[2] Karsten Lehmann and Rafael Peñaloza. The complexity of computing the behaviour of lattice automata on infinite trees. On the decidability status of fuzzy ALC with general concept inclusions. [4] Stefan Borgwardt and Rafael Peñaloza. Consistency reasoning in lattice-based fuzzy description logics. Context-dependent views to axioms and consequences of semantic web ontologies. Classifying soft...

Classical automata theory can not deal with uncertainty. To deal with uncertainty in system modeling, fuzzy automata come into the existence. Fuzzy automaton depends on membership value. For finding the membership degree of strings in fuzzy automata, the concept of max – min automaton and min – max automaton can be used. Many researchers have used the concept of max – min automaton for finding ...

Fuzzy Cellular Automata (FCA) are special couple map lattices that generalize Boolean cellular automata by allowing continuous values for the cell states. The local transition rule of a FCA is the “fuzzification" of the disjunctive normal form that describes the local function of the corresponding Boolean cellular automata. Recently there has been some interest in elementary Fuzzy cellular auto...

Some uniform categorical theoretical treatment of automata and lattice-valued fuzzy automata using quantale theory is studied in this paper. First, L-relational sheaves on a monoidM andQ-enriched categories are introduced for quantales L andQ, the equivalence of the corresponding categories are proved next. Then lattice-valued (fuzzy) automata are described by Q-enriched categories. In fact, la...

Simulations and bisimulations between two fuzzy automata over a complete residuated lattice were defined by Ćirić et al. (2012) [7], [8] as relations the sets of states automata. However, they act crisp relationship In particular, if there exists (forward) bisimulation automata, then languages recognized them are crisply equal. Approximate simulations introduced Stanimirović (2022) [36] aim at ...

We introduce MK-fuzzy automata over a bimonoid K which is related to the fuzzification of the McCarthy-Kleene logic. Our automata are inspired by, and intend to contribute to, practical applications being in development in the LogicGuard project [15, 16]. We investigate closure properties of the class of MK-fuzzy languages accepted by MK-fuzzy automata as well as by their deterministic counterp...

State minimization is a fundamental problem in automata theory. The problem is also of great importance in the study of fuzzy automata. However, most work in the literature considered only state reduction of fuzzy automata, whereas the state minimization problem is almost untouched for fuzzy automata. Thus in this paper we focus on the latter problem. Formally, the decision version of the minim...

This work is towards the study of the relationship between fuzzy preordered sets and Alexandrov (left/right) fuzzy topologies based on generalized residuated lattices here the fuzzy sets are equipped with generalized residuated lattice in which the commutative property doesn't hold. Further, the obtained results are used in the study of fuzzy automata theory.