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Presents fundamental results on fuzzy Mealy machines. Unlike the classical Mealy machine which requires two functions, one to describe the next state and another to describe the output, a fuzzy Mealy machine requires only one fuzzy function to characterize completely the next state and the output produced. Apart from the obvious generalization that can be obtained from corresponding results on fuzzy finite state machines by introduction of an output associated with each transition, introduces the concept of an interval partition of [0, 1] and uses it to obtain more general results.

Studies the concept of the Cartesian composition of fuzzy finite state machines. Shows that fuzzy finite state machines and their Cartesian composition share many structural properties. Some of these properties are singly generated; retrievability, connectedness, strong connectedness, commutativity, perfection and state independence. Thus a fuzzy finite state machine which is a Cartesian composition of submachines can be studied in terms of smaller machines.

In this paper, we define and examine the concept of a fuzzy recognizer. If L(M) is the language recognized by an incomplete fuzzy recognizer M, we show that there is a completion M of M such that L(M) = 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.

The purpose of this research paper is to develop an algorithm/methodology for the reduction of a fuzzy recognizer through an algebraic concept such as homomorphism.

The approach of this research is to introduce the concepts, compatible with the purpose of this paper, and then to find a necessary and sufficient condition for the reduction of a fuzzy recognizer.

A fuzzy Σ‐recognizer M with non‐empty fuzzy initial state and the behavior A is reduced if and only if it is isomorphic to M^A.

The research proposes an algebraic method for the reduction of a fuzzy recognizer. The problem of finding dispensable fuzzy productions of a regular fuzzy grammar may be tackled by the use this algebraic method, as fuzzy recognizers and fuzzy regular grammars are equivalent.

The concepts and the methodology are original. The work is useful to the researchers in the field of fuzzy automata, fuzzy grammars and pattern recognition.