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积格上蕴涵算子的直积分解(英文)

Direct Decomposability of Implication Operators on Product Lattices
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摘要 进一步讨论蕴涵算子的直积分解,描述积格上可以分解为两个蕴涵算子直积的蕴涵算子的特性,并研究积格上S-蕴涵、R-蕴涵、n-反演R-蕴涵和n-反演QL-蕴涵的可分解性。 In this paper, we further discuss direct decompositions of implication operators and characterize the implication operator on a product lattice that is a direct product of two implication operators. Moreover, we study the direct decomposability of S-implications,R-implications,n-reciprocal R-implications and n-reciprocal QL-implications on a product lattice.
作者 王住登
机构地区 浙江万里学院数学研究所
出处 《模糊系统与数学》 CSCD 北大核心 2007年第6期13-17,共5页 Fuzzy Systems and Mathematics
基金 Natural Science Foundation of Zhejiang Province Education Commission Natural Science Foundation of Jiangsu Province Education Commission Science Foundation of Zhejiang Wanli University Science Foundation of Yancheng Teacher’s College
关键词 非经典逻辑 T-模 蕴涵 直积分解 Non-classical Logic t-norm Implication Direct Decomposition
分类号 O141.1 [理学—基础数学]
  • 相关文献

参考文献11

  • 1De Baets B,Mesiar R. Triangular norms on product lattices[J]. Fuzzy Sets and Systems, 1999, 104: 61-75.
  • 2Birkhoff G. Lattice theory[M]. Rhode Island:Amer. Math. Soc. Coll. Publ. ,1967.
  • 3Dubois D-Prade H. Fuzzy sets in approximate reasoning, part 1:inference with possibility distributions[J]. Fuzzy Sets and Systems, 1991,40: 143-202.
  • 4Fodor J C. Contrapositive symmetry of fuzzy implications[J]. Fuzzy Sets and Systems,1995, 69: 141-156.
  • 5Karacal F. On the direct decomposability of strong negations and S-implication operators on product lattices[J]. Information Sciences, 2006,176 : 3011 - 3025.
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  • 8Wang Z D. Generating pseudo-t-norms and implication operators[J]. Fuzzy Sets and Systems,2006,157:398- 410.
  • 9王住登.完备Brouwer格上伪t-模与蕴涵算子的注记(I)(英文)[J].模糊系统与数学,2006,20(1):107-111. 被引量：2
  • 10Wang Z D,Yu Y D. Pseudo-t-norms and implication operators on a complete Brouwerian lattice[J]. Fuzzy Sets and Systems, 2002,132: 113-124.

二级参考文献19

  • 1Baczynski M.Residual implications revisited.Notes on the Smets-Magrez Theorems[J].Fuzzy Sets and Systems,2004,145:267～277.
  • 2De Baets B,Mesiar R.Triangular norms on product lattices[J].Fuzzy Sets and Systems,1999,104:61～75.
  • 3Birkhoff G.Lattice theory[M].Rhode Island:Amer.Math.Soc.Coll.Publ.,1967.
  • 4Dubois D,Prade H.Fuzzy sets in approximate reasoning,part 1:inference with possibility distributions[J].Fuzzy Sets and Systems,1991,40:143～202.
  • 5Fodor J C.On fuzzy implications operators[J].Fuzzy Sets and Systems,1991,42:293～300.
  • 6Fodor J.C.Contrapositive symmetry of fuzzy implications[J].Fuzzy Sets and Systems,1995,69:141～156.
  • 7Jenei S,De Baets B.On the direct decomposability of t-norms on product lattices[J].Fuzzy Sets and Systems,2003,139:699～707.
  • 8Karacal F,Khadjiev D.∨-Distributive and infinitely∨-didtributive t-norms on complete lattices[J].Fuzzy Sets and Systems,2005,151:341～352.
  • 9Klement E P,Mesiar R,Pap E.Triangular norms[M].Kluwer:Dordrecht,2000.
  • 10Ma Z,Wu W M.Logical operators on complete lattices[J].Inform.Sci.,1991,55:77～97.

共引文献1

模糊系统与数学
2007年 第6期

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