Null set concept for optimal solutions of fuzzy nonlinear optimization problems

[1] A. Akrami, M. M. Hosseini, M. Karbassi, An efficient method for solving a class of nonlinear fuzzy optimization
problems, Journal of Mathematical Extension, 10(2) (2016), 101-116.

[2] M. Alshammari, M. Al-Smadi, O. A. Arqub, I. Hashim, Residual series representation algorithm for solving fuzzy
duffing oscillator equations, Symmetry, 12(4) (2020), 572. https://doi.org/10.3390/sym12040572

[3] O. A. Arqub, Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations,
Neural Computing and Applications, 28 (2017), 1591-1610. https://doi.org/10.1007/s00521-015-2110-x

[4] O. A. Arqub, J. Singh, M. Alhodaly, Adaptation of kernel functions-based approach with Atangana-Baleanu-Caputo
distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations, Mathematical
Methods in the Applied Sciences, (2021), 1-28. https://doi.org/10.22541/au.160373702.28850586/v1

[5] O. A. Arqub, J. Singh, B. Maayah, M. Alhodaly, Reproducing kernel approach for numerical solutions of fuzzy
fractional initial value problems under the Mittag-Leffler kernel differential operator, Mathematical Methods in the
Applied Sciences, (2021) 1-22. https://doi.org/10.1002/mma.7305

[6] M. S. Bazaraa, H. D. Sherali, C. M. Shetty, Nonlinear programming: Theory and algorithms, John Wiley and Sons,
2013.

[7] S. K. Behera, J. R. Nayak, Optimal solution of fuzzy nonlinear programming problems with linear constraints,
International Journal of Advances in Science and Technology, 4(2) (2012), 43-92.

[8] R. E. Bellman, L. A. Zadeh, Decision-making in a fuzzy environment, Management Science, 17(4) (1970), 141-164.
https://doi.org/10.1287/mnsc.17.4.B141

[9] 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. https://doi.org/10.22111/IJFS.
2022.6558

[10] Y. Chalco-Cano, W. A. Lodwick, R. Osuna-G´omez, A. Rufi´an-Lizana, The Karush-Kuhn-Tucker optimality conditions
for fuzzy optimization problems, Fuzzy Optimization and Decision Making, 15(1) (2016), 57-73. https:
//doi.org/10.1007/s10700-015-9213-9

[11] A. Compaor´e, K. Som´e, B. Som´e, New approach to the resolution of triangular fuzzy linear program: MOMAplus
method, International Journal of Applied Mathematical Research, 6(4) (2017), 115-120. https://doi.org/10.
14419/ijamr.v6i4.8069

[12] M. Deb, P. K. De, A note on fuzzy multi-objective linear fractional programming problem, International Journal of
Computer Science and Network, 3(6) (2014), 568-572.

[13] B. Dharmaraj, S. Appasamy, Application of a modified Gauss elimination technique for separable fuzzy nonlinear
programming problems, Mathematical Modelling of Engineering Problems, 10(4) (2023), 1481-1486. https://doi.
org/10.18280/mmep.100445

[14] R. Horst, P. M. Pardalos, N. V. Thoai, Introduction to global optimization, 2nd Edition Kluwer Academic Publishers,
Boston, 2000.

[15] A. F. Jameel, A. Sadeghi, Solving nonlinear programming problem in fuzzy environment, International Journal of
Contemporary Mathematical Sciences, 7(4) (2012), 159-170.

[16] A. Kumar, J. Kaur, Fuzzy optimal solution of fuzzy linear programming problems with inequality constraints,
International Journal of Mathematical and Computer Sciences, 6(1) (2010), 37-40. https://doi.org/10.1007/
978-3-319-31274-3_3

[17] S. H. Nasseri, Fuzzy nonlinear optimization, Journal of Nonlinear Sciences and Applications, 1(4) (2008), 230-235.
https://doi.org/10.22436/jnsa.001.04.05

[18] V. D. Pathak, U. M. Pirzada, Necessary and sufficient optimality conditions for nonlinear fuzzy optimization
problem, International Journal of Mathematical Science Education Techno-mathematics Research Foundation, 4(1)
(2011), 1-16.

