New approach to the resolution of triangular fuzzy linear programs: MOMA-plus method.

  • Authors

    • Abdoulaye COMPAORE
    • Kounhinir SOME University of Koudougou
    • Blaise SOME
    2017-10-13
    https://doi.org/10.14419/ijamr.v6i4.8069
  • Fuzzy triangular numbers, Fuzzy linear programming, MOMA-plus method.

  • Abstract

    In this  paper,  we propose  a  new  approach to  the  resolution of linear  programs,  whose coefficients are fuzzy triangular numbers.  This new approach is an adaptation from the method MOMA-plus (Multi-Objective Metaheuristic based on Alienor method) [1] to the resolution of fuzzy linear programs. First of all it consists in using of a new procedure proposed here to the converting of the fuzzy linear program into a deterministic multi-objective linear program, secondly  of the  using  of the  MOMA-plus  procedure for resolution.  Finally, three numerical examples are given  to  explain   the  procedures and  highlight  the performances of  this  new approach.

  • References

    1. [1] Kounhinir Somé; Abdoulaye Compaoré; Wenddabo Olivier Sawadogo; Berthod Ulungu; Blaise Somé, “Improving of numerical performance of the MOMA methodâ€, International Journal of mathematics and computer research, Vol.5, No.05, (2017), pp.1817-1827.

      [2] Kounhinir Somé; Berthold Ulungu; Wenddabo Olivier Sawadogo; Blaise Somé, “A theoretical foundation metaheuristic method to solve some multiobjectif optimization problemsâ€, International Journal of Applied Mathematical Research, Vol.2, No.4, (2013), pp.464-475.

      [3] Yi-hua Zhong; Yan-lin Jia; Dandan Chen; and Yan Yang, “Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Functionâ€, Journal of Applied Mathematics, Vol. (2013), pp.1-9.

      [4] Kounhinir Somé, Nouvelle métaheuristique basée sur la méthode Alienor pour la résolution des problèmes d’optimisation multiobjectif: Théorie et Applications, Thèse de doctorat à l’université de Ouagadougou, Burkina Faso, 27 Juillet 2013.

      [5] P. Pandian, “Multiobjective Programming Approch for Fuzzy Linear Programming Problemsâ€, Applied Mathematical Science, Vol.7, No.37, (2013), pp. 1811-1817.

      [6] S. H. Nasseri; E. Behmanesh, “Linear Programming with Triangular Fuzzy Numbers

      a Case Study in a Finance and Credit Instituteâ€, Fuzzy Inf. Eng., Vol.5, No.3, (2013),

      pp. 295-315.

      [7] Kounhinir Somé; Berthold Ulungu; Ibrahim. Himidi. Mohamed; Blaise Somé, “A new method for solving nonlinear multiobjective optimisation problemsâ€, JP Journal of Mathematical Sciences, Vol.2, No.1-2, (2011), pp.1-18.

      [8] P.A. Thakre; D.S. Shelar; S.P Thakre, “Solving Fuzzy Linear Programming Problem as Multi Objective Linear Programming Problemâ€, Proceedings of the World Congress on Engineering, Vol.II, No., (2009), pp.WCE 2009.

      [9] Mahamat Maimos; Yves Cherruault; Balira O. Konfe; Ange-gar S. Nkokolo Massamba, “Alienor method to solve multi-objective linear programmingâ€, Kybernetes, Vol.38, No.5, (2009), pp.789-799.

      [10] Nezam Mahdavi-Amiri; Seyed Hadi Nasseri; Alahbakhsh Yazdani, “Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problemsâ€, Iranian Journal of Operations Research, Vol.1, No.2, (2009), pp.68-84.

      [11] Balira O. Konfe; Yves Cherruault; Titem Benneouala, “A global optimization method for a large number of variables (variant of Alienor method)â€, Kybernetes, Vol.34, No.7-8, (2005), pp.1070-1083.

      [12] Balira O. Konfe;Yves Cherruault;Blaise Some;Titem Benneouala, “Alienor method applied to operational researchâ€, Kybernetes, Vol.34, No.7-8, (2005), pp.1211-1222.

      [13] T. Benneouala; Y. Cherruault, “Alienor method for global optimization with a large number of variablesâ€, Kybernetes, Vol.34, No.7-8, (2005), pp.1104-1111.

      [14] Y. Cherruault; G. Mora, Optimization global: Théorie des courbes α−denses, Ed. Economica, (2005).

      [15] G. Zhang; Yong-Hong Wu; M. Remias; Jie Lu, “Formulation of fuzzy linear programming problems as four-objective constrained optimization problemsâ€, Applied Mathematics and Computation, Vol.139, No., (2003), pp.383-399.

      [16] H. Ammar and Y. Cherruault, “Approximation of a Several Variables Function by a one Variable Function and Application to Global Optimizationâ€, Mathl. Comput. Modelling, Vol.18, No.2, (1993), pp.17-21.

      [17] H.R. Maleki; M. Tata; M. Mashinchi, “Linear programming with fuzzy variablesâ€, Fuzzy Sets and Systems, Vol.109, No., (2000), pp.21-33.

      [18] L.A. Zadeh, “Fuzzy setsâ€, Information a control, Vol.8, No., (1965), pp.338-353.

      [19] Mariano Jiménez; Mar Arenas; Amelia Bilbao; M. Victoria Rodriguez, “Linear programming with fuzzy parameters: An interactive method resolutionâ€, European Journal of Operational Research, (2005).

      [20] M. Zangiabadi; H. R. Maleki, “A method for solving linear programming problems with fuzzy parameters based on multiobjective linear programming techniqueâ€, Asia-Pacific Journal of Operational Research, Vol.24, No.4, (2007), pp.557-573.

      [21] M. Zarafat Angiz; S. Saati; A. Memariani and M. M. Movahedi, “Solving possibilistic linear programming problem considering membership function of the cÅ“fficientsâ€, Adv in Fuzry Sets and Systems, Vol.1, No.2, (2006), pp.131-142.

      [22] R. E. Bellman; L. A. Zadeh, “Decision making in fuzzy environmentâ€, Management Science, Vol.17, No., (1970), pp.B141-B164.

      [23] Yozo Nakahara; Mitsuo Gen, “A Method for Solving Linear Programming Problems with Tri- angular Fuzzy CÅ“fficients Using New Ranking Indexâ€, Computers and Industrial Engineering, Vol.25, No., (1993), pp.1-4.

      [24] Zimmerman H. J, “Fuzzy Programming and Linear Programming with Several Objective Functionâ€, Fuzzy Set and Systems, Vol.1, No., (1978), pp.45-55.

      [25] Jacques Teghem, Programmation linéaire, Edition de l’université de Bruxelles, (2003).

      [26] D.Lavigne and Y. Cherruault, “Alienor-Gabriel global optimization of a function of several variablesâ€, Mathl. Comput. Modelling, Vol.15, No.10, (1991), pp.125-1991.

      [27] Didier Dubois and Henri Prade, “Operations on fuzzy numbersâ€, Int. J. System SCI, Vol.9, No.6, (1978), pp.613-626.

  • Downloads

  • How to Cite

    COMPAORE, A., SOME, K., & SOME, B. (2017). New approach to the resolution of triangular fuzzy linear programs: MOMA-plus method. International Journal of Applied Mathematical Research, 6(4), 115-120. https://doi.org/10.14419/ijamr.v6i4.8069

    Received date: 2017-07-03

    Accepted date: 2017-08-07

    Published date: 2017-10-13