Fuzzy grammars and recursively enumerable fuzzy languages (Q1186363)

A fuzzy language ( \(L\)-language) is treated as an \(L\)-subset of \(A^*\) with \(A^*\) being a free monoid of an alphabet defined over a finite set \(A\). The main result of the paper states that if \(L\) is finite then an \(L\)-language is generated by an \(L\)-grammar if and only if it is a recursively enumerable \(L\)-subset. The recursive enumerability is also helpful in investigating the properties of generated \(L\)-languages. In particular one can derive that the union, intersection and the concatenation of two generated \(L\)-languages become a generated \(L\)- language. Making use of this concept one transfers the results about relationships existing between imprecision, decidability and recursive enumerability to the \(L\)-languages.