In fuzzy single and multi-objective minimal cost flow (MCF) problems, it is assumed that there is only one conveyance which can be used for transporting the product. However, in real life problems, more than one conveyance is used for transporting the product. To the best of our knowledge untill now no method is proposed in the literature for solving such fuzzy single and multi-objective MCF problems in which more than one conveyance is used for transporting the product and all the parameters, as well as all the decision variables that are represented by fuzzy numbers. In this paper, these types of fuzzy multi-objective MCF problems are called fully fuzzy multi-objective solid minimal cost flow (SMCF) problems and a new method is proposed for solving these problems. The advantages of the proposed methods are also discussed.
Multi-objective linear programming Fuzzy multi-objective solid minimal cost flow problem Ranking function LR flat fuzzy number
The authors would like to thank to the Editor-in-Chief and anonymous referees for various suggestions which have led to an improvement in both the quality and clarity of the paper I, Dr. Amit Kumar, want to acknowledge the adolescent inner blessings of Mehar. I believe that Mehar is an angel for me and without Mehar’s blessing it would not have been possible to attain and fulfil the idea presented in this paper. Mehar is a lovely daughter of Parmpreet Kaur (Research Scholar under my supervision). The authors also acknowledge the financial support given by the University Grant Commission, Govt. of India for completing the Major Research Project (39-40/2010(SR)).
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