Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method
- 1 Department of Basic Sciences and Humanities, University of Asia Pacific, Dhaka, Bangladesh
- 2 General Education Department, City University, Dhaka, Bangladesh
- 3 Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
Abstract
In this paper, the statistical averaging method and the new statistical averag ing methods have been used to solve the fuzzy multi-objective linear pro gramming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. A t first, a numerical example of solving fuzzy multi-objective linear programming prob lem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method.
- Zimmermann, H.J. (1978) Fuzzy Programming and Linear Programming with Several Objective Functions. Fuzzy Sets and System, 1, 45-55. https://doi.org/10.1016/0165-0114(78)90031-3
- Bellman, R.E. and Zadeh, L.A. (1970) Decision-Making in Fuzzy Environment. Management Science, 17, 141-164. https://doi.org/10.1287/mnsc.17.4.B141
- Tanaka, H. and Asai, K. (1984) Fuzzy Linear Programming Problems with Fuzzy Numbers. Fuzzy Sets and Systems, 13, 1-10. https://doi.org/10.1016/0165-0114(84)90022-8
- Loganathan, C. and Lalitha, M. (2016) Solving Multi-Objective Mathematical Programming Problems in Fuzzy Approach. Introduction Journal of Mathematics and Its Applications, 3, 21-25.
- Zimmermann, H.J. (1983) Fuzzy Sets in Operational Research. EJOR, 13, 201-216. https://doi.org/10.1016/0377-2217(83)90048-6
- Behera, S.K., et al. () Mathematical Programming Problem in Fuzzy Approach. International Journal on CSE, 3790-3799.
- Behera, et al. (2021) Solution of Multi-Objective Mathematical Programming Problems in Fuzzy Approach. International Journal on Computer Science and Engineering, 3, 3790-3799.
- Thakre, P.A., Shelar, D.S. and Thakre, S.P. (2009) Solving Fuzzy Linear Programming Problem as MOLPP. World Congress on Engineering, London, 1-3 July 2009, 978-988.
- Nahar, S. and Alim, M.A. (2017) A New Geometric Average Technique to Solve Multi-Objective Linear Fractional Programming Problem and Comparison with New Arithmetic Average Technique. IOSR Journal of Mathematics, 13, 39-52. https://doi.org/10.9790/5728-1303013952
- Nahar, S. and Alim, M.A. (2017) A New Statistical Averaging Method to Solve Multi-Objective Linear Programming Problem. International Journal of Science and Research, 6, 623-629.
- Veeramani, C. and Sumathi, M. (2014) Fuzzy Mathematical Programming Approach for Solving Fuzzy Linear Fractional Programming Problem. RAIRO-Operations Research, 48, 109-122. https://doi.org/10.1051/ro/2013056
- Ebrahimnejad, A. and Tavana, M. (2014) A Novel Method for Solving Linear Programming Problems with Symmetric Trapezoidal Fuzzy Numbers. Applied Mathematical Modelling, 38, 4388-4395. https://doi.org/10.1016/j.apm.2014.02.024
- Das, S.K., Mandal, T. and Edalatpanah, S.A. (2017) A New Approach for Solving Fully Fuzzy Linear Fractional Programming Problems Using the Multi-Objective Linear Programming. RAIRO-Operations Research, 51, 285-297. https://doi.org/10.1051/ro/2016022