IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i10p1602-d1655078.html
   My bibliography  Save this article

Study of Educational Information Resource Download Quality with Optimal Symmetrical Interval Solution of Fuzzy Relation Inequality in the Format of a System of Differential Equations

Author

Listed:
  • Lei Zhang

    (School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China)

Abstract

The min–max fuzzy relation inequalities are currently considered for representing the place-to-place (P2P) education knowledge, including resource sharing from one terminal to another. One terminal is the acceptor—receiving information—while the other terminal is the sink resource for educational information sharing, acting like an extractor. In the current manuscript, the idea of sharing educational information is established in the form of a dynamical system in which the unknown quantities represent the quality of downloading educational resources on different terminals. The download quality, measured in bits per second (bps), has been converted to a fuzzy format as it oscillates from low to high. Every solution of the min–max dynamical model is surely an optimal interval approach in the corresponding terminal-to-terminal network sharing system. Such a solution implies the stability of the interval solution with fluctuations from the minimum (low) to maximum (high) values of the interval. Furthermore, like the objective function in the linear programming and stability of the system, we study the system with the maximum fluctuation for a given solution in the form of download quality educational informative resources. Further, the solution will be treated in optimal relative local regions (MRO) and global regions (MAO). Bi-approaches are constructed to solve these maximal symmetrical interval fuzzy solutions for our analysis. The illustrations show that the bi-approaches are valid and effective for the studied model.

Suggested Citation

  • Lei Zhang, 2025. "Study of Educational Information Resource Download Quality with Optimal Symmetrical Interval Solution of Fuzzy Relation Inequality in the Format of a System of Differential Equations," Mathematics, MDPI, vol. 13(10), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1602-:d:1655078
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/10/1602/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/10/1602/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Li, Bo & Liang, Houjun & He, Qizhi, 2021. "Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wu, Huagan & Gu, Jinxiang & Guo, Yixuan & Chen, Mo & Xu, Quan, 2024. "Biphasic action potentials in an individual cellular neural network cell," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Li, Bo & Liang, Houjun & Shi, Lian & He, Qizhi, 2022. "Complex dynamics of Kopel model with nonsymmetric response between oligopolists," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Li, Xiaoliang & Li, Bo & Liu, Li, 2023. "Stability and dynamic behaviors of a limited monopoly with a gradient adjustment mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Zorica Dodevska & Sandro Radovanović & Andrija Petrović & Boris Delibašić, 2023. "When Fairness Meets Consistency in AHP Pairwise Comparisons," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    5. Hu, Dongpo & Ma, Linyi & Song, Zigen & Zheng, Zhaowen & Cheng, Lifang & Liu, Ming, 2024. "Multiple bifurcations of a time-delayed coupled FitzHugh–Rinzel neuron system with chemical and electrical couplings," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    6. Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2023. "A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets," Mathematics, MDPI, vol. 11(2), pages 1-26, January.
    7. Qian, Jiamin & Chen, Lincong, 2021. "Stochastic P-bifurcation analysis of a novel type of unilateral vibro-impact vibration system," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    8. Li, Peiluan & Han, Liqin & Xu, Changjin & Peng, Xueqing & Rahman, Mati ur & Shi, Sairu, 2023. "Dynamical properties of a meminductor chaotic system with fractal–fractional power law operator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    9. Dongpo Hu & Xuexue Liu & Kun Li & Ming Liu & Xiao Yu, 2023. "Codimension-Two Bifurcations of a Simplified Discrete-Time SIR Model with Nonlinear Incidence and Recovery Rates," Mathematics, MDPI, vol. 11(19), pages 1-24, September.
    10. Abdelkader Moumen & Abdelaziz Mennouni, 2022. "A New Projection Method for a System of Fractional Cauchy Integro-Differential Equations via Vieta–Lucas Polynomials," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
    11. Najariyan, Marzieh & Qiu, Li, 2023. "Singular fuzzy fractional quadratic regulator problem," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    12. Kuznetsov, A.P. & Sedova, Y.V. & Stankevich, N.V., 2024. "Dynamics of non–identical coupled Chialvo neuron maps," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    13. Shi, Jian-Fei & Gou, Peng-Bing & Gou, Xiang-Feng & Jin, Wu-Yin & Chen, Guo-Long, 2025. "Rich hidden dynamics in a two-parameter plane for spur gear system," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1602-:d:1655078. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.