اخبار و اعلانات
آمار
| تعداد نشریات | 29 |
| تعداد شماره‌ها | 630 |
| تعداد مقالات | 6,368 |
| تعداد مشاهده مقاله | 9,730,896 |
| تعداد دریافت فایل اصل مقاله | 6,362,499 |
Riemann integrability based optimality criteria for fractional optimization problems with fuzzy parameters | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 12، دوره 19، شماره 2، خرداد و تیر 2022، صفحه 151-168 اصل مقاله (245.28 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2022.6796 | ||
| نویسندگان | ||
| D. Agarwal1؛ P. Singh* 2 | ||
| 1Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, India | ||
| 2Department of Mathematics, G L Bajaj Institute of Technology and Management, Greater Noida, India | ||
| چکیده | ||
| This paper aims to establish the Karush-Kuhn-Tucker type optimality criteria for linear fractional optimization problems with fuzzy parameters. To evolve the desired criteria first, the fractional optimization problem is transformed into the non-fractional optimization problem with fuzzy parameters. Then Hukuhara differentiability for the differentiation of functions with fuzzy parameters and Hausdorff metric to expound the distance between the fuzzy numbers is invoked. Optimality criteria are then elicited for the non-fractional optimization problems by introducing Lagrange multipliers and Riemann integration theory. In order to validate the developed theory, two numerical optimization problems are also verified. | ||
| کلیدواژه‌ها | ||
| Hukuhara difference؛ Hausdorff metric؛ H-differentiability؛ Riemann integration؛ Lagrange multipliers | ||
| مراجع | ||
|
[1] D. Agarwal, P. Singh, D. Bhati, S. Kumari, M. S. Obaidat, Duality-based branch-bound computational algorithm for sum-of-linear-fractional multi-objective optimization problem, Soft Computing, 23(1) (2019), 197-210.
[2] D. Agarwal, P. Singh, X. Li, S. Kumari, Optimality criteria for fuzzy-valued fractional multi-objective optimization problem, Soft Computing, 23(19) (2019), 9049-9067.
[3] T. M. Apostol, Mathematical analysis, Reading, MA: Addison-Wesley, 2, 1974.
[4] M. S. Bazaraa, H. D. Sherali, C. M. Shetty, Nonlinear programming, The New York Academy of Sciences - Wiley, 1993.
[5] R. E. Bellman, L. A. Zadeh, Decision-making in a fuzzy environment, Management Science, 17(4) (1970), B-141.
[6] M. Borza, A. S. Rambely, An approach based on α-cuts and max-min technique to linear fractional programming with fuzzy coefficients, Iranian Journal of Fuzzy Systems, 19(1) (2022), 153-169.
[7] L. S. Chen, The KKT optimality conditions for optimization problem with interval-valued objective function on Hadamard manifolds, Optimization, (2020), 1-20.
[8] J. Chen, S. Al-Homidan, Q. H. Ansari, J. Li, Y. Lv, Robust necessary optimality conditions for nondifferentiable complex fractional programming with uncertain data, Journal of Optimization Theory and Applications, 189(1) (2021), 221-243.
[9] J. Chen, L. Huang, Y. Lv, C. F. Wen, Optimality conditions of robust convex multiobjective optimization via ε-constraint scalarization and image space analysis, Optimization, 69(9) (2020), 1849-1879.
[10] B. A. Dar, A. Jayswal, D. Singh, Optimality, duality and saddle point analysis for interval-valued nondifferentiable multiobjective fractional programming problems, Optimization, 70(5-6) (2021), 1275-1305.
[11] W. Dinkelbach, On nonlinear fractional programming, Management Science, 13(7) (1967), 492-498.
[12] E. Fathy, Building fuzzy approach with linearization technique for fully rough multi-objective multi-level linear fractional programming problem, Iranian Journal of Fuzzy Systems, 18(2) (2021), 139-157.
[13] N. A. Gadhi, F. Z. Rahou, M. El Idrissi, L. Lafhim, Optimality conditions of a set valued optimization problem with the help of directional convexificators, Optimization, 70(3) (2021), 575-590.
