广义弗雷格方程的两类模糊蕴涵解  

Two Types of FuzzyImp lication Solutions of Generalized Frege’s Equation

作　　者：刘夏夏 宗浩 张凤霞[1] LIUXiaxia;ZONGHao;ZHANGFengxia(School of Mathematics Science,Liaocheng University,Liaocheng252059,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《聊城大学学报（自然科学版）》2025年第1期147-158,共12页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金项目(12171220);聊城大学强特色学科建设-智能科学与技术项目(319462208)资助

摘　　要：由于模糊蕴涵是经典(布尔)蕴涵的推广,探究布尔定律在模糊环境下成立的条件是必要的。在模糊环境下,布尔定律将作为函数方程或函数不等式进行研究,这被称为类布尔定律。在模糊数学领域,特别是在模糊逻辑的框架内,类布尔定律中的广义弗雷格定律因其在模糊控制系统,模糊关系方程等方面的应用,近几年已经得到广泛的关注和研究。本文旨在基于Cruz,Peng以及Zhang等人的研究工作,进一步研究两类模糊蕴涵,即常见的一致模剩余蕴涵和生成蕴涵,是否满足广义弗雷格方程,并刻画使方程成立的模糊蕴涵结构。这项工作将进一步丰富广义弗雷格方程的研究成果,并为相关应用领域提供更多的算子选择空间。As fuzzy implication serves as a generalization of classical(Boolean)implication,it is essential to investigate the conditions which Boolean Law holds in fuzzy environment.In this setting,Boolean laws will be examined as functional equations or inequalities,referred to as Boolean-like laws.Within the realm of fuzzy mathematics particularly in the iramework of fuzzy logic the generalized Frege's law among t hese Boolean-like laws has garnered significant attention and research interest in recent years due to its ap plications in fuzzy control systems and fuzzy relational equations.Building upon the foundational work by Cruz,Peng,and Zhang et al.,this paper seeks to further investigate whether the generalized Frege’s e quation holds for t wo specific types of fuzzy implications:namely,the residual implications derived from common uninorms and generated implications.Additionally,we aim to characterize the structure of those implications that satisfy this equation.This study not only aims to enrich research on the generalized Frege's equation but also intends to expand operator selection options for related application domains.

关 键 词：一致模剩余蕴涵 生成蕴涵 广义弗雷格方程 

分 类 号：O159[理学—数学] O231[理学—基础数学]