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

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

Mathematics, 2025, vol. 13, issue 10, 1-22

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.

Keywords: peer-to-peer model; method for relative fluctuations; method for absolute fluctuations; interval solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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