On fuzzy recognizers

In this paper, we define and examine the concept of a fuzzy recognizer. If L(M) is the language recognized by M incomplete fuzzy recognizer M, zee show that there is a completion (M) over bar of M such that L((M) over bar) = L(M). We also show that if A is a recognizable set of words, then there is a complete accessible fuzzy recognizer M-A such that L(M-A) = A. We lay groundwork to determine rational decompositions of recognizable sets.