Applying the lexicographic maximum solution of min-product fuzzy relational inequalities for finding the optimal pricing with a fixed priority in a supply chain system

Wu, Yan-Kuen; Wen, Ching Feng; Hsu, Yuan Teng; Xian, Wang Ming

doi:10.22111/ijfs.2023.44035.7759

Document Type : Research Paper

Authors

¹ *School of International Business, Shaoxing Key Laboratory of Intelligent Monitoring and Prevention of Smart City, Zhejiang Yuexiu University of Foreign Languages.

² Center for Fundamental Science and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwa

³ Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung, 80708, Taiwan, ROC

⁴ Research Center of Finance, Shanghai Business School, Shanghai, China

⁵ School of Digital Commerce, Zhejiang Yuexiu University of Foreign Languages

https://doi.org/10.22111/ijfs.2023.44035.7759

Abstract

Fuzzy relational inequalities composed by the min-product operation are established to model the optimal pricing with fixed priority in a single product supply chain system. The solution algorithm has been proposed for solving such an optimization problem and finding the optimal solution (is called lexicographic maximum solution). In this study, a novel approach is proposed to finding the optimal pricing with fixed priority in a single product supply chain system. This approach is based on new properties of solution set in a min-product fuzzy relational inequality. These new properties allow us directly determine the optimal value of variable without many duplicate checks in the solution procedure. A numerical example is provided to illustrate the procedure.

Keywords

Main Subjects

Optimization

References

[1] S. Aliannezhadi, A. A. Molai, Geometric programming with a single-term exponent subject to bipolar max-product
fuzzy relation equation constraints, Fuzzy Sets and Systems, 397 (2020), 61-83.

[2] Z. L. Chai, Solving fuzzy relation equations with max-continuous t-norm composition graphically, 2015 12th Inter-
national Conference on Fuzzy Systems and Knowledge Discovery (FSKD). DOI:10.1109/fskd.2015.7381937.

[3] Y. L. Chiu, S. M. Guu, J. Yu, Y. K. Wu, A single-variable method for solving min-max programming problem with
addition-min fuzzy relational inequalities, Fuzzy Optimization and Decision Making, 18 (2019), 433-449.

[4] A. Di Nola, S. Sessa, W. Pedrycz, E. Sanchez, Fuzzy relation equations and their applications in knowledge engi-
neering, Kluwer Academic Publishers, Dordrecht, Boston, London, 1989.

[5] S. C. Fang, G. Li, Solving fuzzy relation equations with a linear objective function, Fuzzy Sets and Systems, 103
(1999), 107-113.

[6] M. J. Fernandez, P. Gil, Some speci c types of fuzzy relation equations, Information Sciences, 164 (2004), 189-195.

[7] S. Freson, B. De Baets, H. De Meyer, Linear optimization with bipolar max-min constraints, Information Sciences,
234 (2013), 3-15.

[8] A. Ghodousian, An algorithm for solving linear optimization problems subjected to the intersection of two fuzzy
relational inequalities de ned by Frank family of t-norms, International Journal in Foundations of Computer Science
and Technology, 8(3) (2018), 1-20.

[9] A. Ghodousian, Optimization of linear problems subjected to the intersection of two fuzzy relational inequalities
de ned by Dubois-Prade family of t-norms, Information Sciences, 503 (2019), 291-306.

[10] A. Ghodousian, E. Khorram, Linear optimization with an arbitrary fuzzy relational inequality, Fuzzy Sets and
Systems, 206 (2012), 89-102.

[11] A. Ghodousian, M. Raeisian Parvari, A mod ed PSO algorithm for linear optimization problem subject to the
generalized fuzzy relational inequalities with fuzzy constraints (FRI-FC), Information Sciences, 418 (2017), 317-345.

[12] F. F. Guo, L. P. Pang, D. Meng, Z. Q. Xia, An algorithm for solving optimization problems with fuzzy relational
inequality constraints, Information Sciences, 252 (2013), 20-31.

[13] 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 Systems, 25(4) (2017), 985-992.

[14] G. J. Klir, B. Yuan, Fuzzy sets and fuzzy logic theory and applications, Prentice Hall PTR, Pearson Education,
Inc., 1995.

[15] P. Li, S. C. Fang, On the resolution and optimization of a system of fuzzy relational equations with sup-T compo-
sition, Fuzzy Optimization and Decision Making, 7 (2008), 169-214.

[16] P. Li, Y. Liu, Linear optimization with bipolar fuzzy relational equation constraints using the Lukasiewicz triangular
norm, Soft Computing, 18 (2014), 1399-1404.

