General Fuzzy Automata Research Articles

A new characterization of congruences and the discrete Sugeno integral on LB-valued general fuzzy automata

The present study aimed at exploring the idempotent and compatible aggregation functions on a complete infinitely distributive lattice B of propositions about the LB-valued general fuzzy automata (for simplicity, LB-valued GFA), where the compatibility is related to the congruences on B. Further, we have shown that all aggregation functions on B can be obtained as usual composition of lattice operations ∨,∧ and certain unary and binary aggregation functions. Moreover, our results yield a new characterization of discrete Sugeno integrals on B.

Isomorphism Between Two Vector General Fuzzy Automata

In this paper, at first, we define the notion of general fuzzy automaton over a field; we call this automaton vector general fuzzy automaton (VGFA). Moreover, we present the concept of max-min vector general fuzzy automaton. We show that if two max-min VGFA are similar, they constitute an isomorphism. After that, we prove that if two VGFA constitute an isomorphism with threshold α, they are equivalent with threshold α, where $\alpha \in [0,1]$. Also, some examples are given to clarify these new notions.

An algebraic study of LB-valued general fuzzy automata: On the concept of the layers

An algebraic study of LB-valued general fuzzy automata: On the concept of the layers

LB-valued general fuzzy automata

This study aims to develop the notion of general fuzzy automata (GFA) to a new one which is known as “LB-valued general fuzzy automata”. Instead of the term LB-valued general fuzzy automata, for simplicity, LB-valued GFA is used where B is regarded as a set of propositions about the GFA, in which its underlying structure has been a complete infinitely distributive lattice. Further, LB-valued GFA is scrutinized via different operators and also the interrelationship among these operators is examined. Specifically, it is shown that LB-valued successor, LB-valued predecessor and LB-valued residuated operators play an important role in the algebraic study of LB-valued general fuzzy automaton and that under certain conditions these operators are interrelated. In addition, the concept of a homomorphism between LB-valued general fuzzy automata is introduced and studied. Finally, the concepts of equivalence and congruence are defined, the quotient LB-valued GFA with respect to congruence is formulated and the equivalence between LB-valued GFA and its quotient automaton is proved. To clarify the notions and the results obtained in this study, some examples are submitted as well.

Tense and dynamic algebras related to GFA

The present paper is an attempt to suggest and scrutinize tense operators in the dynamic logic $textbf{B}$ which is regarded as a set of propositions about the general fuzzy automaton $ tilde{F} $, in which its underlying structure has been a bounded poset. Here, the operators $ T_{delta}, P_{delta}, H_{delta}$ and $ F_{delta} $ are proposed regardless of what propositional connectives the logic comprises. For this purpose, the axiomatization of universal quantifiers is applied as a starting point and these axioms are modified. In this study, firstly, we demonstrate that the operators can be identified as modal operators and the pairs $ (T_{delta},P_{delta}) $ are examined as the so-called dynamic pairs. In addition, constructions of these operators are attained in the corresponding algebra and in the following a transition frame is suggested. Besides, the problem of finding a transition frame is solved in the case when the tense operators are given. Specifically, this study shows that the tense algebra $ textbf{B} $ is representable in its Dedekind-MacNeille completion. Representation theorems for dynamic and tense algebra are explicated in details in the related given theorems.

New directions in LB-valued general fuzzy automata: A topological view

In the current study, we define the different L-valued operators on LB-valued general fuzzy automata or simply LB-valued GFA, where B is considered as a complete infinitely distributive lattice of propositions about the GFA. In particular, this study demonstrates that the L-valued successor and predecessor operators induce L-valued co-topologies while the L-valued residuated and approximation operators induce L-valued topologies on the state set of given LB-valued GFA. Further, we show that the continuity and separation properties of such LB-valued general fuzzy automaton can be examined in terms of these topologies. Moreover, we study and explicate the LB-valued GFA structure space and LB-valued GFA homotopy in more details.

General Fuzzy Finite Switchboard Automata

The constructions of finite switchboard state automata are known to be an extension of finite automata in the view of commutative and switching state machines. This research incorporated an idea of a switchboard in the general fuzzy automata to introduce general fuzzy finite switchboard automata. The attained output reveals that a strongly connected general fuzzy finite switchboard automaton is equivalent to the retrievable general fuzzy automata. Further, the notion of the switchboard subsystem and strong switchboard subsystem of general fuzzy finite switchboard automata are examined. Finally, the concept of fuzzy topology on general fuzzy finite switchboard automata in terms of these characterisations is formulated.

Bisimulation of type 2 for BL-general fuzzy automata

In this note, first, we define bisimulation of type 2 for a basic logic general fuzzy automaton and show that if there exists a bisimulation of type 2 between two basic logic general fuzzy automata, then they have the same behavior. Also, by using the greatest bisimulation of type 2, we obtain a quotient basic logic general fuzzy automaton in which this quotient is minimal. Moreover, we prove that if there exists a bisimulation of type 1 between two automata, then there is a bisimulation of type 2 between them, but the converse is not valid. Moreover, we give an algorithm, which determines the bisimulation of type 2 between any two basic logic general fuzzy automata and show that the time complexity of this algorithm is so better than the time complexity of the algorithm computing bisimulation of type 1. After that, we present some examples to clarify the notions and results of this paper.

