Fuzzy languages and fuzzy automata are considered using techniques from algebraic theory of automata. Syntactic monoids of fuzzy languages play a crucial role in the study. Varieties of fuzzy languages are introduced and an Eilenberg-type correspondence between varieties of fuzzy languages, varieties of ordinary languages and varieties of monoids is established.

Fuzzy tree automata are mathematical devices for modeling and analyzing vaguely defined structures. The behavior of a fuzzy automaton generates language by mapping set regular trees on ranked alphabet to membership values. It calculates the grade using rules that process their structural characteristics. This paper deals with constructing models satisfies given logical propositions (called prop...

BL-algebras, introduced by P.Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that BL-algebras are the duals of bounded representable DRl-monoids. This duality enables us to describe some structure properties of BL-algebras.

Traditional automata accept or reject their input, and are therefore Boolean. Lattice automata generalize the traditional setting and map words to values taken from a lattice. In particular, in a fully-ordered lattice, the elements are 0, 1, . . . , n − 1, ordered by the standard ≤ order. Lattice automata, and in particular lattice automata defined with respect to fully-ordered lattices, have i...

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 a project on runtime network monitoring based on predicate logic. We investigate closure properties of the class of recognizableMK-fuzzy languages accepted by MKfuzzy automat...

1. Introduction Cellular Automata have generated much interest [1,2,3] because of their diverse behavior and usefulness as a discrete model for many processes. Wolfram's 1984 paper on universality and complexity in cellular automata [3,4] described four classes of behavior for automata: class 1 for homogeneous stable behavior, class 2 for simple periodic patterns, class 3 for chaotic aperiodic ...

Chaudhari S. R. ,Komejwar D. D. , On Fuzzy Pushdown Automata and their covering , International Journal of Computer Applications Vol. 46(8),2012 pp 27-33 Comon H. ,Dauchet M. ,Gilleron R. ,Jacquemard F. , Lugiez D. ,Loding C. ,Tison S. , and Tommasi M. , Tree Automata: techniques and apllications. (2007) Lee E. T. Fuzzy tree automata and syntactic pattern recognition, IEEE Trans Pattern Anal Ma...

Automata-based methods have been successfully employed to prove tight complexity bounds for reasoning in many classical logics, and in particular in Description Logics (DLs). Very recently, the ideas behind these automata-based approaches were adapted for reasoning also in fuzzy extensions of DLs, with semantics based either on finitely many truth degrees or the Gödel t-norm over the interval [...