Abstract

The present paper deals with cut-point languages accepted by R-fuzzy automata whose coefficients of the initial and final vectors and each transition matrix are elements of a partially ordered semiring R. To formulate algebraically the problems we are concerned with a mapping A from the class P0S of all partially ordered semirings into the class of all (abstract) fsm~lies of languages will be defined by assigning the set ~R of all R-fuzzy languages to each R of POS. A language is said to be an R-fuzzy language if it is accepted by an R-fuzzy automaton with respect to a cut-point of R. A is neither a one-to-one nor an onto mapping. Thus a non-trivial equivalence relation ~ on P0S can be introduced by setting R ~ R' if and only if ~R = ~R' holds.

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