Fuzzy Mathematical Machine as Fuzzy System

Abstract — In this paper an attempt has been made to study fuzzy mathematical machines in a systematic manner. Results of fuzzy finite-state machines which are natural generalisation of respective concepts of ordinary mathematical machines have been reported. The concept of fuzzy finite-state machines with output actually leads to a natural definition of a fuzzy finite-state automaton — a generalisation of ordinary finite-state automaton. A realistic version of the concept of fuzzy mathematical machine is introduced in which the state, the input, the output as well as the state transition function are all fuzzy concepts. This definition actually leads us to realize a fuzzy mathematical machine as a fuzzy system. Copyright c © 2008 Yang’s Scientific Research Institute, LLC. All rights reserved. Index Terms — Finite-state machine, fuzzy finite state machine, automata, fuzzy automata, fuzzy system. 1