Distributive equation of implications based on continuous triangular norms

被引：0
|
作者：
Qin, Feng [1 ,2 ]
Baczynski, Michal [3 ]
Xie, Aifang [4 ]
机构：
[1] Jiangxi Normal Univ, Coll Math & Informat Sci, Nanchang 330022, Jiangxi, Peoples R China
[2] Nanchang Hangkong Univ, Coll Math & Informat Sci, Nanchang 330063, Jiangxi, Peoples R China
[3] Univ Silesia, Inst Math, PL-40007 Katowice, Poland
[4] Shandong Univ, Sch Math, Jinan 250100, Peoples R China
来源：
PROCEEDINGS OF THE 7TH CONFERENCE OF THE EUROPEAN SOCIETY FOR FUZZY LOGIC AND TECHNOLOGY (EUSFLAT-2011) AND LFA-2011 | 2011年
基金：
中国国家自然科学基金;
关键词：
Combs methods; functional equations; fuzzy implication; t-norm; continuous t-norm; FUZZY RULE CONFIGURATION; DISJUNCTIVE UNINORMS;
D O I：
暂无
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In order to avoid combinatorial rule explosion in fuzzy reasoning, in this work we explore the distributive equations of implications. In details, by means of the section of I, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(x, T-1(y, z)) = T-2(I(x, y), I(x, z)), when T-1 is a continuous but not Archimedean triangular norm, T-2 is a continuous Archimedean triangular norm and I is an unknown function. Our methods of proof can be applied to the three other functional equations related closely to the distributive equation of implication.
引用
收藏
页码：246 / 253
页数：8
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