Theme of master's work:

The Factors Ranging of the Internet Shop Advancement by Multisets

Summary of research and developments

Will consider the new approach of ranging of factors of advancement the Internet of shop which exist in a considerable quantity and with differing values of signs. As the problem decision application of the device of multisets which allows to consider all factors and their signs is offered.

Concepts of multisets

Multiattribute objects Ai, i=1, …, n it is usually accepted to represent as vectors or trains qi = (…,) in space Q=Q1 ?… ?Qm, where Qs = {} – a continuous or discrete scale of s th sign, es=1?hs, s=1, …, m. The situation essentially becomes complicated, if one can correspond to same object Ai not, and some m-dimensional vectors. For example, object Ai is estimated k by independent experts on m to criteria, or it is necessary to consider simultaneously m the parametres of object Ai measured k in the various ways. In such cases object Ai is represented in m-dimensional space Q any more one vector qi, and the group consisting from k of vectors {qi (1), …, qi (k)} a kind qi (j) = (…,), j=1, …, k which should be considered as a unit. Thus, obviously, values of signs can be similar, differing and even inconsistent, that in turn can lead несравнимости m-dimensional vectors qi (j), characterising the same object Ai.
Set of such "compound" objects can have in space Q difficult structure, difficult enough for the analysis. Uneasy to enter in this space and the metrics for measurement of distances between objects. The specified difficulties can be overcome if to take advantage of a representation different way multiattribute the objects, based on a formalism of the theory of multisets [1].
Let's enter instead of direct product m scales of signs Q=Q1 ?… ?Qm the generalised scale of signs – set G={Q1, …, Qm}, consisting of m groups of signs, and we will present object Ai in such symbolical kind:
Ai = {kAi (q11) •q11, …, kAi () •, …, kAi (qm1) •qm1, …, kAi () •},
Where the number kAi () specifies, how many time sign IQs meets in the description of object Ai, the sign • designates frequency rate of a sign. Set G characterises properties of set of objects A = {A1..., An}. Such record of object Ai represents it as set with repeating elements or multiset.
Over multisets are carried out traditional teoretiko-mno-zhestvennye operations, such as association, crossing, subtraction, addition, a symmetric difference, direct product, and a number of new operations: addition, multiplication, multiplication to number, and also linear combinations of operations. New types of operations over multisets open new possibilities for grouping multiattribute objects. For example, group Xt of objects can be received as sum Xt=aiAi, association Xt=UiAi or crossing Xt=IiAi of multisets Ai describing objects Ai, or as a linear combination of various multisets of kind Xt=aiti•Ai, Xt=Uiti•Ai or Xt=Iiti•Ai, ti> 0.
Various classes of metric spaces of multisets (A, d) are defined by following metrics (pseudo-metrics) [1]:
d1p (A, B) = [m (A?B)] 1/p; d2p (A, B) = [m (A?B) /m (Z)] 1/p;
d3p (A, B) = [m (A?B) /m (AUB)] 1/p,
Where p - an integer, m - the multiset measure, the valid non-negative function set on algebra of multisets L (Z).
Representation multiattribute objects by means of multisets allows to expand considerably a circle of considered problems and to solve various problems of classification, sorting, ranging, cluster the analysis of objects.

The Mathematical Model of Factors Ordering of Internet Shop Advancement

In considered model we range the factors of Internet shop advancement. As there is considerable quantity of promotion factors cannot be established between them certain linear or nonlinear dependence, then we will apply the multisets means to ranging of factors.
On the basis of the collected statistical data, which are a resulted in table 1, we will allocate as objects of the analysis the set which , which represents the basic indicators of an overall performance of Internet shop: