| 非可换模糊逻辑系统PL~*及其完备性 |
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| 引用本文： | 张小红.非可换模糊逻辑系统PL~*及其完备性[J].数学学报,2007,50(2):421-442. |
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| 作者姓名： | 张小红 |
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| 作者单位： | 宁波大学数学系,宁波315211 |
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| 基金项目： | 国家自然科学基金资助项目（60474022）;浙江省自然科学基金资助项目（Y605389） |
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| 摘 要： | 首先建立了非可换R_0t-模,以此为语义背景将模糊逻辑形式系统L~*拓广到非可换情形,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PR_0t-模及PL~*系统可能的应用方向．
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| 关 键 词： | 伪t-模 非可换模糊逻辑 正规素滤子定理 |
| 文章编号： | 0583-1431（2007）02-0421-22 |
| 收稿时间： | 2005-8-26 |
| 修稿时间： | 2005-08-24 |
Non-Commutative Fuzzy Logic System PL~* and Its Completeness |
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| Xiao Hong ZHANG.Non-Commutative Fuzzy Logic System PL~* and Its Completeness[J].Acta Mathematica Sinica,2007,50(2):421-442. |
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| Authors: | Xiao Hong ZHANG |
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| Institution: | Department of Mathematics, Faculty of Sciences, Ningbo University, Ningbo 315211, P. R. China |
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| Abstract: | Firstly,non-commutative R_0 t-norms (called PR_0 t-norms) are established, and based on PR_0 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. |
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| Keywords: | pseudo-t-norm non-commutative fuzzy logic normal prime filter theorem |
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