A New Approach Utilizing Addition-Min Composition in a Two-Sided Fuzzy Relation

Authors

  • Narjes Amiri Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran.
  • Hadi Nasseri Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran.
  • Davood Darvishi Salookolaei * Department of Applied Mathematics, Payame Noor University, Tehran, Iran. https://orcid.org/0000-0001-5039-2469

https://doi.org/10.48314/anowa.v1i1.36

Abstract

This study focuses on the bilateral requirements of terminals within a Peer-To-Peer (P2P) network system, specifically examining two-sided fuzzy relation inequalities using addition-min composition. Each solution derived from this two-sided fuzzy relation system represents a viable flow control strategy for the associated P2P network. The main topics covered include 1) identifying a minimal solution that is less than or equal to a specified solution, 2) identifying a maximal solution that is greater than or equal to a specified solution, and 3) outlining the structure of the solution set for the fuzzy relation system. The goals of 1) and 2) are to pinpoint particular minimal or maximal solutions within the two-sided system. We introduce two algorithms, Algorithm I and II, to determine these specific minimal and maximal solutions with polynomial computational complexities. Their effectiveness is demonstrated through various numerical examples. It is observed that all minimal and maximal solutions can entirely characterize the complete solution set for the two-sided system, and it may also be non-convex.

Keywords:

Addition-min composition, Fuzzy relation inequality, Maximal solutions, Two-sided

References

  1. [1] Sanchez, E. (1976). Resolution of composite fuzzy relation equations. Information and control, 30(1), 38–48. https://B2n.ir/xm7761
  2. [2] Fang, B. W. (2022). Minimizing a linear objective function under a max-overlap function fuzzy relational equation constraint. Fuzzy sets and systems, 447, 1–21. https://doi.org/10.1016/j.fss.2021.12.005
  3. [3] Guo, F. F., & Shen, J. (2020). A novel smoothing approach for linear objective optimizations subject to fuzzy relation inequalities with addition-min composition. IEEE transactions on fuzzy systems, 29(8), 2444–2450. https://doi.org/10.1109/TFUZZ.2020.2991304
  4. [4] Li, J. X., & Yang, S. (2012). Fuzzy relation inequalities about the data transmission mechanism in bittorrent-like peer-to-peer file sharing systems. 2012 9th international conference on fuzzy systems and knowledge discovery (pp. 452–456). IEEE. https://doi.org/10.1109/FSKD.2012.6233956
  5. [5] Li, P., & Fang, S. C. (2008). On the resolution and optimization of a system of fuzzy relational equations with sup-T composition. Fuzzy optimization and decision making, 7, 169–214. https://doi.org/10.1007/s10700-008-9029-y
  6. [6] Hanif, R., Mustafa, S., Iqbal, S., & Piracha, S. (2023). A study of time series forecasting enrollments using fuzzy interval partitioning method. Journal of computational and cognitive engineering, 2(2), 143–149. https://doi.org/10.47852/bonviewJCCE2202159
  7. [7] Pérez-Canedo, B., & Verdegay, J. L. (2023). On the application of a lexicographic method to fuzzy linear programming problems. Journal of computational and cognitive engineering, 2(1), 47–56. https://doi.org/10.47852/bonviewJCCE20235142025
  8. [8] Yang, X. P. (2020). Leximax minimum solution of addition-min fuzzy relation inequalities. Information sciences, 524, 184–198. https://doi.org/10.1016/j.ins.2020.03.047
  9. [9] Yang, X. P., Lin, H. T., Zhou, X. G., & Cao, B. Y. (2018). Addition-min fuzzy relation inequalities with application in BitTorrent-like Peer-to-Peer file sharing system. Fuzzy sets and systems, 343, 126–140. https://doi.org/10.1016/j.fss.2017.04.002
  10. [10] Mi, X., & Wang, X. (2021). Minimal solutions of fuzzy relation inequalities with addition-min composition. Journal of intelligent & fuzzy systems, 41(6), 6089–6095. https://doi.org/10.3233/JIFS-202590
  11. [11] Yang, X., & Wang, Z. (2023). Two-sided fuzzy relation inequalities with addition-min composition. Alexandria engineering journal, 64, 483–491. https://doi.org/10.1016/j.aej.2022.09.009

Downloads

Published

2025-02-25

Issue

Vol. 1 No. 1 (2025): Annals of Optimization With Applications (ANOWA)

Section

Articles

How to Cite

A New Approach Utilizing Addition-Min Composition in a Two-Sided Fuzzy Relation. (2025). Annals of Optimization With Applications, 1(1), 32-40. https://doi.org/10.48314/anowa.v1i1.36

Similar Articles

You may also start an advanced similarity search for this article.