A new matrix-based-algorithm for solving latticized linear programming subject to max-min-product fuzzy relation inequalities

[1] A. Abbasi Molai, A new algorithm for resolution of the quadratic programming problem with fuzzy relation inequality
constraints, Computers and Industrial Engineering, 72 (2014), 306-314. http://dx.doi.org/10.1016/j.cie.2014.
03.024

[2] A. Abbasi Molai, S. Aliannezhadi, Linear fractional programming problem with max-Hamacher FRI, Iranian
Journal of Science and Technology, Transactions A: Science, 42 (2018), 693-705. https://doi.org/10.1007/
s40995-016-0108-6

[3] S. Aliannezhadi, A. Abbasi Molai, Geometric programming with a single-term exponent subject to bipolar maxproduct
fuzzy relation equation constraints, Fuzzy Sets and Systems, 397 (2020), 61-83. https://doi.org/10.
1016/j.fss.2019.08.012

[4] A. Ghodousian, Optimization of linear problems subjected to the intersection of two fuzzy relational inequalities
defined by Dubois-Prade family of t-norms, Information Sciences, 503 (2019), 291-306. https://doi.org/10.1016/
j.ins.2019.06.058

[5] A. Ghodousian, A. Babalhavaeji, An efficient genetic algorithm for solving nonlinear optimization problems defined
with fuzzy relational equations and max- Lukasiewicz composition, Applied Soft Computing, 69 (2018), 475-492.
https://doi.org/10.1016/j.asoc.2018.04.029

[6] A. Ghodousian, M. S. Chopannavaz, Solving linear optimization problems subject to bipolar fuzzy relational equalities
defined with max-strict compositions, Information Sciences, 650 (2023), 1-19. https://doi.org/10.1016/j.ins.
2023.119696

[7] A. Ghodousian, M. Naeeimi, A. Babalhavaeji, Nonlinear optimization problem subjected to fuzzy relational equations
defined by Dubois-Prade family of t-norms, Computers and Industrial Engineering, 119 (2018), 167-180. https:
//doi.org/10.1016/j.cie.2018.03.038

[8] A. Ghodousian, B. Sepehri Rad, O. Ghodousian, A non-linear generalization of optimization problems subjected to
continuous max-t-norm fuzzy relational inequalities, Soft Computing, 28 (2024), 4025-4036. https://doi.org/10.
1007/s00500-023-09376-2

[9] S. M. Guu, Y. K. Wu, A linear programming approach for minimizing a linear function subject to fuzzy relational
inequalities with addition-min composition, IEEE Transactions on Fuzzy System, 25(4) (2017), 985-992. https:
//doi.org/10.1109/TFUZZ.2016.2593496

[10] S. M. Guu, Y. K. Wu, Multiple objective optimization for systems with addition-min fuzzy relational inequalities,
Fuzzy Optimization and Decision Making, 18 (2019), 529-544. https://doi.org/10.1007/s10700-019-09306-8

[11] M. Hosseinyazdi, The optimization problem over a distributive lattice, Journal of Global Optimization, 41 (2008),
283-298. https://doi.org/10.1007/s10898-007-9230-5

[12] P. Li, S. C. Fang, Latticized linear optimization on the unit interval, IEEE Transactions on Fuzzy Systems, 17(6)
(2009), 1353-1365. https://doi.org/10.1109/TFUZZ.2009.2031561

[13] H. Li, Y. Wang, A matrix approach to latticized linear programming with fuzzy-relation inequality constraints, IEEE
Transactions on Fuzzy Systems, 21(4) (2013), 781-788. https://doi.org/10.1109/TFUZZ.2012.2232932

[14] J. X. Li, S. J. Yang, Fuzzy relation inequalities about the data transmission mechanism in BitTorrent-like Peer-to-
Peer file sharing systems, Proceedings of the 2012 9th International Conference on Fuzzy Systems and Knowledge
Discovery, FSKD (2012).

