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New directions in general fuzzy automata: a dynamic-logical view | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 11، دوره 1، شماره 2، آذر 2020، صفحه 251-262 اصل مقاله (418.61 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2020.18629.1040 | ||
| نویسندگان | ||
| Khadijeh Abolpour* 1؛ Mohammad Mehdi Zahedi2، 3؛ Marzieh Shamsizadeh2، 3 | ||
| 1Dept. of Math., Shiraz Branch, Islamic Azad University, Shiraz, Iran | ||
| 2Dept. of Math., Graduate University of Advanced Technology, Kerman, Iran | ||
| 3Dept. of Math., Behbahan Khatam Alanbia University of Technology, Behbahan, Iran | ||
| چکیده | ||
| In the current study, by a general fuzzy automaton we aim at showing a set of propositions related to a given automaton showing that the truth-values are depended on thestates, inputs and membership values of active states at time t. This new approach enables us to consider automata from a different point of view which is more close to logical treatment and helps us make estimations about the behavior of automaton particularly in a nondeterministic mode. The logic consists of propositions on the given GFA and its dynamic nature is stated by means of the so-called transition functor. This logic enables us to derive a certain relation on the set of states labeled by inputs. In fact, it is shown that if our set of propositions is large enough, this recovering of the transition relation is possible. Through a synthesis in the theory of systems, this study contributes to construct a general fuzzy automaton which realizes a dynamic process at least partially known to the user, which has been fully achieved in Theorem 3.6. Also, we study the theory of general fuzzy automata by using the concepts of operators. Such operators help us in the algebraic study of general fuzzy automata theory and provide a platform to use fuzzy topological therein. Further, a Galois connection is obtained between the state-transition relation on states and thetransition operators on propositions. To illustrate the proposed approach, the subject matter is more elaborated in detail through examples. | ||
| کلیدواژهها | ||
| Dynamic logic؛ General fuzzy automata؛ Proposition؛ Functor؛ Modal؛ Transition؛ Active state | ||
| مراجع | ||
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