[14] M. A. Hejazi, S. Nobakhtian, Optimality conditions for multiobjective fractional programming, via convexificators, Journal of Industrial and Management Optimization, 16(2) (2020), 623.
[15] R. Horst, P. M. Pardalos, N. Van Thoai, Introduction to global optimization, Springer Science and Business Media, 2000.
[16] E. Hosseinzade, H. Hassanpour, The Karush-Kuhn-Tucker optimality conditions in interval-valued multiobjective programming problems, Journal of Applied Mathematics and Informatics, 29 (2011), 1157-1165.
[17] R. Jagannathan, On some properties of programming problems in parametric form pertaining to fractional programming, Management Science, 12(7) (1966), 609-615.
[18] R. Jagannathan, Duality for nonlinear fractional programs, Zeitschrift fur Operations Research, 17 (1973), 1-3.
[19] V. D. Pathak, U. M. Pirzada, Necessary and sufficient optimality conditions for nonlinear fuzzy optimization problem, International Journal of Mathematical Science Education, 4(1) (2011), 1-16.
[20] M. L. Puri, D. A. Ralescu, Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications, 91(2) (1983), 552-558.
[21] W. Rudin, Principles of mathematical analysis, New York: McGraw-hill, 3(2), 1976.
[22] P. Singh, D. Agarwal, D. Bhati, R. N. Mohapatra, A Branch-bound cut technique for non-linear fractional multiobjective optimization problems, International Journal of Applied and Computational Mathematics, 6(2) (2020), 1-17.
[23] D. Singh, B. A. Dar, D. S. Kim, KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions, European Journal of Operational Research, 254(1) (2016), 29-39.
[24] L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Sets and Systems, 161(11) (2010), 1564-1584.
[25] T. V. Su, D. V. Luu, Higher-order Karush-Kuhn-Tucker optimality conditions for Borwein properly efficient solutions of multiobjective semi-infinite programming, Optimization, (2020), 1-27.
[26] L. T. Tung, Karush-Kuhn-Tucker optimality conditions and duality for multiobjective semi-infinite programming via tangential subdifferentials, Numerical Functional Analysis and Optimization, 41(6) (2020), 659-684.
[27] H. Z. Wei, C. R. Chen, S. J. Li, Necessary optimality conditions for nonsmooth robust optimization problems, Optimization, (2020), 1-21.
[28] H. C. Wu, Saddle point optimality conditions in fuzzy optimization problems, Fuzzy Optimization and Decision Making, 2(3) (2003), 261-273.
[29] H. C. Wu, The Karush-Kuhn-Tucker optimality conditions for the optimization problem with fuzzy-valued objective function, Mathematical Methods of Operations Research, 66(2) (2007), 203-224.
[30] H. C. Wu, The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function, European Journal of Operational Research, 176(1) (2007), 46-59.
[31] H. C. Wu, On interval-valued nonlinear programming problems, Journal of Mathematical Analysis and Applications, 338(1) (2007), 299-316.
[32] H. C. Wu, The optimality conditions for optimization problems with fuzzy-valued objective functions, Optimization, 57(3) (2008), 473-489.
[33] H. C. Wu, The optimality conditions for optimization problems with convex constraints and multiple fuzzy-valued objective functions, Fuzzy Optimization and Decision Making, 8(3) (2009), 295-321.
[34] H. C. Wu, The Karush-Kuhn-Tucker optimality conditions for multi-objective programming problems with fuzzyvalued objective functions, Fuzzy Optimization and Decision Making, 8(1) (2009), 1-28.
[35] H. C. Wu, The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with intervalvalued objective functions, European Journal of Operational Research, 196(1) (2009), 49-60.
[36] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338-353.
[37] H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1(1) (1978), 45-55.
[38] H. J. Zimmermann, Fuzzy set theory and its applications, (2nd Ed.), Kluwer-Nijhoff, Hinghum, 1991. | ||
|
آمار تعداد مشاهده مقاله: 426 تعداد دریافت فایل اصل مقاله: 409 |
||