Reza Ameri

School of Mathematics, Statistics and Computer Science, College of Sciences, University of Tehran, P.O. Box 14155-6455, Teheran, Iran

[ 1 ] - Fuzzy Inner Product and Fuzzy Norm \of Hyperspaces

We introduce and  study  fuzzy (co-)inner product and fuzzy(co-)norm of hyperspaces. In this regard by considering  the notionof hyperspaces, as a generalization of vector spaces, first we willintroduce the notion of fuzzy (co-)inner product in hyperspaces and will apply it to formulate the notions offuzzy (co-)norm and fuzzy (co-)orthogonality  in hyperspaces. Inparticular, we will prove that ...

[ 2 ] - DIMENSION OF FUZZY HYPERVECTOR SPACES

In this paper we investigate the algebraic properties of dimension of fuzzy hypervector spaces. Also, we prove that two isomorphic fuzzy hypervector spaces have the same dimension.

[ 3 ] - FUZZY BASIS OF FUZZY HYPERVECTOR SPACES

The aim of this paper is the study of fuzzy basis and dimensionof fuzzy hypervector spaces. In this regard, first the notions of fuzzy linearindependence and fuzzy basis are introduced and then some related results areobtained. In particular, it is shown that for a large class of fuzzy hypervectorspace the fuzzy basis exist. Finally, dimension of a fuzzy hypervector space isdefined and the basi...

[ 4 ] - On exact category of $(m, n)$-ary hypermodules

We introduce and study category of $(m, n)$-ary hypermodules as a generalization of the category of $(m, n)$-modules as well as the category of classical modules. Also, we study various kinds of morphisms. Especially, we characterize monomorphisms and epimorphisms in this category. We will proceed to study the fundamental relation on $(m, n)$-hypermodules, as an important tool in the study of a...

[ 5 ] - Direct Limit of Krasner (m, n)-Hyperrings

The purpose of this paper is the study of direct limits in category of Krasner (m, n)-hyperrings. In this regards we introduce and study direct limit of a direct system in category (m, n)-hyperrings. Also, we consider fundamental relation , as the smallest equivalence relation on an (m, n)-hyperring R such that the quotient space is an (m, n)-ring, to introdu...

[ 6 ] - Cayley graph associated to a semihypergroup

The purpose of this paper is the study of Cayley graph associated to a semihypergroup(or hypergroup). In this regards first  we associate a Cayley graph to every semihypergroup and then we study theproperties of this graph, such as  Hamiltonian cycles in this  graph.  Also, by some of examples we will illustrate  the properties and behavior of  these Cayley  graphs, in particulars we show that ...