Minimum cost flow problems in generalized fuzzy environments. Credibilistic CVaR minimization approach

Abstract

The paper focuses on the problems of linear programming (LP) with generalized fuzzy numbers (GFNs) as coefficients of the objective function. It is necessary to characterize consistent arithmetic operations to lower the error and information loss compared to the minimum operator usage and normalization in cases where experts are not completely certain of their subjective opinions. The uncertainty is eliminated using the total cost as a loss function and credibilistic conditional value at risk (CVaR) minimization. To crispify and generate a GFN, we utilize a ranking function that allows us to consider risky realizations. By solving many deterministic problems with LP solvers, projections of the error in the objective function can be presented. To describe and implement our methodology, we mainly focus on network optimization problems, especially generalized fuzzy transportation, assignment, and shortest path problems.