[17] J. X. Li, S. J. Yang, Fuzzy relation inequalities about the data transmission mechanism in Bit-Torrent-like Peer-to-
Peer le sharing systems, 2012 9th International Conference on Fuzzy systems and Knowledge Discovery (FSKD),
(2012), 452-456. DOI:10.1109/fskd.2012.6233956.

[18] J. L. Lin, Y. K. Wu, S. M. Guu, On fuzzy relational equations and the covering problem, Information Sciences, 181
(2011), 2951-2963.

[19] H. T. Lin, X. B. Yang, H. M. Guo, C. F. Zheng, X. P. Yang, Maximin optimization problem subject to min-
product fuzzy relation inequalities with application in supply and demand scheme, Complexity, (2019), 13 pages.
DOI:10.1155/2019/4960638.

[20] C. C. Liu, Y. Y. Lur, Y. K. Wu, Linear optimization of bipolar fuzzy relational equations with max- Lukasiewicz
composition, Information Sciences, 360 (2016), 149-162.

[21] J. Loetamonphong, S. C. Fang, An ecient solution procedure for fuzzy relation equations with max-product com-
position, IEEE Transactions on Fuzzy Systems, 7(4) (1999), 441-445.

[22] A. A. Molai, E. Khorram, An algorithm for solving fuzzy relation equations with max-T composition operator,
Information Sciences, 178 (2008), 1293-1308.

[23] K. Peeva, Resolution of fuzzy relational equations-method, algorithm and software with applications, Information
Sciences, 234 (2013), 44-63.

[24] B. S. Shieh, Solutions of fuzzy relation equations based on continuous t-norms, Information Sciences, 177 (2007),
4208-4215.

[25] B. S. Shieh, New resolution of nite fuzzy relation equations with max-min composition, International Journal of
Uncertainty, Fuzziness and Knowledge-Based Systems, 16(1) (2008), 19-33.

[26] B. S. Shieh, Minimizing a linear objective function under a fuzzy max-t-norm relation equation constraint, Infor-
mation Sciences, 181 (2011), 832-841.

[27] E. Shivania, E. Khorram, Optimization of linear objective function subject to fuzzy relation inequalities constraints
with max-product composition, Iranian Journal of Fuzzy Systems, 7(3) (2010), 51-71.

[28] G. B. Stamou, S. G. Tzafestas, Resolution of composite fuzzy relation equations based on Archimedean triangular
norms, Fuzzy Sets and Systems, 120 (2001), 395-407.

[29] V. L. Tiwari, A. Thapar, Covering problem for solutions of max-Archimedean bipolar fuzzy relation equations,
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 28(4) (2020), 613-634.

[30] Y. K. Wu, S. M. Guu, An ecient procedure for solving a fuzzy relational equation with max-Archimedean t-norm
composition, IEEE Transactions on Fuzzy Systems, 16(1) (2008), 73-84.

[31] S. J. Yang, An algorithm for minimizing a linear objective function subject to the fuzzy relation inequalities with
addition-min composition, Fuzzy Sets and Systems, 255 (2014), 41-51.

[32] X. P. Yang, Solutions and strong solutions of min-product fuzzy relation inequalities with application in supply
chain, Fuzzy Sets and Systems, 384 (2020), 54-74.

[33] X. P. Yang, G. Z. Zheng, X. G. Zhou, B. Y. Cao, Lexicography minimum solution of fuzzy relation inequalities:
Applied to optimal control in P2P le sharing system, International Journal of Machine Learning and Cybernetics,
8(5) (2017), 1555-1563.

[34] X. P. Yang, X. G. Zhou, B. Y. Cao, Min-max programming problem subject to addition-min fuzzy relation inequal-
ities, IEEE Transactions on Fuzzy Systems, 24(1) (2016), 111-119.

[35] X. G. Zhou, X. P. Yang, B. Y. Cao, Posynomial geometric programming problem subject to max-min fuzzy relation
equations, Information Sciences, 328 (2016), 15-25.

[36] X. G. Zhou, X. G. Zhong, H. T. Lin, Z. J. Qin, X. P. Yang, Lexicographic maximum solution of min-product
fuzzy relation inequalities for modeling the optimal pricing with xed priority grade in supply chain, IEEE Access,
6 (2018), 71306-71316. DOI:10.1109/ACCESS.2018.2878748.

Applying the lexicographic maximum solution of min-product fuzzy relational inequalities for finding the optimal pricing with a fixed priority in a supply chain system

References

References

Volume 21, Issue 1January and February 2024Pages 19-31

Volume 21, Issue 1
January and February 2024
Pages 19-31