A New Approach to Find an Optimal Solution of a Fuzzy Linear Programming Problem by Fuzzy Dynamic Programming

  • Authors

    • T. Nagalakshmi
    • G. Uthra
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.20935
  • Fuzzy dynamic Programming, Triangular Fuzzy numbers, Fuzzy Linear Programming Problem, Fuzzy Recursive Equations, Fuzzy Optimal Solution

  • This paper mainly focuses on a new approach to find an optimal solution of a fuzzy linear programming problem with the help of Fuzzy Dynamic Programming. Linear programming deals with the optimization of a function of variables called an objective function, subject to a set of linear inequalities called constraints. The objective function may be maximizing the profit or minimizing the cost or any other measure of effectiveness subject to constraints imposed by supply, demand, storage capacity, etc., Moreover, it is known that fuzziness prevails in all fields. Hence, a general linear programming problem with fuzzy parameters is considered where the variables are taken as Triangular Fuzzy Numbers. The solution is obtained by the method of FDP by framing fuzzy forward and fuzzy backward recursive equations. It is observed that the solutions obtained by both the equations are the same. This approach is illustrated with a numerical example. This feature of the proposed approach eliminates the imprecision and fuzziness in LPP models. The application of Fuzzy set theory in the field of dynamic Programming is called Fuzzy Dynamic Programming.

     

  • References

    1. [1] M.A. Abo-Sinna, “Multiple objective (fuzzy) dynamic programming problems: a survey and some applicationsâ€, Applied Mathematics and Computation, Vol. 157, No. 3 (2004), 861-888.

      [2] M. Alkan, A.M. Erkmen, I. Erkmen, “Fuzzy Dynamic programmingâ€, Proceedings of 7th Mediterranean Electro Technical Conference, Turkey, (1994).

      [3] R.E. Bellman, L.A. Zadeh, “Decision-making in a fuzzy environmentâ€, Management Science, Vol. 17 (1970), B141-B164.

      [4] Chung-Ching Su, Yuan-Yih Hsu, “Fuzzy Dynamic Programming: an application to unit commitmentâ€, IEEE Transactions on Power Systems, Vol. 6, No. 3 (1991), 1231-1237.

      [5] A.O. Esoqbue, J. Kacprzyk, “Fuzzy sets in Decision Analysisâ€, Operations Research and Statistics, Kluwer Academic Publishers, Boston (1998).

      [6] J. Kacprzyk, A.O. Esogbue, “Fuzzy dynamic programming: Main developments and applicationsâ€, Fuzzy Sets and Systems, Vol. 81, No. 1 (1996), 31-45.

      [7] Lushu Li, K.K. Lai, “Fuzzy dynamic programming approach to hybrid multi objective multi stage decision making problemsâ€, Fuzzy sets and systems, Vol. 117, No. 1 (2001), 13-25.

      [8] P.V. Narendra Kumar, Ch. Chengaiah, “Issues of Unit Commitment and Load Scheduling: A Fuzzy Dynamic Programming Approachâ€, International Journal of Pure and Applied Mathematics, Vol. 114, No. 9 (2017), 157-165.

      [9] G.A. Schweickardt, V. Miranda, “A Fuzzy dynamic programming approach for evaluation of Expansion distribution cost in uncertainty environmentsâ€, Latin American Applied Research, Vol. 37 (2007), 227-234.

      [10] L.A. Zadeh, “Fuzzy setsâ€, Information and control, Vol. 8 (1965), 338-353.

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  • How to Cite

    Nagalakshmi, T., & Uthra, G. (2018). A New Approach to Find an Optimal Solution of a Fuzzy Linear Programming Problem by Fuzzy Dynamic Programming. International Journal of Engineering & Technology, 7(4.10), 360-363. https://doi.org/10.14419/ijet.v7i4.10.20935