Fuzzy implication based on power of continuous T-conorm
ZONG Hao
LIU Xiaxia
ZHANG Fengxia
Abstract：Approximate reasoning plays a crucial role in many fields such as fuzzy control,image process-ing,and data mining.In the reasoning process,it is often required that when the same linguistic modifiers are added to the antecedent and consequent of a reasoning rule,the truth value of the rule remains un-changed.This requires that the operator reflecting the reasoning process,namely,fuzzy implication,has power invariance.T-power based implication,as an important class of fuzzy implications satisfying this property,is obtained by generalizing Zadeh's linguistic powering modifiers to relax the consequent.In-spired by this method,by generalizing Zadeh's linguistic powering modifiers to relax the antecedent,a class of fuzzy implications based on the powers of continuous t-conorms,namely,S-power based implica-tion,is proposed.The research about the properties and characterization of S-power based implication as well as its relationship with common classes of fuzzy implications,shows that S-power based implication is a new class of fuzzy implications,and most of its members satisfy power invariance with respect to contin-uous t-conorms.In addition,the research on the generalized hypothetical syllogism(GHS)in the reason-ing mechanism of S-power implication,will further provide a theoretical basis for the research on applica-tions such as fuzzy control,image processing,and data mining.
Keywords：fuzzy implicationpowers of continuous t-conormsT-power based implicationS-power based implication
Publication Date：2025-06-25
Online Publishing Date：2026-08-28(First online date of this platform, not the publication date of the document)
Pages：13( 333-345 )