Automata are the prime example of general computational systems over discrete spaces. The incorporation of fuzzy logic into automata theory resulted in fuzzy auotomata which can handle continuous spaces. Moreover, they are able to model uncertainty which is inherent in many applications. Deterministic Finite-state Automata (DFA) have been the architecture, most used in many applications, but, t...

In this paper, the concept of somewhat-connected space will be introduced and characterized. Its connection with the other well-known concepts such as the classical connectedness, the $omega_theta$-connectedness, and the $omega$-connectedness will be determined. Moreover, the concept of textit{somewhat}-continuous function from an arbitrary topological space into the product space will be chara...

This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for e...

Continuous cellular automata (or coupled map lattices) are cellular automata where the state of the cells are real values in [0, 1] and the local transition rule is a real function. The classical observation medium for cellular automata, whether Boolean or continuous, is the space-time diagram, where successive rows correspond to successive configurations in time. In this paper we introduce a d...

We propose a quartic function to represent a family of continuous quality loss functions. Depending on the choice of its parameters the shape of this function within the specification limits can be either symmetric or asymmetric, and it can be either similar to the ubiquitous quadratic loss function or somewhat closer to the conventional step function. We examine this family of loss functions i...

The present paper is an attempt to study the minimal BL-general fuzzy automata which realizes the given fuzzy behavior. Of two methods applied for construction of such automaton presented here, one has been based on Myhill-Nerode's theory while the other has been based on derivatives of the given fuzzy behavior. Meanwhile, the categories of BL-general fuzzy automata and fuzzy behavior, along wi...

Fuzzy cellular automata (FCA) are continuous cellular automata where the local rule is defined as the “fuzzification” of the local rule of a corresponding Boolean cellular automaton in disjunctive normal form. In this paper, we consider circular FCA; their asymptotic behaviours had previously been observed through simulation and FCA had been empirically classified accordingly. However, no analy...

We show that logical paradoxes based on self-reference (of which the Liar is the best known example) are equivalent to the non-existence of solutions to a numerical system of equations, the so-called truth-value equations. Furthermore, we show that in many cases a self-referential system which does not posses a crisp (Boolean) solution can be solved by expanding the solution set to include fuzz...

in the last decade, cellular automata models have been widely used for simulation spatial phenomena; however, exact nature of these models have been lead to various limitations for essential simulation of these phenomena. in this research, traditional cellular automata models have been developed through fuzzy theory, in which, transition rules are expressed based on fuzzy logic control methodol...

To deal with system uncertainty, finite automata have been generalized into fuzzy automata. Stamenkovic and Ciric proposed an approach using the position automata for the construction of fuzzy automata from fuzzy regular expressions. There exist multifarious methodologies for the construction of finite automata from regular expressions known as Thompson construction, Antimirov partial derivativ...