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[0,1]格上的无限＠-Fuzzy关系方程的解集 被引量：3

The Solution Sets on [0,1] Lattice of ＠-Fuzzy Relational Equation in Infinite Domains
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摘要 主要对[0,1]格上,论域无限时,＠-Fuzzy关系方程(其中＠表示inf-α合成)的解作了深入地讨论.从方程的系数出发,给出了存在可达解和不可达解的充要条件.进一步,在解集不空时,刻画了＠-Fuzzy关系方程的解集的结构. This paper deals with @-Fuzzy relational equation in infinite domains. A necessary and sufficient condition describing the attainable solution （ resp. the unattainable solution） is given based on the coefficients of the equation. When the solution set of the equation is not empty, the structure of the solution set is characterized.
作者 舒乾宇 王学平
机构地区 四川师范大学数学与软件科学学院
出处 《四川师范大学学报（自然科学版）》 CAS CSCD 北大核心 2007年第3期326-329,共4页 Journal of Sichuan Normal University（Natural Science）
基金 国家自然科学基金(10671138) 四川省青年基金资助项目
关键词 @-Fuzzy关系方程 充要条件 极大解 解集 @-Fuzzy relational equation Necessary and sufficient condition Maximal solution Solution set
分类号 O159 [理学—基础数学]
  • 相关文献

参考文献15

  • 1Sanchez E.Resolution of composite fuzzy relation equations[J].Inform Control,1976,30:38-48.
  • 2Higashi M,George J K.Resolutions of finite fuzzy relation equations[J].Fuzzy Sets and Systems,1984,13:65-82.
  • 3Zhao C K.On matrix equations in a class of complete and completely distributive lattice[J].Fuzzy Sets and Systems,1987,22:303-320.
  • 4Guo Si-zhong,Wang Pei-zhuang,Nola A D,et al.Further contributions to the study of finite relation equations[J].Fuzzy Sets and Systems,1988,26:93-104.
  • 5Sessa S.Finite fuzzy relation equations with unique solution in complete Brouwerian lattices[J].Fuzzy Sets and Systems,1989,29:103-113.
  • 6Nola A D.On solving relational equations in Brouwerian lattices[J].Fuzzy Sets and Systems,1990,34:365-376.
  • 7De Baets B.Sup-T equations:state of the art,computational intelligence:soft computing and fuzzy-neural integration with applications[A].New York:Springer-Verlag,1998,162:80-93.
  • 8Wang Xue-ping.Method of solution to fuzzy relation equations in a complete Brouwerian lattice[J].Fuzzy Sets and Systems,2001,120:409-414.
  • 9Wang Xue-ping.Infinite fuzzy relational equations in a complete Brouwerian lattice[J].Indian J Pure and Applied Mathematics,2002,33(1):87-95.
  • 10王学平.完备Brouwerian格上Fuzzy关系方程有极小解的条件[J].数学进展,2002,31(3):220-228. 被引量：32

二级参考文献11

  • 1Birkhoff G. Lattice Theory. 3th Ed., Vol.XXV, AMS Colloquium Publications, 1979.
  • 2Sanchez E. Resolution of composite fuzzy relation equations. Inform. and Control, 1976, 30: 38-48.
  • 3Szaz G. Introduction to Lattice Theory. 3rd Ed., New York: Academic Press, 1963.
  • 4Di Nola A, Sessa S, Pedrycz W and Sanchez E. Fuzzy Relation Equations and Their Applications to Knowledge Engineering. Dordrecht, Boston/London: Kluwer Academic Publishers, 1989.
  • 5Di Nola A, Sessa S, Pedrycz W, Higashi M. Minimal and maximal solutions of a decomposition problem of fuzzy relations. Int. J. General Systems, 1985, 11: 103-116.
  • 6Higashi M and George J K. Resolutions of finite fuzzy relation equations. Fuzzy Sets and Systems, 1984,13: 65-82.
  • 7Di Nola A. On solving relational equations in Brouwerian lattices. Fuzzy Sets and Systems, 1990, 34:365-376.
  • 8Wang Xueping. Method of solution to fuzzy relation equations in a complete Brouwerian lattice. Fuzzy Sets and Systems, to appear.
  • 9Birkhoff G. Lattice Theory. Revised Ed., Vol. XXV, AMS Colloquium Publications, 1984.
  • 10Crawley P and Dilworth R P. Algebraic Theory of Lattice. Englewood Cliffs, NJ: Prentice-Hall, 1973.

共引文献31

同被引文献16

引证文献3

二级引证文献11

四川师范大学学报（自然科学版）
2007年 第3期

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