The solution and duality of imprecise network problems

  • Authors:

  • Mehdi Ghatee;S. Mehdi Hashemi;Behnam Hashemi;Mehdi Dehghan

  • Affiliations:

  • Department of Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15875-4413, Iran;Department of Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15875-4413, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2008

Quantified Score

Hi-index 0.09

Visualization

Abstract

Duality properties have been investigated by many researchers in the recent literature. They are introduced in this paper for a fully fuzzified version of the minimal cost flow problem, which is a basic model in network flow theory. This model illustrates the least cost of the shipment of a commodity through a capacitated network in terms of the imprecisely known available supplies at certain nodes which should be transmitted to fulfil uncertain demands at other nodes. First, we review on the most valuable results on fuzzy duality concepts to facilitate the discussion of this paper. By applying Hukuhara's difference, approximated and exact multiplication and Wu's scalar production, we exhibit the flow in network models. Then, we use combinatorial algorithms on a reduced problem which is derived from fully fuzzified MCFP to acquire fuzzy optimal flows. To give duality theorems, we utilize a total order on fuzzy numbers due to the level of risk and realize optimality conditions for providing some efficient combinatorial algorithms. Finally, we compare our results with the previous worthwhile works to demonstrate the efficiency and power of our scheme and the reasonability of our solutions in actual decision-making problems.