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WBR_0-代数成为Boole代数的条件

Conditions for WBR_0-algebras to be Boolean Algebras
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摘要 在WBR_0-代数中引入了蕴涵式条件(Imp)和可分解性条件(Dis),证明了在WBR_0-代数中这两个条件等价。引入了(正定)关联WBR_0-代数概念,并证明了满足(Imp)条件的WBR_0-代数与(正定)关联BR0-代数等价。我们也证明了蕴涵式WBR_0-代数与Boole代数等价,由此获得了WBR_0-代数成为Boole代数的四个充要条件。 In WBR0-algebras,we introduced the implication type condition(Imp)and dissoluble condition(Dis).It is proved that in WBR_0-algebras,the two conditions are equivalent.We also introduced the concept of(positive)implicative WBR0-algebras.It is proved that implication type WBR0-algebras are equivalent to(positive)implicative BR0-algebras.We also proved that implication type WBR0-algebras are equivalent to Boolean algebras,obtaining four necessary and sufficient conditions for WBR0-algebras to be Boolean algebras.
作者 凌雪岷 徐罗山 杨凌云 LING Xue-min;XU Luo-shan;YANG Ling-yun(Department of Common Education, Anhui Xinhua University, Hefei 230011, China;Department of Mathematics, Yangzhou University, Yangzhou 225002, China;Schoolof Mathematics and Statistics,Jiangsu Normal University,Xuzhou 222116 ,China)
出处 《模糊系统与数学》 北大核心 2018年第3期16-22,共7页 Fuzzy Systems and Mathematics
基金 国家自然科学基金资助项目(11671008 61300153) 江苏省高校自然科学基金资助项目(15KJD110006) 江苏高校品牌专业建设工程项目(PPZY2015B109 PPZY2015A013) 安徽省质量工程一般项目(2017jyxm30)
关键词 BOOLE代数 WBR0-代数 蕴涵式条件 可分解条件 Boolean Algebra WBR0-algebra Implication Type Condition Dissoluble Condition
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  • 1吴洪博,王小敏,韩诚.L^*系统中的模糊演绎定理的改进形式[J].四川大学学报(自然科学版),2005,42(1):27-32. 被引量:8
  • 2吴望名.关于模糊逻辑的—场争论[J].模糊系统与数学,1995,9(2):1-10. 被引量:58
  • 3吴洪博.修正的Kleene系统中广义重言式理论[J].中国科学:E辑,2001,44(3):233-238.
  • 4Yang Xu, Da Ruan, Key Qin, Jun Liu. Lattice-valued Logic[M]. Germany: Springer-Verlag, Berlin Heidelberg, 2003
  • 5Petr. Hajek. Metamathematics of Fuzzy Logic[M]. Netherlands: Kluwer Academic Publishers, 1998
  • 6Wu Hong-bo. A kind of simplified formal deductive system L0^* for the system L^* [J]. Journal of Fuzzy Mathematics, 2001, 9(2): 365-381
  • 7吴洪博.模糊命题形式演算系统L^*及其重言式理论的研究[D].四川大学博士学位论文,2001
  • 8Zadeh L A. Outline of a new approach to the analysis of complex and decision processes [J]. IEEE Trans,Systems, Man and Cybernetics, 1973, 1: 28-44.
  • 9Wang Guo-jun. On the logic foundation of fuzzy reasoning [J]. Information Science, 1997, 177: 47-88.
  • 10Pert, Hajek. Metaanathematics of Fuzzy Logic [M]. Boston: Kluwer Academic Publishers, 1998.

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