fuzzy goal An iterative goal to solve bi-level fractional integer programming problem using fuzzy approach
bi level fraction integer
Abstract
This paper solves the bi-level integer linear fractional programming problems based on fuzzy goal approach. At the first phase of the solution algorithm and to avoid the complexity of non-convexity of this problem, the authors finding the convex hull of its original set of constraints using the cutting-plane algorithm, and then the. It makes an extension work of Moitra and Pal (2002) and Pal et al. (2003). In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by first-level decision maker are developed first in the model formulation of the problem. Then a fuzzy goal programming model to minimize the group regret of degree of satisfactions of both the decision makers is developed to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both decision makers. The method of variable change on the under- and over-attainment variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Illustrative numerical example is given to demonstrate the procedure.
Downloads
References
[2]H.Calvete, C.Galé, and J. Iranzo, Planning of decentralized distribution network using bi-level, optimizatio.(2014), Omega, 49, (11), 30–41.
[3]O. Emam , E.Fathy , and A.Abdullah, On fuzzy bi-level multi-objective large scale integer quadratic programming problem, International Journal of Computer Applications .( 2017), 159 –(2), 0975 – 8887 .
[4]O. Emam, Interactive approach to bi-level integer multi objective fractional programming problem,Applied Mathematics and Computation .(2013), 223, (9) , 17-24.
[5]R. Gomory , All-integer programming algorithm, in ; J. F. Muth and G. L.Thompson (Eds.), Industrial Schedulil18, Prentice-Hall, Englewood Cliffs.(1963), NJ, Rc 189, (29) , 1-29.
[6] B. Ibrahim , A. Eid, and M. Elsayed, Bi-level multi-objectiveprogramming problem with fuzzy demands: a fuzzy goal programmingalgorithm.(2014), J. Oper. Res. Soc. India, 51,.( 2), 280–296.
[7]K. Lachhwani and A. Dwivedi, Bi-level and Multi-Level Programming Problems: Taxonomyof Literature Review and Research Issues, Springer , (2017) ,511831,(31), 017-9216.
[8] S. Mishra, A. Bihar, andI.verma, An algorithm based on the fitness function for solving bi-level linear fractional programming problems, International Journal of Modern Mathematical Sciences.(2015),13, (4), 404-416.
[9] A. Nachammai and P. Thangaraj , Solving fuzzy linear fractional programming problem using metric distance ranking, Applied Mathematical Sciences. (2012), 6, (26) , 1275-1285.
[10] M. Osman, O.Emam, and A.Elsayed, Interactive Approach for Multi-Level Multi-Objective Fractional Programming Problems with Fuzzy Parameters, Beni-Suef Univ. J. Basic Appl. Sci. xxx (2017).
[11] B. Pal, B. Moitra, and U. MaulikA, goal programming procedure for fuzzy multiobjective linear fractional programming problem, Fuzzy Sets and Systems .( 2003), 139, (2), 395–405.
[12] X. Pand and L.Wang, An exact algorithm for the bi-level mixed integer linear programming problem under three simplifying assumptions ,Computers & operations research.(2014) , 41 , (9), 309-318 .
[13] S.Pramanik and P. Pratim, Bi-level Linear Fractional Programming Problem based on Fuzzy Goal Programming Approach, International Journal of Computer Applications. (2011),25,(11), 0975-8887.
[14] A. Ren and Y. Wang, A cutting plane method for bilevel linear programming with interval coefficients, Springer Science+Business Media New York.(2014) , 223, (23), 355–378.
[15] O.Saad , T.Mohmed , M.Alshafae , and E.Abdella , On the solution of multi objective integer linear fractional programming problems with uncertain data, International Journal of Mathematical Archive.( 2012), 8, (3), 2983-2989.
[16] V. Sharmaa , K.Dahiya , and V.Verma, A class of integer linear fractional bi level programming problems, Optimization. (2014), 63, (10), 1565–1581.
[17] M. Toksari and y. Bilim, Interactive fuzzy goal programming based on jacobian matrix to solve decentralized bi-level multi-objective fractional programmingproblems, Int. J. Fuzzy Syst.(2015) , 17 , (4), 499–508 .
[18] E. Youness , O.Emam, and S.Hafez, Fuzzy bi-level multi-objective fractional integer programming , Applied Mathematics & Information Sciences.(2014) , 8, (6), 2857-2863,
Copyright (c) 2019 IJRDO - Journal of Applied Science (ISSN: 2455-6653)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Author(s) and co-author(s) jointly and severally represent and warrant that the Article is original with the author(s) and does not infringe any copyright or violate any other right of any third parties, and that the Article has not been published elsewhere. Author(s) agree to the terms that the IJRDO Journal will have the full right to remove the published article on any misconduct found in the published article.
