m. m. zahedi

The current study aimed to describe the notion of the L-graph, which is constructed on a residuated lattice, presenting the idea of the maximal product of two L-graphs.    Moreover, the applied algorithm demonstrated its efficiency to a great extent to improve the educational system.    The results showed that the maximal product of both G and H and reversely, H    and  G are isomorphic L-graphs.    The maximal product of two L-graph automata was represented as a new notion,    followed by investigating their self-sufficiency conditions in two different modes.    In addition,  A(Z(G))star~A(Z(H)) and A(Z(H))star~A(Z(G))  were proved as two isomorphic-related L-graph automata considering the residuated lattice properties.    Then, correlations among A(Z(G))star A(Z(H)),  A(Z(G)),  and A(Z(H)) behaviors were explained.    As a result, some theorems of the relationship between L-graph automata and their maximal product were introduced.    Subsequently, some related theorems were proved, and several examples were provided to illustrate these new notions. Further, an application of the maximal product of two related L-graph automata was expressed in the factors affecting the spared of the coronavirus,  and accordingly,    some solutions were suggested to reduce the spread of the virus.

The contribution of generl fuzzy automata to neural networks has been considerable, and dynamical fuzzy systems are becoming more and more popular and useful. Basic logic, or BL for short, has been introduced by Hájek [5] in order to provide a general framework for formalizing statements of fuzzy nature. In this note, some of the closure properties of the BL-general fuzzy automaton based on lattice valued such as union, intersection, connection and a serial connection are considered, after that, the behavior of them are discussed. Moreover, for a given BL-general fuzzy automaton on the basis of lattice valued, a complete BL-general fuzzy automaton on the basis of lattice valued is presented. Afterward, we may test the Pumping Lemma for the BL-general fuzzy automaton based on lattice valued. In particular, a connection between the behavior of BL-general fuzzy automaton based on lattice valued and its language is presented. Also, it is proven that L is a recognizable set if and only if L is rational. Also, it is driven that Kleen’s Theorem is valid for the BL-general fuzzy automaton on the basis of lattice valued. Finally, we give some examples to clarify these notions.

The current study aims to establish a connection between graphs and automata theory, which apparently demonstrate different mathematical structures. Through searching out some properties of one of these structures, we try to find some new properties of the other structure as well. This will result in obtaining some unknown properties. At first, a novel automaton called zero-forcing (Z-F) finite automata is defined according to the notion of a zero-forcing set of a graph. It is shown that for a given graph and for some zero forcing sets, various Z-F-finite automata will be obtained. In addition, the language and the closure properties of Z-F-finite automata, in particular; union, connection, and serial connection are studied. Moreover, considering some properties of graphs such as the closed trail, connected and complete; some new features for Z-F-finite automata are presented. Further, it is shown that there is not any finite graph such that f be a part of the language of its Z-F-finite automata. Actually, it is proved that for every given graph, the Z-F-finite automata of it does not show any closed trail containing all edges for every zero forcing set, but if the graph G has been a closed trail containing all edges, then the Z-F-finite automata of it has a weak closed trail containing all edges. Some examples are also given to clarify these new notions.

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.

In this paper, we are supposed to introduce the definitions of n-fold commutative, and implicative hyper K-ideals. These definitions are the generalizations of the definitions of commutative, and implicative hyper K-ideals, respectively, which have been defined in [12]. Then we obtain some related results. In particular we determine the relationships between n-fold implicative hyper K-ideal and n-fold commutative hyper K-ideals of a hyper K-algebra of order 3, which satisfy the simple condition. Then, generally we study n-fold commutative hyper K-ideals in simple hyper K-algebras.