جستجوی مقالات مرتبط با کلیدواژه "modal operator" در نشریات گروه "ریاضی"

In this paper, modal operators on BCK-algebras, especially BCK-algebras with condition (S) are introduced and several properties and characterizations of them are investigated. Also, it is investigated under what conditions these modal  operators form a lattice. Furthermore, some special modal operators are introduced and their properties and  characterizations of them are obtained, especially in some classes of BCK-algebras such as positive implicative BCK- algebras.

The main goal of this paper is to introduce analogously modal operators on $L$-algebras and study their properties. To begin with, we introduce the notion of modal operators on $L$-algebras and investigate some important properties of this operator. In order for the kernel of modal operator to be ideal, we investigate what conditions are required. Relations between modal operator and endomorphism of $L$-algebras are investigated. Also, we define the concept of positive $L$-algebra and some characterizations of positive $L$-algebra are established. Finally, we introduce a map $k_{a}$ and show that $k_{a}$ is a modal operator and we prove that the set of all $k_{a}$ on a positive $L$-algebra makes a dual BCK-algebra.

In this paper, we define and study the modal operators on pseudo-BE algebras as special cases of closure operators on these structures.We prove that the composition of two modal operators is a modal operator if and only if they commute.For the particular case of a good pseudo-BCK algebra an equivalent definition of the modal operators is given, and the notion of a strong modal operator is introduced and studied.We also define the notions of modal deductive systems and modal homomorphisms on pseudo-BE algebras and we investigate their properties. It is proved that, if two modal operators have the same image, then they coincide.Also, given a normal modal deductive system H of a distributive modal pseudo-BE algebra $(A,f)$ we construct a modal operator on the quotient pseudo-BE algebra A/H.

Intuitionistic Fuzzy Modal Operator was defined by Atanassov in cite{at3} in 1999. In 2001, cite{at4}, he introduced the generalization of these modal operators. After this study, in 2004, Dencheva cite{dencheva} defined second extension of these operators. In 2006, the third extension of these was defined in cite{at6} by Atanassov. In 2007,cite{gc1}, the author introduced a new operator over Intuitionistic Fuzzy Sets which is a generalization of Atanassov's and Dencheva's operators. At the same year, Atanassov defined an operator which is an extension of all the operators defined until 2007. The diagram of One Type Modal Operators on Intuitionistic Fuzzy Sets was introduced first in 2007 by Atanassov cite{at10}. In 2008, Atanassov defined the most general operator and in 2010 the author expanded the diagram of One Type Modal Operators on Intuitionistic Fuzzy Sets with the operator $Z_{alpha, beta}^{omega}$. Some relationships among these operators were studied by several researchers% cite{at5}-cite{at8} cite{gc1}, cite{gc3}, cite{dencheva}- cite% {narayanan}. The aim of this paper is to expand the diagram of one type modal operators over intuitionistic fuzzy sets. For this purpose, we defined a new modal oparator $Z_{alpha, beta}^{omega, theta}$ over intuitionistic fuzzy sets. It is shown that this oparator is the generalization of the operators$Z_{alpha, beta}^{omega},E_{alpha, beta},boxplus _{alpha, beta},boxtimes _{alpha, beta}.$