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Resolution of the sec-max-product fuzzy relation inequalities system and its lexicographic minimum solution

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Abstract

In this paper we consider the wireless Server-to-Client (S2C) network system with server peers and user (client) peers. The server peers provide the data resources to the user peers. In order to describe the wireless S2C network system in which there exists at least one candidate server for each user, we define and investigate the so-called sec-max-product fuzzy relation inequalities. Basic properties and the structure of the solution set have been studied for the sec-max-product fuzzy relation inequalities system. Moreover, the optimal solution under a lexicographic order, namely the lexicographic minimum solution, is further proposed and studied in the sec-max-product system, for minimizing all the variables under some fixed priority grade. An efficient resolution algorithm is developed for computing the lexicographic minimum solution of the sec-max-product system, with several illustrative examples.

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Funding

This study was funded by the National Natural Science Foundation of China (12471441, 12271132), the Guangdong Basic and Applied Basic Research Foundation (2024A1515010532, 2023A1515011093, 2022A1515011460) and the characteristic innovation project of Guangdong Universities (2022KTSCX074, 2023KQNCX041, 2024ZDZX1027).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, 524048, China

    Jianjun Qiu

  2. School of Humanities Education, Guangdong Innovative Technical College, Dongguan, 523960, China

    Guocheng Zhu

  3. School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610066, China

    Qianyu Shu

  4. School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China

    Xiaopeng Yang

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  1. Jianjun Qiu
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  2. Guocheng Zhu
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  3. Qianyu Shu
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Correspondence to Xiaopeng Yang.

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Xiaopeng Yang has received research grants from the National Natural Science Foundation of China. The authors declare that they have no Conflict of interest.

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Supported by the National Natural Science Foundation of China (12471441, 12271132), the Guangdong Basic and Applied Basic Research Foundation (2024A1515010532, 2023A1515011093, 2022A1515011460) and the characteristic innovation project of Guangdong Universities (2022KTSCX074, 2023KQNCX041, 2024ZDZX1027).

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Qiu, J., Zhu, G., Shu, Q. et al. Resolution of the sec-max-product fuzzy relation inequalities system and its lexicographic minimum solution. Comp. Appl. Math. 43, 439 (2024). https://doi.org/10.1007/s40314-024-02945-7

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  • DOI: https://doi.org/10.1007/s40314-024-02945-7

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