[19] M. L. Puri, D. A. Ralescu, Fuzzy random variables, Journal of Mathematical Analysis and Applications, 114
(1986), 409-422. https://doi.org/10.1016/0022-247X(86)90093-4

[20] S. Saghi, A. Nazemi, S. Effati, M. Ranjbar, Simplex algorithm for hesitant fuzzy linear programming problem with
hesitant cost coefficient, Iranian Journal of Fuzzy Systems, 20(1) (2023), 137-152. https://doi.org/10.22111/
IJFS.2023.7351

[21] J. C. Sama, K. Som´e, A. Compaor´e, Hybrid approach for solving fractional linear optimization problems, Annals
of Fuzzy Mathematics and Informatics, 25(2) (2023), 111-123. https://doi.org/10.30948/afmi.2023.25.2.111

[22] N. R. Shankar, G. Ananda-Rao, J. Madh-Latha, V. Sireesha, Solving a fuzzy nonlinear optimization problem by
genetic algorithm, International Journal of Contemporary Mathematical Sciences, 5(16) (2010), 791-803.

[23] J. Tang, D.Wang, Modelling and optimization for a type of fuzzy nonlinear programming problems in manufacturing
systems, Proceedings of the 35th Conference on Decision and Control, 1996. https://doi.org/10.1109/CDC.1996.
577485

[24] H. Tsai, T. R. Chen, A fuzzy nonlinear programming approach for optimizing the performance of a four-objective
fluctuation smoothing rule in a wafer fabrication factory, Journal of Applied Mathematics, 2013 (2013), 1-15.
https://doi.org/10.1155/2013/720607

[25] P. Umamaheswari, K. Ganesan, A solution approach to fuzzy nonlinear programming problems, International Journal
of Pure and Applied Mathematics, 113(13) (2017), 291-300.

[26] H. C. Wu, Saddle point optimality conditions in fuzzy optimization problems, Fuzzy Optimization and Decision
Making, 2 (2003), 261-273. https://doi.org/10.1023/A:1025098722162

[27] H. C. Wu, A solution concept for fuzzy multiobjective programming problems based on convex cones, Journal of
Optimization Theory and Applications, 121 (2004), 397-417. https://doi.org/10.1023/B:JOTA.0000037411.
25509.6a

[28] H. C.Wu, On interval-valued nonlinear programming problems, Journal of Mathematical Analysis and Applications,
338 (2008), 299-316. https://doi.org/10.1016/j.jmaa.2007.05.023

[29] H. C. Wu, Solution of fuzzy multiobjective programming problems based on the concept of scalarization, Journal of
Optimization Theory and Applications, 139 (2008), 361-378. https://doi.org/10.1007/s10957-008-9419-x

[30] H. C. Wu, The optimality conditions for optimization problems with fuzzy-valued objective functions, Fuzzy Optimization
and Decision Making, 8 (2009), 295-321. https://doi.org/10.1080/02331930601120037

[31] H. C. Wu, The Karush-Kuhn-Tucker optimality conditions for multi-objective programming problems with
fuzzy-valued objective, Fuzzy Optimization and Decision Making, 8 (2009), 1-28. https://doi.org/10.1007/
s10700-009-9049-2

[32] H. C. Wu, Applying the concept of null set to solve the fuzzy optimization problems, Fuzzy Optimization and
Decision Making, 18 (2019), 279-314. https://doi.org/10.1007/s10700-018-9299-y

[33] L. A. Zadeh, The concept of linguistic variable and its application to approximate reasoning I, Information Sciences,
8 (1975), 199-249. https://doi.org/10.1016/0020-0255(75)90036-5

[34] L. A. Zadeh, The concept of linguistic variable and its application to approximate reasoning II, Information Sciences,
8 (1975), 301-357. https://doi.org/10.1016/0020-0255(75)90046-8

[35] L. A. Zadeh, The concept of linguistic variable and its application to approximate reasoning III, Information
Sciences, 9 (1975), 43-80. https://doi.org/10.1007/978-1-4684-2106-4_1