--to recompute path costs and quantify sensitivity via the mean percentage deviation and its standard deviation. Finally, a large-scale case study on the FAA air traffic network demonstrates that the proposed GGFN--SPP framework scales efficiently to real-world networks, balances cost and reliability through $α$--cut aggregation and risk-aware ranking, and exhibits stable performance under Monte Carlo simulations with subnormal fuzzy costs.