Two Types of Fuzzy Implication Solutions of
Generalized Frege’s Equation
LIU Xiaxia
ZONG Hao
ZHANG Fengxia
Abstract：As fuzzy implication serves as a generalization of classical(Boolean) implication，it is eaaential 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 framework of fuzzy logic -the generalized Frege’s law among these 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 two 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.
Keywords：residual implications of uninormsgenerated implicationsgeneralized Frege's equation
Publication Date：2025-02-27
Online Publishing Date：2026-08-28(First online date of this platform, not the publication date of the document)
Pages：12( 147-158 )