Why triangular membership functions?
Fuzzy Sets and Systems
A general approach to solving a wide class of fuzzy optimization problems
Fuzzy Sets and Systems
A shortest path problem on a network with fuzzy arc lengths
Fuzzy Sets and Systems
A survey on benders decomposition applied to fixed-charge network design problems
Computers and Operations Research
Optimization of logistic systems using fuzzy weighted aggregation
Fuzzy Sets and Systems
Ranking function-based solutions of fully fuzzified minimal cost flow problem
Information Sciences: an International Journal
Modeling capacitated location-allocation problem with fuzzy demands
Computers and Industrial Engineering
The solution and duality of imprecise network problems
Computers & Mathematics with Applications
Computers and Industrial Engineering
Synthetic realization approach to fuzzy global optimization via gamma algorithm
Mathematical and Computer Modelling: An International Journal
Fuzzy optimization problemsbased on the embedding theorem and possibility and necessity measures
Mathematical and Computer Modelling: An International Journal
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We treat with the Minimal Cost Multicommodity Flow Problem (MCMFP) in the setting of fuzzy sets, by forming a coherent algorithmic framework referred to as a fuzzy MCMFP. Given the character of granular information captured by fuzzy sets, the objective is to find multiple flows satisfying the demands of commodities, by using available supplies consuming the least possible cost. With this regard, the supply and demand of nodes may be presented linguistically; the travel cost and capacity of links can be defined under uncertainty as well. To solve this problem, two efficient algorithms are motivated. In the first, we utilize fuzzy shortest paths and K-shortest paths to generate preferred and absorbing paths, and then we find the flow on them by solving a classic MCMFP. The second algorithm exhibits with fuzzy supply-demand, and employs a total order on trapezoidal fuzzy numbers to reduce the fuzzy MCMFP into four classic MCMFPs. Some examples are solved to demonstrate the performance of the presented methods. Among the various applications of this scheme in providing a suitable interface between the model and physical world, we focus on network design under fuzziness. The granular nature of the description of the future travel demand contributes to the generality of the planning model, and determines a certain perspective from which we will looking at the network.