发表机构
University of Bojnord; University of Tehran（博尔诺德大学; 德黑兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出容许映射作为生成模糊子超空间的构造机制，证明极大容许映射类似经典基的作用，并在实数与有限超向量空间上给出示例，为超代数模糊建模奠定基础。
AI 中文摘要
模糊超向量空间为具有多值运算的代数系统中的分级不确定性提供了一个结构框架。本文引入并研究了容许映射，作为生成模糊子超空间的一种构造性机制。这些映射通过模糊点族来表示模糊子结构，并允许对生成元进行系统刻画。我们证明了极大容许映射以类似于经典线性理论中基的方式生成模糊子超空间，并在实数超向量空间和有限超向量空间上给出了示例，以阐明极大性的作用。所提出的方法有助于超代数环境中模糊建模的结构基础，并可能支持涉及分级和非确定性结构的软计算环境的进一步发展。
英文摘要
Fuzzy hypervector spaces provide a structural framework for modeling graded uncertainty in algebraic systems with multivalued operations. In this paper, we introduce and investigate admissible mappings as a constructive mechanism for generating fuzzy subhyperspaces. These mappings represent fuzzy substructures through families of fuzzy points and allow a systematic characterization of generators. We prove that maximal admissible mappings generate fuzzy subhyperspaces in a manner analogous to bases in classical linear theory, and we present examples over real and finite hypervector spaces to clarify the role of maximality. The proposed approach contributes to the structural foundations of fuzzy modeling in hyperalgebraic settings and may support further developments in soft computing environments involving graded and non-deterministic structures.
CommentsSubmitted to the journal
