基于左连续伪T-模的非可换模糊逻辑系统PUL＊  

Non-commutative Fuzzy Logic System PUL＊ Based on Left Continuous Pseudo T-norms

作　　者：张小红[1] 

机构地区：[1]宁波大学数学系,宁波浙江315211

出　　处：《数学进展》2007年第3期295-308,共14页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.60474022);浙江省自然科学基金(No.Y605389);宁波市青年基金(No.2005A620032)

摘　　要：对P.Hájek建立的模糊逻辑系统psMTL进行了扩充,基于一般左连续伪T-模提出了非可换模糊逻辑系统PUL＊,证明了它的可靠性定理.同时,以PUL＊系统的Lindenbaum代数结构为背景引入PUL＊.代数概念,建立了相应的滤子理论,得到PUL＊-代数的正规素滤子定理,借此证明了PUL＊系统的完备性.Based on left continuous pseudo t-norms,a new non-commutative fuzzy logic system PUL＊ is constructed as an extension of the fuzzy logic system psMTL which is proposed by P.Hájek.The soundness theorem of system PUL＊ is proved.Moreover,by the introducing the notion of PUL＊-algebras and constructing the normal prime filter theorem of PUL＊- algebras, the completeness of system PUL＊ is proved.

关 键 词：伪T-模 非可换模糊逻辑系统PUL＊ 正规素滤子定理 完备性 

分 类 号：O141.1[理学—数学] O153.1[理学—基础数学]