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一类模糊蕴涵性质的研究 被引量：2

A Study on Properties of a Family of Fuzzy Implications
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摘要 对一类模糊蕴涵IT,N的性质进行了详细研究,其主要内容涉及三个方面。首先讨论了IT,N满足常见的模糊蕴涵性质的条件;其次给出了IT,N是S蕴涵,R蕴涵和QL蕴涵的等价条件,重点为QL蕴涵的等价条件;最后我们讨论了此蕴涵满足性质I(x,N(x))=N(x)和I(x,y)=I(x,I(x,y))的条件。 In this paper,we study properties of a family of fuzzy implications IT,N in detail which involve three aspects mainly.Firstly,we investigate the conditions under which IT,N satisfies common properties of fuzzy implications.Secondly,we give some conditions under which IT,N is an S-implication,R-implication or QL-implication,particularly the last one.Finally,we present the conditions under which IT,N satisfies the properties I（x,N（x））=N（x） and I（x,y）=I（x,I（x,y））.
作者 孙伟忠 王绪柱
机构地区 太原理工大学数学系
出处 《模糊系统与数学》 CSCD 北大核心 2010年第6期27-33,共7页 Fuzzy Systems and Mathematics
基金 山西省自然科学基金资助项目(2009011006)
关键词 T-模 t-余模 强非 模糊蕴涵 矛盾律 Triangular Norm Triangular Conorm Strong Negation Fuzzy Implication Law of Contradiction
分类号 O159 [理学—基础数学]
  • 相关文献

参考文献18

  • 1Baczynski M,Jayaram B.(S,N)-and R-implications:A state-of-the-art survey[J].Fuzzy Sets and Systems,2008,159:1836-1859.
  • 2Baczynski M,Jayaram B.QL-implications:Some properties and intersections[J].To appear in Fuzzy Sets and Systems.
  • 3Fodor J C.Contrapositive symmetry of fuzzy implications[J].Fuzzy Sets and Systems,1995,69:141-156.
  • 4Wang X Z,Ruan D,Kerre E E.Mathematics of fuzziness-basic issues[M].Springer,2009.
  • 5Klement E P,Mesiar R,Pap E.Triangular norms.Position paper I:basic analytical and algebraic properties[J].Fuzzy Sets and Systems,2004,143:5-26.
  • 6Shi Y,Ruan D,Kerre E E.On the first place antitonicity in QL-implications[J].Fuzzy Sets and Systems,2008,159:2988-3013.
  • 7Baczynski M,Jayaram B.On the characterization of(S,N)一implications[J].Fuzzy Sets and Systems,2007,158:1713-1727.
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同被引文献25

  • 1Wang L X. A course in fuzzy system and control[M]. Engewood Cliffs NJ :Prentice-Hall PTR, 1997.
  • 2Klement E P, Mesiar R, Pap E. Triangular norms[M]. Dordrecht :Kluwer Academic Publishers,2000.
  • 3Alsina C, Trillas E. On iterative boolean-like law of fuzzy sets[C]//Proc. 4th Conf. Fuzzy Logic and Technolgic, Barcelona, Spain, 2005: 389 - 394.
  • 4覃锋.基于信息聚合的数学模型研究[D].西安:陕西师范大学博士后出站报告,2007.
  • 5Trillas E, Alsina C. Standard theories of fuzzy sets with the law (μ V σ' )'= σV (μ' A σ')[J]. International Journal of Approximate Reasoning, 2004,37 : 87 - 92.
  • 6Shi Y, Ruan D, Kerre E E. On the characterization of fuzzy implications satisfying I(x,y)=I(x,I(x,y))[J]. Information Science, 2007,177 : 2954- 2970.
  • 7Xie A F, Qin F. Solutions to the functional equation I (x, y) = I (x, I (x, y) ) [J]. Information Science, 2010,188: 2487-2497.
  • 8Trillas E, Mas M, Monserat M, Torrens J. On tne represention of fuzzy rules[J]. International Journal of Approximate Reasoning, 2008,48 : 583 - 597.
  • 9Fodor J C. Contrapositive symmetry of fuzzy implications[J]. Fuzzy Sets and Systems, 1995,69 : 141- 156.
  • 10Bustince H, Burillo P, Soria F. Automorphisms, negations and implication operators[J]. Fuzzy Sets and Systems, 2003,134:209-229.

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模糊系统与数学
2010年 第6期

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