模糊自动机的强连通性及群自动机

为了更好地研究模糊自动机的结构和性质,采用代数的方法,在传统的模糊有限状态自动机的基础上,通过定义状态集合为代数群的自动机,讨论了这一类自动机的连通性和正则性,这丰富了模糊自动机理论．     

Bisimulations for fuzzy automata

Bisimulations have been widely used in many areas of computer science to model equivalence between various systems, and to reduce the number of states of these systems, whereas uniform fuzzy relations have recently been introduced as a means to model the fuzzy equivalence between elements of two possible different sets. Here we use the conjunction of these two concepts as a powerful tool in the study of equivalence between fuzzy automata. We prove that a uniform fuzzy relation between fuzzy automata A and B is a forward bisimulation if and only if its kernel and co-kernel are forward bisimulation fuzzy equivalence relations on A and B and there is a special isomorphism between factor fuzzy automata with respect to these fuzzy equivalence relations. As a consequence we get that fuzzy automata A and B are UFB-equivalent, i.e., there is a uniform forward bisimulation between them, if and only if there is a special isomorphism between the factor fuzzy automata of A and B with respect to their greatest forward bisimulation fuzzy equivalence relations. This result reduces the problem of testing UFB-equivalence to the problem of testing isomorphism of fuzzy automata, which is closely related to the well-known graph isomorphism problem. We prove some similar results for backward-forward bisimulations, and we point to fundamental differences. Because of the duality with the studied concepts, backward and forward-backward bisimulations are not considered separately. Finally, we give a comprehensive overview of various concepts on deterministic, nondeterministic, fuzzy, and weighted automata, which are related to bisimulations.     

New directions in fuzzy automata

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, the increasing interest in using fuzzy logic for many new areas necessitates that the formalism of fuzzy automata be more developed and better established to fulfill implementational requirements in a well-defined manner. This need is due to the fact that despite the long history of fuzzy automata and lots of research being done on that, there are still some issues which have not been well-established and issues which need some kind of revision. In particular, we focus on membership assignment, output mapping, multi-membership resolution, and the concept of acceptance for fuzzy automata. We develop a new general definition for fuzzy automata, and based on that, develop well-defined and application-driven methodologies to establish a better ground for fuzzy automata and pave the way for forthcoming applications.     

BL-general fuzzy automata and accept behavior

In this note, we focus on behavior of BL-general fuzzy automata (for simplicity BL-GFA) and we obtain the free realization for a given behavior, that is, a BL-general fuzzy automaton whose behavior is given behavior. Then we find the realization with the minimum number of states. The minimization takes two steps: at first discard all superfluous states, and then we merge all pairs of states which have the same behavior. Moreover we prove some theorems. In particular, we show that the minimal reduction of the reachable part of an BL-GFA is the minimal realization of the behavior it. Finally we give some examples to clarify these notions.     

Minimization algorithm of fuzzy finite automata

In this paper, a class of fuzzy finite automata corresponding to the Mealy type of ordinary automata is formulated, and also two types of statewise equivalence relations are introduced. From the equivalence relations, a minimal form is defined and a minimization algorithm of the Mealy type of fuzzy finite automata is obtained.     

Behavior of finite-nonstationary deterministic automata in a fuzzy environment

The paper presents a method of finding optimal control of generalized deterministic abstract automaton, the structure of which is given by an arbitrary finite graph in a fuzzy environment. The control is found in order to achieve a fuzzy goal, which is given as a fuzzy set in any fixed finite vertex of the automaton structural graph. The problem solution is divided into two stages. The first stage provides the greatest possible degree of achieving the fuzzy goal depending on the path from the initial graph vertex to the fixed one, while the second stage makes it possible to construct a set of input words that ensure the achievement of this goal on the selected path. The conclusion presents an example of the application of the proposed method for constructing a regular expression of control sequences for the given abstract finite-nonstationary deterministic automaton.     

On free and torsion-free automata

In this paper we define free, torsion-free and torsion-free completely on an automaton. We prove some properties of them which are important     

A theory for the multiset sampler

The multiset sampler (MSS) can be viewed as a new data augmentation scheme and it has been applied successfully to a wide range of statistical inference problems. The key idea of the MSS is to augment the system with a multiset of the missing components, and construct an appropriate joint distribution of the parameters of interest and the missing components to facilitate the inference based on Markov chain Monte Carlo. The standard data augmentation strategy corresponds to the MSS with multiset size one. This paper provides a theoretical comparison of the MSS with different multiset sizes. We show that the MSS converges to the target distribution faster as the multiset size increases. This explains the improvement in convergence rate for the MSS with large multiset sizes over the standard data augmentation scheme.     

On existence of sets of distinct representatives for families of subsets of a multiset

IfX is a family ofl-subsets of a multiset, then there is a set of distinct representatives of the members ofX among the (l-k)-subsets of the members ofX provided the cardinality ofX does not exceed a certain bound. An algorithm for calculating this bound is given.     

On fuzzy cliques in fuzzy networks

A definition of fuzzy clique in social networks is suggested which overcomes five limitations of current definitions. This definition is based on the networks in which the 0–1 strengths, the weighted strengths, and fuzzy strengths are all allowed. The fuzzy distance in such a network is defined. The node‐clique and clique‐clique coefficients are suggested. The core and the periphery of fuzzy cliques are discussed formally. A “cone like” property of the cores is discovered. The network structures are discussed using the new definition. A “no circle” property of networks is found. Basic fuzzy tools and the related algorithms are also discussed. Some examples are analyzed to demonstrate the theory.     

On the free automata and tensor product

In this paper we shall introduce the algebraic structure of a tensor product for arbitrarily given automata, giving a defintion of the tensor product for automata. We introduce and study that for any setX there always exists a free automaton onX. The existence of a tensor product for automata will be investigated in the same way like modules do.     

On concrete characterization of universal hypergraphic automata

In this paper, we consider structured automata without output signals whose state sets are endowed with an algebraic structure of hypergraphs. The main result of the paper is a theorem where we obtain necessary and sufficient conditions for the possibility of defining on the state set of some automaton A a structure of a hypergraph H such that the automaton A will be the universal hypergraphic automaton.