On the Best Approximate Solutions
of the Inverse Fuzzy Relational Equation
and Their Applications
报告专家：温庆丰 教授 （云林科技大学 ）
报告时间：1月22日（周四）15:30-16:30
报告地点：四川大学数学学院西109
报告摘要：
This study investigates the theoretical foundations and practical applications of deriving best approximate solutions to the inverse fuzzy relational equation (IFRE), which is defined as follows: Q ◦ A = I_n, where A is a given fuzzy matrix, Q is unknown, I_n is the identity matrix, and “◦” denotes the max–min composition. Determining the unknown matrix Q in IFRE is fundamental for enabling fuzzy abductive inference and backward reasoning. However, an exact fuzzy preinverse rarely exists unless the matrix A contains a permutation matrix of order n as a submatrix, thereby rendering most systems mathematically inconsistent. Consequently, this work focuses on computing best approximate preinverse matrices by minimizing the residual error vector. The associated optimization problems exhibit non-smoothness and non-convexity, presenting significant analytical challenges. From an application standpoint, the IFRE framework has been utilized to model the cognitive mechanisms of working memory. Previous studies have demon strated that integrating fuzzy Petri nets (FPN) with the Unified Particle Swarm Optimization (UPSO) algorithm enables the reconstruction of original encoding signals from EEG recordings collected during memory recall. This approach achieves a reconstruction accuracy of 87.92% while maintaining structural reciprocity and cognitive interpretability. However, UPSO-based methods are computationally intensive and typically yield only a single optimal solution. To overcome these limitations, our recent works introduce analytical methods for computing the best approximate preinverse matrices. In contrast to UPSObased numerical strategies, the proposed analytical framework provides substantially improved computational efficiency and yields the complete set of optimal solutions. This advancement not only deepens the theoretical understanding of IFRE solvability but also strengthens the applicability of IFRE-based modeling in cognitive science and intelligent system design.
专家简介：
温庆丰，2003年于台湾成功大学获得博士学位，2013年被高雄医科大学基础科学研究中心聘为教授，历任基础科学研究中心和非线性分析与优化研究中心主任，现任云林科技大学教授。其研究领域包括最优化、非线性分析、Fuzzy集理论及应用等。目前已在国际重要学术期刊上发表论文多篇，担任多个SCI收录期刊的编委和客座编辑，曾多次应邀参加国际学术会议并作报告。2011年-2024年连续获得高雄医科大学杰出研究奖。
邀请人：黄南京
