非可换模糊逻辑系统PL~*及其完备性  

Non-Commutative Fuzzy Logic System PL~* and Its Completeness

作　　者：张小红[1] 

机构地区：[1]宁波大学数学系,宁波315211

出　　处：《数学学报（中文版）》2007年第2期421-442,共22页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(60474022);浙江省自然科学基金(Y605389)

摘　　要：首先建立了非可换R0 t-模，以此为语义背景将模糊逻辑形式系统L^＊拓广到非可磬情形，提出了新的模糊逻辑形式系统PL^＊，证明了系统PL^＊的可靠性定理．其次，引入PL^＊-代数及其滤子概念，得到PL^＊-代数的正规素滤子定理，借此证明了PL^＊系统的完备性．最后说明了PR0 t-模及PL^＊系统可能的应用方向．Firstly, non-commutative R0 t-norms （called PRo t-norms） are established, and based on PRo t-norms a new fuzzy logic formal system PL^＊ is constructed as a non-commutative generalization of the formal system L^＊. The soundness theorem of PL^＊ is proved. Secondly, the notion of PL^＊-algebra is introduced, and the filter theory of PL^＊-algebra is constructed. By the normal prime filter theorem of PL^＊-algebra, the completeness theorem of formal system PL^＊ is proved. Finally, the role of formal system PL^＊ in application field is explained.

关 键 词：伪T-模 非可换模糊逻辑 正规素滤子定理 

分 类 号：O141.1[理学—数学] O153.1[理学—基础数学]