Applications of a group in general fuzzy automata

‎Let $tilde{F}=(Q,S,tilde{R},Z,omega,tilde{delta},‎ F_1,F_2)$‎ ‎be a general fuzzy automaton and the set of its states be a group.‎ ‎The aim of this paper is the study of applications of a group in a‎ ‎general fuzzy automaton‎. ‎For this purpose‎, ‎we define the concepts‎ ‎of fuzzy normal kernel of a general fuzzy automaton‎, ‎fuzzy kernel‎ ‎of a general fuzzy automaton‎, ‎adjustable‎, ‎multiplicative‎. ‎Then we‎ ‎obtain the relationships between them.‎

IRREDUCIBILITY ON GENERAL FUZZY AUTOMATA

The aim of this paper is the study of a covering of a max-mingeneral fuzzy automaton by another, admissible relations, admissiblepartitions of a max-min general fuzzy automaton,$tilde{delta}$-orthogonality of admissible partitions, irreduciblemax-min general fuzzy automata. Then we obtain the relationshipsbetween them.

Intuitionistic general fuzzy automata

In this paper, by considering the notions of general fuzzy automata, admissible relation, admissible partition and intuitionistic fuzzy set based on the Atanassov (Fuzzy Sets Syst 20(1):87---96, 1986), we define the concepts intuitionistic general fuzzy automaton (IGFA), max---min intuitionistic general fuzzy automaton, admissible relation for the IGFA, admissible partition for the IGFA, quotient IGFA and language for an IGFA. In particular, a connection between the admissible partition and the quotient IGFA is presented and it is shown that any quotient of a given IGFA and the IGFA itself has the same language. Also, using the above notions, some related theorems are proved and, finally, some examples are given to clarify these new notions.

Some (Fuzzy) Topologies on General\ Fuzzy Automata

In this paper, by presenting some notions and theorems, we obtaindifferent types of fuzzy topologies. In fact, we obtain someLowen-type and Chang-type fuzzy topologies on general fuzzyautomata. To this end, first we define a Kuratowski fuzzy interioroperator which induces a Lowen-type fuzzy topology on the set ofstates of a max- min general fuzzy automaton. Also by provingsome theorems, we can define two fuzzy closure (two fuzzyinterior) operators on the certain sets related to a general fuzzyautomaton and then according to these notions we give some theoremsand obtain some different Chang-type fuzzy topologies.

Isomorphism between two BL-general fuzzy automata

In this note first we develop the notion of general fuzzy automata (GFA) to a new one which is called “BL-general fuzzy automata” and for simplicity, we write BL-GFA, instead of BL-general fuzzy automata. Then we focus on derivation, active state set, membership assignment, output mappings, and concept of belonging to an output label according to the entrance input strings $$X \, (X \in \Upsigma^{*})$$ for BL-general fuzzy automata. Therefore, we define the concepts of run map and behavior of BL-GFA. After that we present the morphism with threshold $$ \tfrac{{\tau_{1} }}{{\tau_{2} }} $$ between two BL-general fuzzy automata. Moreover we give some examples, to clarify these notions. Finally, we prove some theorems. In particular, we show that the isomorphic BL-general fuzzy automata have the same behavior.

SOME HYPER K-ALGEBRAIC STRUCTURES INDUCED BY MAX-MIN GENERAL FUZZY AUTOMATA

We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different types of (positive implicative) commutative hyper K-ideals. As a generalization, we extend the definition of this hyper BCK-algebra to a bounded hyper K-algebra and obtain relative results. Automata are the prime examples of general computational systems over dis- crete spaces. The incorporation of fuzzy logic into automata theory resulted in fuzzy automata which can handle continuous spaces. In particular, the concept of membership assignment, output mapping, multi-membership resolution, and the concept of acceptance for fuzzy automata were developed in general fuzzy automata. The concept of BCK-algebra has originated on two different ways. One mo- tivation is based on set theory. In set theory, there are three most elementary and fundamental operations introduced by L. Kantorovic and E. Livenson. These fundamental operations are union, intersection and the set difference. Another mo- tivation is taken from classical and non-classical propositional calculi. There are some systems which contain the only implication functor among the logical func- tors. These examples are systems of positive implicational calculus, weak positive implicational calculus by A. Church and BCK-systems by C.As. Meredith. Corsini and Leoreanu (7) presented some connections between a deterministic finite automaton and the hyper algebraic structure theory. Now, here we intend to find some relationships between max-min general fuzzy automata and the hyper K-algebraic structures. So, first we introduce a hyper BCK-algebra induced by max-min general fuzzy automata. Then, we discuss the properties of this BCK- algebra and obtain some useful results. A fuzzy finite-state automaton (FFA) is a six-tuple denoted by ˜

HYPERGROUPS AND GENERAL FUZZY AUTOMATA

In this paper, we first define the notion of a complete general fuzzy automaton with threshold c and construct an H - group, as well as commuta- tive hypergroups, on the set of states of a complete general fuzzy automaton with threshold c. We then define invertible general fuzzy automata, discuss the notions of homogeneity, separation, thresholdness connected, thresh- oldness inner irreducible and principal and strongly connected, as applied to them and use these concepts to construct a quasi-order hypergroup on an invertible general fuzzy automaton. Finally, we derive relationships between the properties of an invertible general fuzzy automaton and the induced hy- pergroup.

UNIFORM AND SEMI-UNIFORM TOPOLOGY ON GENERAL FUZZY AUTOMATA

In this paper, we de ne the concepts of compatibility between twofuzzy subsets on Q, the set of states of a max- min general fuzzy automatonand transitivity in a max-min general fuzzy automaton. We then construct auniform structure on Q, and de ne a topology on it. We also de ne the conceptof semi-uniform structures on a nonempty set X and construct a semi-uniformstructure on the set of states of a general fuzzy automaton. We then constructa semi-uniform structure on , the set of all nite words on , the set ofinput symbols of a general fuzzy automaton and, nally, using these semi-uniform structures, we construct two topologies on Q and  and discuss theirproperties.