Usual operations with symbolic data under normal symbolic form (Q2711692)

Symbolic objects provide a good and efficient way to summarize a large amount of information in a single object. Symbolic objects are represented by symbolic tables, like usual statistical tables, in the form of rows and columns, the former representing individual (in this case a symbolic object), the latter representing variables. However, instead of containing a single value in each cell, a symbolic table contains a set of values or an interval depending on the type of the variable concerned (nominal or continuous). The Cartesian product of the cells of a given row in a symbolic table is a symbolic object. The aim of symbolic data analysis is to extend some of the usual methods of traditional data analysis to such tables. When a symbolic table is not constrained by links between the variables these computations are polynomial or linear in time. Unfortunately, when constraints appear, they introduce holes in the description space, and , because of these holes, the complexity becomes combinatorial.NEWLINENEWLINENEWLINETo avoid this kind of problem, the present authors propose a representation of symbolic objects where only the coherent part of an object is represented. People dealing with databases have long been familiar with relations: they use a relational model and \textit{E.F. Codd} [Data base systems. Courant Comp. Sci. Symp. Ser., Vol. 6 (1972)] introduced normal forms to structure more efficiently databases. All this has led the present authors to introduce a normalization of symbolic objects, inspired by Codd's third normal form, which allows a representation of only the coherent part of a symbolic object. By reference to the relational normalization they call it normal symbolic form (NSF). In previous papers they have provided a first approach to the NSF. In this paper, previous definitions are slightly modified, and the different operations one can do with NSFs are detailed. This method is applied only to nominal variables, but it can also be applied to numerical variables.