Homomorphisms of fuzzy recognizers

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

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.

Originality/value

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.

Citation

Chaudhari, S.R. (2007), "Homomorphisms of fuzzy recognizers", Kybernetes, Vol. 36 No. 5/6, pp. 768-775. https://doi.org/10.1108/03684920710749839