New directions in general fuzzy automata: a dynamic-logical view

Document Type : Original Article

Authors

1 Dept. of Math., Faculty Member, Islamic Azad University, Shiraz, Iran

2 Dept. of Math., Graduate University of Advanced Technology, Kerman, Iran

3 Dept. of Math., Behbahan Khatam Alanbia University of Technology, Behbahan, Iran

10.22060/ajmc.2020.18629.1040

Abstract

In the current study, by a general fuzzy automaton we aim at showinga set of propositions related to a given automaton showing that the truth-values aredepended on thestates, inputs and membership values of active states at time t. Thisnew approach enables us to consider automata from a different point of view which ismore close to logical treatment and helps us make estimations about the behavior ofautomaton particularly in a ondeterministic mode. The logic consists of propositionson the given GFA and its dynamic nature is stated by means of the so-called transitionfunctor. This logic enables us to derive a certain relation on the set of states labeledby inputs. In fact, it is shown that if our set of propositions is large enough, thisrecovering of the transition relation is possible. Through a synthesis in the theory ofsystems, this study contributes to construct a general fuzzy automaton which realizesa dynamic process at least partially known to the user, which has been fully achievedin Theorem 3.6. Also, we study the theory of general fuzzy automata by using theconcepts of operators. Such operators help us in the algebraic study of general fuzzyautomata theory and provide a platform to use fuzzy topological therein. Further,a Galois connection is obtained between the state-transition relation on states andthetransition operators on propositions. To illustrate the proposed approach, thesubject matter is more elaborated in detail through examples.

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