Max-min fuzzy bi-level programming: resource sharing system with application

This study delves into the application of min-max fuzzy relation systems, specifically focusing on equality and inequality, in the examination of educational institution networks and their resource-sharing dynamics, akin to a P2P network structure. Expanding upon this framework, this article intricately explores a mathematical system featuring three or more terminals within an education resource system, each comprising distinct sharing capabilities. The terminals exchange information on various educational facets, encompassing variations and expenditures per share data, within the framework of a programming-type fuzzy objective function, constrained by the parameters of an educational information system. In these scenarios, the transfer of resources from one terminal to another is interlinked, introducing complexities that warrant a comprehensive examination. Notably, the consideration of greater downloading resources in specific cases is proposed for enhanced practicality. The primary objective of this article is to minimize network congestion within different educational networks, given fixed priority grades assigned to the terminals. To achieve this, the concept of a Lexicographic minimum solution is introduced to address max-min fuzzy relation inequalities, aligning with the defined objectives. The article presents a detailed and effective scenario for implementing the Lexicographic minimal solution. For validation purposes, the proposed scenario is supported by illustrative examples, offering tangible insights into its applicability and efficacy.