On a conformal net $\mathcal{A}$, one can consider collections of unital completely positive maps on each local algebra $\mathcal{A}(I)$, subject to natural compatibility, vacuum preserving and covariance conditions. We call \emph{quantum operations} $\mathcal{A}$ the subset extreme such maps. The usual automorphisms (the invertible *-algebra morphisms) are examples quantum operations, we show ...

The combination of two elements in a group structure is an element, while, hypergroup, the non-empty set. use hypergroups appears mainly certain subclasses. For instance, polygroups, which are special subcategory hypergroups, used many branches mathematics and basic sciences. On other hand, multi-fuzzy set, element universal set may occur more than once with possibly same or different membershi...

in this paper we determine the sequences of join spaces and atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.

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 ...

In this paper first we introduce the notion of weak $Gamma$-(semi)hypergroups, next some classes of equivalence relations which are called good regular and strongly good regular relations are defined.  Then we investigate some properties of this kind of relations on weak $Gamma$-(semi)hypergroups.

It is well known that the generalized translation operator T associated with the Bessel function of the first kind is positive in the sense if f > 0, then Tf > 0. This property is easily seen when we write Tf as an integral representation with a kernel involving the area of some triangle ([1],[9]) and has several applications in many mathematical fields such that hypergroup structure, heat equa...

An algebraic quantum group is a regular multiplier Hopf algebra with integrals. In this paper we will develop a theory of algebraic quantum hypergroups. It is very similar to the theory of algebraic quantum groups, except that the comultiplication is no longer assumed to be a homomorphism. We still require the existence of a left and of a right integral. There is also an antipode but it is char...

In this paper, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzyset are  introduced. By means of this new idea, the  concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  andit is shown that, in 16 kinds of $(alpha,beta...

We are interested in generalizations of the concepts of t-norm and t-conorm. In a companion chapter in this volume [14] we have presented a family of hypert-norms ∧q and a family of hyper-t-conorms ∨p. The prefix hyper is used to indicate multi-valued operations, also known as hyperoperations (see [5, 14]), i.e. operations which map pairs of elements to sets of elements. See [14] for the constr...