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完备格上Fuzzy关系方程的解是极小元的一个充要条件 被引量：14

A Necessary and Sufficient Condition that a Solution of a Fuzzy Relational Equation on a Complete Lattice is a Minimal Solution
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摘要 在完备格L上给出方程∨j∈J(aj∧xj) =b的解集非空时 ,解集中的解是极小元的一个充要条件及解集中的解有极小元的一个充分条件 .讨论了与格论有关的一些性质 ,并给出了一个开问题 . In this paper, a necessary and sufficient condition that a solution of a fuzzy relational equation on a complete lattice is a minimal solution is given, and a sufficient condition that a solution has a minimal element is also obtained, under the condition that the solution set of a fuzzy relational equation is nonempty. Some properties relevant to lattice are given, and an open problem is risen on.
作者 王学平
机构地区 四川师范大学公共计算机教学中心
出处 《四川师范大学学报（自然科学版）》 CAS CSCD 2002年第6期591-594,共4页 Journal of Sichuan Normal University（Natural Science）
基金 四川省教育厅重点科研基金资助项目
关键词 FUZZY关系方程 极小元 充要条件 完备格 极小解 布尔矩阵方程 Complete lattice Relational equation Minimal solution
分类号 O159 [理学—基础数学] O153.2 [理学—基础数学]
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参考文献9

  • 1Sanchez E. Resolution of composite fuzzy relation equations[J]. Inf Control,1976,30:38～48.
  • 2Luce R D. A note on Boolean matrix theory[J]. Proc Am Math Soc,1952,3:382～388.
  • 3Higashi M, George J K. Resolutions of finite fuzzy relation equations[J]. Fuzzy Sets and Systems,1984,13:65～82.
  • 4Wagenknecht M, Hartmann K. On the existence of minimal solutions for fuzzy equations with tolerances[J]. Fuzzy Sets and Systems,1990,34:237～244.
  • 5Imai H, Miyakoshi M, Da-te T. Some properties of minimal solutions for a fuzzy relation equation[J]. Fuzzy Sets and Systems,1997,90:335～340.
  • 6Di Nola A. On solving relational equations in Brouwerian lattices[J]. Fuzzy Sets and Systems,1990,34:365～376.
  • 7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
  • 8Birkhoff G. Lattice Theory XXV (3th ed)[M]. Providence Rhode Island:Am Math Soc,1979.
  • 9Di Nola A, Sessa S, Pedrycz W, et al. Fuzzy Relation Equations and Their Applications to Knowledge Engineering[M]. Dordrecht,Boston, London:Kluwer Academic Publishers,1989.

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140

引证文献14

二级引证文献41

四川师范大学学报（自然科学版）
2002年 第6期

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