[15] D. Lobo, V. Lopez-Marchante, J. Medina, Reducing fuzzy relation equations via concept lattices, Fuzzy Sets and
Systems, 463 (2023), 1-21. https://doi.org/10.1016/j.fss.2022.12.021

[16] J. Qiu, X. P. Yang, Min-max programming problem with constraints of addition-min-product fuzzy relation
inequalities, Fuzzy Optimization and Decision Making, 21 (2022), 291-317. https://doi.org/10.1007/
s10700-021-09368-7

[17] E. Sanchez, Resolution of composite fuzzy relation equations, Information and Control, 30 (1976), 38-48. https:
//doi.org/10.1016/S0019-9958(76)90446-0

[18] I. Stankovic, Z. Jancic, M. Ciric, I. Micic, S. Stanimirovic, Two-mode weakly linear systems of fuzzy relation
equations: Structures of solutions, computation methods, and applications, Information Sciences, 686 (2025), 1-22.
https://doi.org/10.1016/j.ins.2024.121319

[19] D. Wang, K. Yu, X. Zhu, Z. Yu, Optimal solutions to granular fuzzy relation equations with fuzzy logic operations,
Applied Soft Computing, 47 (2008), 1-11. https://doi.org/10.1016/j.asoc.2024.111861

[20] P. Z. Wang, D. Z. Zhang, E. Sanchez, E. S. Lee, Latticized linear programming and fuzzy relation inequalities,
Journal of Mathematical Analysis and Applications, 159 (1991), 72-87. https://doi.org/10.1016/0022-247X(91)
90222-L

[21] Z. Wang, G. Zhu, X. P. Yang, Tri-composed fuzzy relation inequality with weighted-max-min composition and the
relevant min-max optimization problem, Fuzzy Sets and Systems, 489 (2024), 1-26. https://doi.org/10.1016/j.
fss.2024.109011

[22] Y. K. Wu, Optimizing the geometric programming problem with single-term exponents subject to max-min fuzzy
relational equation constraints, Mathematical and Computer Modlling, 47 (2008), 352-362. https://doi.org/10.
1016/j.mcm.2007.04.010

[23] X. P. Yang, Linear programming method for solving semi-latticized fuzzy relation geometric programming with
max-min composition, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 23(5) (2015),
781-804. https://doi.org/10.1142/S0218488515500348

[24] X. P. Yang, Optimal-vector-based algorithm for solving min-max programming subject to addition-min fuzzy relation
inequality, IEEE Transactions on Fuzzy Systems, 25(5) (2017), 1127-1140. https://doi.org/10.1109/TFUZZ.
2016.2598367

[25] X. P. Yang, Random-term-absent addition-min fuzzy relation inequalities and their lexicographic minimum solutions,
Fuzzy Sets and Systems, 440 (2022), 42-61. https://doi.org/10.1016/j.fss.2021.08.007

[26] X. P. Yang, Optimal pricing with weighted factors in a product transportation system based on the min-plus fuzzy
relation inequality, IEEE Transactions on Fuzzy Systems, 31(5) (2023), 1506-1517. https://doi.org/10.1109/
TFUZZ.2022.3201982

[27] J. Yang, B. Cao, Monomial geometric programming with fuzzy relation equation constraints, Fuzzy Optimization
and Decision Making, 6 (2007), 337-349. https://doi.org/10.1007/s10700-007-9017-7

[28] X. P. Yang, H. T. Lin, X. G. Zhou, B. Y. Cao, Addition-min fuzzy relation inequalities with application in
BitTorrent-like Peer-to-Peer file sharing system, Fuzzy Sets and Systems, 343 (2018), 126-140. https://doi.org/
10.1016/j.fss.2017.04.002

[29] X. P. Yang, X. G. Zhou, B. Y. Cao, Multi-level linear programming subject to addition-min fuzzy relation inequalities
with application in peer-to-peer file sharing system, Journal of Intelligent and Fuzzy Systems, 28(6) (2015), 2679-
2689. https://doi.org/10.3233/IFS-151546

[30] X. P. Yang, X. G. Zhou, B. Y. Cao, Single-variable term semi-latticized fuzzy relation geometric programming with
max-product operator, Information Sciences, 325 (2015), 271-287. https://doi.org/10.1016/j.ins.2015.07.015

[31] X. P. Yang, X. G. Zhou, B. Y. Cao, Latticized linear programming subject to max-product fuzzy relation inequalities
with application in wireless communication, Information Sciences, 358-359 (2016), 44-55. https://doi.org/10.
1016/j.ins.2016.04.014

[32] X. P. Yang, X. G. Zhou, B. Y. Cao, Min–max programming problem subject to addition-min fuzzy relation inequalities,
IEEE Transactions on Fuzzy Systems, 24 (2016), 1-9. https://doi.org/10.1109/TFUZZ.2015.2428716

[33] X. Zhou, R. Ahat, Geometric programming problem with single-term exponents subject to max-product fuzzy relational equations, Mathematical and Computer Modelling, 53 (2011), 55-62. https://doi.org/10.1016/j.mcm.
2010.07.018