We give a new version of fuzzy alternating Büchi automata over distributive lattices: weights are putting in every leaf node of run trees rather than along with edges from every node to its children. Such settings are great benefit to obtain complement just by taking dual operation and replacing each final weight with its complement. We prove that L-fuzzy nondeterministic Büchi automata have th...

We generalize the previous results that were obtained by Kohout for relations based on fuzzy Basic Logic systems (BL) of Hájek and also for relational systems based on left-continuous tnorms. The present paper extends generalized morphisms into the realm of Monoidal Fuzzy Logics by first proving and then using relational inequalities over pseudo-associative BK-products of relations in these log...

This paper is a contribution to the discussion of the problem, whether there is a fuzzy logic that can be considered as the real fuzzy logic. We give reasons for taking IMTL, BL, LΠ and Ev L (fuzzy logic with evaluated syntax) as those fuzzy logics that should be indeed taken as the real fuzzy logics.

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.

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 ...