研究双极模糊关系方程在乘积t-范数下的解的存在性与结构。
Bipolar fuzzy relation equations systems based on the product t-norm
- 基于最大-乘积t-范数构建双极模糊关系方程系统
- 给出方程组可解性的判定条件及解集的代数结构
- 适用于需同时处理变量及其否定的人类推理场景
双极模糊关系方程是模糊关系方程的推广，同时考虑未知变量及其逻辑否定。变量与其否定同时出现能为人类推理起关键作用的框架提供有用信息。因此，求解双极模糊关系方程系统是一个重要研究方向。本文聚焦于基于最大-乘积t-范数组合的双极模糊关系方程系统，研究其可解性以及解集的代数结构，包括独立项为零的情况。本研究补充了作者此前关于双极最大-乘积模糊关系方程可解性的成果。
原文摘要 · Abstract (English)
Bipolar fuzzy relation equations arise as a generalization of fuzzy relation equations considering unknown variables together with their logical connective negations. The occurrence of a variable and the occurrence of its negation simultaneously can give very useful information for certain frameworks where the human reasoning plays a key role. Hence, the resolution of bipolar fuzzy relation equations systems is a research topic of great interest. This paper focuses on the study of bipolar fuzzy relation equations systems based on the max-product t-norm composition. Specifically, the solvability and the algebraic structure of the set of solutions of these bipolar equations systems will be studied, including the case in which such systems are composed of equations whose independent term be equal to zero. As a consequence, this paper complements the contribution carried out by the authors on the solvability of bipolar max-product fuzzy relation equations.
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