We investigate the mean dimension of a cellular automaton (CA for short) with compact non-discrete space states. A formula is established (near) strongly permutative, permutative algebraic and unit one-dimensional automata. In higher dimensions, CA or having spaceship has infinite dimension. However, building on Meyerovitch’s example [Mey08], we give an surjective positive finite

We describe and analyze the surprising evolution of an overflow error which has occurred during the simulation of a class of continuous complex systems called ‘fuzzy cellular automata’. This error not only perturbs the global behavior of the system but it generates its own interesting dynamics; in fact, it propagates over the original evolution as a binary cellular automaton in a structured, fr...

Berstel and Pin have characterized local languages by introducing local automaton. In this paper fuzzy local language is introduced and the fuzzy local languages recognized by partial fuzzy local automata in max-min and min-max compositions are studied. Some closure properties of fuzzy local languages are provided. Mathematics Subject Classification: 68Q45

A recent advance on Signal Detection Theory (SDT) promises to enhance measurement of performance in complex real world domains. This development, Fuzzy Signal Detection Theory (FSDT), combines traditional SDT with Fuzzy Set Theory to extend signal detection analysis beyond the traditional crisp, categorical model. FSDT permits events to simultaneously be in more than one state category (e.g. si...

We present optimal upper bounds for the deviation of a fuzzy continuous function from its fuzzy average over [a, b] ⊂ R, error is measured in the D-fuzzy metric. The established fuzzy Ostrowski type inequalities are sharp, in fact attained by simple fuzzy real number valued functions. These inequalities are given for fuzzy Hölder and fuzzy differentiable functions and these facts are reflected ...

The aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. Several characterizations and properties of these multifunctions along with their mutual relationships are established in $L$-fuzzy topological spaces

This paper extends a comparison measure called the statisfaction function(SF). The SF estimates the degree to which arithmetic comparisons between two fuzzy values are satissed. The previously proposed SF was deened on a discrete domain(SFD). So, in order to compare continuous fuzzy values, the fuzzy values should be converted into discrete ones. This paper deenes a satisfaction function on a c...

This paper extends a comparison measure called the statisfaction function(SF). The SF estimates the degree to which arithmetic comparisons between two fuzzy values are satissed. The previously proposed SF was deened on a discrete domain(SFD). So, in order to compare continuous fuzzy values, the fuzzy values should be converted into discrete ones. This paper deenes a satisfaction function on a c...

A model for finite automaton with an open quantum evolution is introduced, and its basic properties are studied. It is shown that the (fuzzy) languages accepted by open evolution quantum automata obey various closure properties. More importantly, it is shown that major other models of finite automata, including probabilistic, measure once quantum, measure many quantum, and Latvian quantum autom...