Algebras of Recursively Enumerable Sets and Their Applications to Fuzzy Logic
| Autor: | S. N. Manukian |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Statistics and Probability
Discrete mathematics Mathematics::Combinatorics Applied Mathematics General Mathematics Recursively enumerable set Fuzzy set Subalgebra Fuzzy logic Combinatorics TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Recursive set Recursively enumerable language ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Maximal set Unrestricted grammar Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 130:4598-4606 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-005-0354-1 |
| Popis: | 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 θ0 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 Ω0 of the algebra Ω is constructed such that fuzzy recursively enumerable sets representable in Ω0 can be treated as fuzzy counterparts of sets representable by formulas of Presburger’s system. Bibliography: 16 titles. |
| Databáze: | OpenAIRE |
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