A New Approach for Solving Fully Fuzzy Bilevel Linear Programming Problems
محورهای موضوعی : مجله بین المللی ریاضیات صنعتیS. F. Tayebnasab 1 , F. Hamidi 2 , M. Allahdadi 3
1 - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
2 - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
3 - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
کلید واژه: Triangular fuzzy numbers, Bilevel linear programming, Optimal solution, Unconstrain variables, Ranking function,
چکیده مقاله :
This paper addresses a type of fully fuzzy bilevel linear programming (FFBLP) wherein all the coefficients and decision variables in both the objective function and constraints are triangular fuzzy numbers. This paper proposes a new simple-structured, efficient method for FFBLP problems based on crisp bilevel programming that yields fuzzy optimal solutions with unconstraint variables and parameters. some examples have been provided to illustrate these methods.
در این مقاله، یک نوع از مسئله برنامه‌ریزی خطی دو ترازه تماما فازی را که در آن تمام ضرایب و متغیرهای تصمیم‌گیری در هر دو تابع هدف و قید ها به عنوان اعداد فازی مثلثی بیان شده‌اند در نظر میگیریم. به منظور بدست آوردن جواب بهینهی فازی، رهیافت کارامد جدیدی برای مسئلهی برنامه ریزی خطی دوترازهی تماما فازی با پارامترها و متغیرهای فازی ارایه شده است. این رهیافت بر اساس برنامه ریزی دوترازهی قطعی می‌باشد. در نهایت، مثال‌های عددی برای نشان دادن قابلیت پیاده‌سازی روش‌های مورد نظر ارائه گردیده است.
[1] T. Allahviranloo, F. H. Lotfi, M. K. Kiasary, N. A. Kiani, L. Alizadeh, Solving fully fuzzy linear programming problem by the ranking function, Applied Mathematical Sciences 2 (2008) 19-32.
[2] R. E. Bellman, L. A. Zadeh, Decision Making in A Fuzzy Environment, Management Science 17 (1970) 141-164.
[3] M. Cecchini, J. Ecker, M. Kupferschmid, R. Leitch, Solving nonlinear principal-agent problems using bilevel programming, Eur. J. Oper. Res. 230 (2013) 364-373.
[4] S. Dempe, Foundations of bilevel programming, Kluwer, Dordrecht, 2002.
[5] S. Dempe, Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints, Optimization 52 (2003) 333-359.
[6] S. Dempe, V. Kalashnikov, G. A. PrezValds, N. Kalashnykova, Bilevel programming problems, Springer, Berlin, 2015.
[7] F. Hosseinzadeh Lotfi, T. Allahviranloo, M. Alimardani Jondabeh, L. Alizadeh, Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution, Applied Mathematical Modelling 33
(2009) 3151-3156.
[8] V. V. Kalashnikov, S. Dempe, G. A. PrezValds, N. I. Kalashnykova, J. F. CamachoVallejo, Bilevel programming and applications, Mathematical Problems in Engineering (2015) http://dx.doi.org/10.1155/
2015/310301/.
[9] J. Kaur, A. Kumar, Exact fuzzy optimal solution of fully fuzzy linear programming problems with unrestricted fuzzy variables,Appl. Intell. 37 (2012) 145-154.
[10] A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Applied Mathematical Modelling 35 (2011) 817-823.
[11] M. Labb , A. Violin, Bilevel programming and price setting problems, 4OR-Q J. Oper. Res. 11 (2013) 1-30.
[12] H. S. Najafi, S. A. Edalatpanah, A note on A new method for solving fully fuzzy linear programming problems, Appl. Math. Model. 37 (2013) 7865-7867.
[13] ] A. Ren, A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem, Mathematical Problems in Engineering (2015) http://dx.doi.org/10.1155/2015/280380/.
[14] A. Ren, Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method, Mathematical Problems in Engineering (2016) http://dx.doi.org/10.1155/2016/7069804/.
[15] A. Ren, Y. Wang, X. Xue, Interactive programming approach for solving the fully fuzzy bilevel linear programming problem, Knowledge-Based Systems 99 (2016) 103-111.
[16] A. Ruziyeva, Fuzzy bilevel optimization [Ph.D. thesis], Freiberg,Technical University Bergakademie (2013).
[17] N. Safaei, M. Saraj, A new method for solving fully fuzzy linear bilevel programming problems, International Journal of Applied Operational Research 4 (2014) 51-58.
[18] M. Sakawa, I. Nishizaki, Y. Uemura, Interactive fuzzy programming for multilevel linear programming problems with fuzzy parameters, Fuzzy Set Syst. 109 (2000) 3-19.
[19] J. Xu, P. A. Wei, Bilevel model for locationallocation problem of construction and demolition waste management under fuzzy random environment, Int. J. of Civ. Eng. 10 (2012) 1-12.
[20] M. W. Xu, J. J. Ye, A smoothing augmented Lagrangian method for solving simple bilevel programs, Comput. Optim. Appl. 59 (2014) 353-377.
[21] R. R. Yager, A procedure for ordering fuzzy numbers of the unit interval, Information Sciences 24 (1981) 143-161.
[22] G. Zhang, G. Zhang, Y. Gao , J. Lu, Competitive strategic bidding optimization in electricity markets using bilevel programming and swarm technique, IEEE Transactions on Industrial Electronics 58 (2011) 2138-2146.
[23] G. Zhang, J. Lu, T. Dillon, Fuzzy linear bilevel optimization: solution concepts, approaches and applications, In: P. P. Wang, D. Ruan, E. E. Kerre (eds) Fuzzy Logic. Studies in Fuzziness and Soft Computing, vol 215. Springer, Berlin, Heidelberg (2007) 351- 379.
