R-fuzzy computation (Q1072368)

The presented paper studies so-called R-fuzzy recursive program schemes which are finitely specified by systems of equations \(x_ i=p_ i\), \(i=1,...,n\). Thereby, \(X=\{x_ 1,...,x_ n\}\) is a finite set of variables and the \(p_ i's\) are polynomials built up over X unioned with a finite set F of function symbols and with coefficients in a given semiring R that determines the different kind of fuzziness by evaluating possible choices. Using power series on F-tree with variables of X the meaning of R-fuzzy recursive program schemes can formally be computed. The main result shows the equivalence of equational (fixed point) and operational semantics of such program schemes.