Typical Hesitant Fuzzy Automata: Theory and applications
Formal Languages; Fuzzy Languages; Fuzzy Automata, Typical Hesitant Fuzzy Sets, Data Classification.
As a method of trying to extrapolate the Church’s thesis, using the ideas of the fuzzy sets presented by Zadeh, the fuzzy automaton theory emerges in the late 1960s, as an extension of the finite automata theory, adding the possibility of computing with some level of uncertainty. Over the years, due to the maturation of the extensions of the fuzzy sets, different generalizations of fuzzy automata started to emerge in the literature, such as interval-valued fuzzy automata, intuitionist fuzzy automata, etc. Fuzzy automata, in addition to being the fundamental part of the fuzzy computation theory, also present a relative success in practical applications, mainly in the field of pattern recognition, through uncertainty modeling. This work presents a new generalization of fuzzy automata based on the definitions of typical hesitant fuzzy sets (which we will call typical hesitant fuzzy automata), as well as the motivation for this generalization and for bringing to the domain nof computing the possibility of working with uncertainties and also being able to work with hesitation. Therefore, this new generalization aims to enable new ways to face problems that were not easily modeled before, using only uncertainties. Besides, we will show ways to apply this new type of automata in the fields of digital image processing and data classification.