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首页> 外文期刊>Journal of Mathematical Sciences >ALGEBRAS OF RECURSIVELY ENUMERABLE SETS AND THEIR APPLICATIONS TO FUZZY LOGIC
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ALGEBRAS OF RECURSIVELY ENUMERABLE SETS AND THEIR APPLICATIONS TO FUZZY LOGIC

机译：递归可数集的代数及其在模糊逻辑中的应用

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摘要

Algebras of operations defined on recursively enumerable sets of different kinds are considered. Every such algebra is specified by a list of operations involved and a list of basic elements. An element of an algebra is said to be representable in this algebra if it can be obtained from given basic elements by operations of the algebra. Two kinds of recursively enumerable sets are considered: recursively enumerable sets in the usual sense and fuzzy recursively enumerable sets. On binary, i.e., two-dimensional recursively enumerable sets of these kinds, algebras of operations are introduced. An algebra θ is constructed in which all binary recursively enumerable sets are representable. A subalgebra θ~0 of θ is constructed in which all binary recursively enumerable sets are representable if and only if they are described by formulas of Presburger's arithmetic system. An algebra Ω is constructed in which all binary recursively enumerable fuzzy sets are representable. A subalgebra Ω~0 of the algebra Ω is constructed such that fuzzy recursively enumerable sets representable in Ω~0 can be treated as fuzzy counterparts of sets representable by formulas of Presburger's system.
机译：考虑在不同种类的递归可枚举集合上定义的运算代数。每个这样的代数都由涉及的操作列表和基本元素列表指定。如果可以通过代数的运算从给定的基本元素中获得代数元素，则该代数元素在该代数中是可表示的。考虑了两种递归可枚举集：通常意义上的递归可枚举集和模糊递归可枚举集。在二进制（即这些类​​型的二维递归可枚举集）上，引入了运算代数。构造了一个代数θ，其中所有二进制递归可枚举集都是可表示的。构造一个θ的子代数θ〜0，其中所有且仅当用Presburger算术系统的公式描述时，所有二进制递归可枚举集都是可表示的。构造了一个代数Ω，其中所有二进制递归可枚举的模糊集都是可表示的。构造代数Ω的子代数Ω〜0，使得可以将在Ω〜0中表示的模糊递归可枚举集视为可由Presburger系统公式表示的集的模糊对应物。

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  • 来源
    《Journal of Mathematical Sciences》 |2005年第2期|p.4598-4606|共9页
  • 作者

    S. N. Manukian;

  • 作者单位

    Institute for Informatics and Automation Problems of the National Academy of Sciences of Armenia and Yerevan State University, Yerevan, Armenia;

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  • 正文语种 eng
  • 中图分类 数学;
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