Abbas Hasankhani

Islamic Azad University Kerman Branch · Math.

In this paper the soft vectorial MV-algebra has been studied. In first, we defined the concept of soft vectorial MV-algebra and give some examples. Then we establish some basic properties and investigate the effect of the extended intersection, restricted intersection, ∧-Intersection, extended union, restricted union, ∨-union and soft function on t...

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is stud...

In this paper, we define soft nexuses over a nexus NN. After that we define the notions cyclic soft nexus, prime and maximal soft subnexuses and we obtain some results about the above definitions. Finally, we define the integer number induced by soft nexus (α,A)(α,A) and denoted by |(α,A)||(α,A)| and show that for any n∈ℵn∈ℵ, there exists soft nexu...

In this paper, by using the notion of fuzzy subsets, the con-cept of F-permutation is introduced. Then by applying this notion the concepts of presentation of an F-polygroup, graph of an F-permutation and F-permutation matrices are investigated.

The notion of fuzzy prime subnexus of a nexus is defined, and some related results are obtained. In particular, by considering the concept of homomorphism, some theorems about the coimage and preimage are proved. Finally, the notion of quotient nexus induced by a fuzzy subnexus is introduced and some its properties are investigated.

In this paper, we introduce the notion of an implicative topological residuated lattice and study its properties. We define uniform topology on a residuated lattice by use the concept of filters and find some properties of this topological structure. Also, we obtain some relationship between these topologies.

In the present paper we define the notion of fuzzy inner product and study the properties of the corresponding fuzzy norm. In particular, it is shown that the Cauchy-Schwarz inequality holds. Moreover, it is proved that every such fuzzy inner product space can be imbedded in a complete one and that every subspace of a fuzzy Hilbert space has a comp...

We define the notions of fuzzy congruence relations and fuzzy convex subalgebras of a commutative residuated lattice and we obtain some related results. In particular, we show that there exists a one-to-one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras of a commutative residuated lattic...

In this paper, we solve an open problem in an special case. The problem is to give a characterization for Heyting algebras by means of fractions. Here, we give a representation for a class of Heyting algebras by means of fractions. Fractions on a bounded distributive lattice is a new algebraic structure, which was recently studied by the authors.

In this paper, we consider uniform topology on a residuated lattice. We use this to define the quotient topology and the uniform topology on a quotient residuated lattice. We investigate the relationship between these topologies on a quotient residuated lattice and study the properties of these topologies.

In this paper we study the category of hyper MV-algebras and we prove that it has a terminal object and a coequalizer. We show that Jia's construction can be modified to provide a free hyper MV-algebra by a set. We use this to show that in the category of hyper MV-algebras the monomorphisms are exactly the one-to-one homomorphisms. (© 2009 WILEY-VC...

S-reflexive hyper MV-filters of a hyper MV-algebra, uniform structure and uniform topology are introduced, and it is proved that the uniform topology on an MV-algebra is discrete. Next, a (strong) prime hyper MV-filter and spectral topology are studied.

In this paper, we use the concept of fuzzy filters of a residu-ated lattice to define a uniform topology. We study some properties of this topology. Then we construct a quotient residuated lattice by a fuzzy filter and define the quotient topology on it. We discuss some properties of this topology.

We define the concepts of good H-congruence relations, weak positive implicative subsets, positive implicative subsets, weak maximal hyper MV-filters and maximal hyper MV-filters in hyper MV-algebras. We then use some of the above notions to define quotient hyper MV-algebras. We state and prove some related theorems with appropriate results. In par...

In this paper some properties of the uniformity topology on a BCI-algebras are discussed.

The following results for the space X of the fuzzy prime spectrum of a given bounded implicative BCK-algebra Y are proved: 1. The topological space X is Lindelöf and disconnected. 2. If Y is an integral domain, then X is irreducible.

First we show that the cosets of a fuzzy idea µ in a BCK-algebra X form another BCK-algebra X µ (called the fuzzy quotient BCK-algebra of X by µ). Also we show that X µ is a fuzzy partition of X, and prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BC...

In this note, we first construct an i.p.s hypergroup from an arbitrary finite i.p.s hypergroup. Then we show that for each positive integer n, there is an i.p.s hypergroup (which is not a group) of order n. Finally we give some classifications of i.p.s hypergroups of order 9. In fact, first we define the notion of a primary frame for an i.p.s hyper...

Let (H;*;0) be a hyper K-algebra and q:H→P * (H) be a function, where P * (H) is the set of all nonempty subsets of H. We consider the set H q ={q(a):a∈H}, and we answer the following question: What are the conditions on the function q such that (H q ;∘;q(0)) is a hyper K-algebra? Here ∘ is a function: H q ×H q →P * (H q ) which is defined by (q(a)...

We first show that the answers to the open problems posed by Y. B. Jun and E. H. Roh [Math. Jap. 41, No. 2, 297-302 (1995; Zbl 0819.06019)] are positive. Then we give some counterexamples to Theorem 6 of Y. B. Jun and E. H. Roh [ibid. 41, No. 3, 553-556 (1995; Zbl 0826.06010)], Theorem 2.3 of Y. B. Jun. [ibid. 38, No. 1, 67-71 (1993; Zbl 0762.06011...

We define the notions of hyperI/hyperK-algebras, (weak) hyperK-ideals and the union of two hyperK-algebras (hyperBCK-algebras). Then we state and prove some related theorems. In particular we show by some examples that these definitions are different from the notions of hyperBCK-algebras, hyperBCK-ideals etc., which we have introduced in “On hyperB...

First we define the notions of fuzzy prime and fuzzy prime dual ideals in a BCK-algebra. Then we state and prove some related theorems on these notions. By an example we show that the product of two fuzzy prime dual ideals is not necessarily prime. However, this is true under some conditions. Then by introducing some new fuzzy subsets extracted fro...

In the first part of this note the relationship between fuzzy ideals and fuzzy congruence relations on a positive implicative BCK-algebra with condition (S), are specified. Then, by considering the concepts of product of fuzzy ideals and product of fuzzy congruence relations, some related results are obtained.

The concepts of scalars, fuzzy sub-F-polygroups and fuzzy congruence relations of an F-polygroup are defined and some theorems are proved.

The notion of a hyper BCK-algebra, which is a generalization of a BCK-algebra, is introduced and some basic properties for such algebras are proved. Then the notions of P-ideals and hyper-congruence relations are introduced, and relationships between them on a positive implicative hyper BCK-algebra with condition (S) are specified.

First, a product between two F-subpolygroups of a given F-polygroup is defined, and then a necessary and sufficient condition is given in order that the product be an F-subpolygroup. Then, by considering the notion of homomorphism of F-polygroups, some related results are obtained. Finally, the concept of quotient F-polygroup is defined and then so...

Using the notion of fuzzy subset, the concept of F-hypermodule is defined and some basic results are obtained. Then the notions of (weak) F-subhypermodule, quotient F-hypermodule and (weak) F-hypermodule homomorphism are defined and some related theorems are proved. In particular it is proved that if N is an F-subhypermodule of an F-hypermodule M,...

The relationships between fuzzy ideals and fuzzy congruence relations on a positive implicative BCK-algebra with condition (S), are specified.