Special and Related Problems

Abstract

Let an object to be recognized or classified be characterized by a vector of features u ∈ U which may be observed, and the index of a class j to which the object belongs; j ∈ {1, 2, ..., M} ≜ J, M is a number of the classes. The set of the objects may be described by a relational knowledge representation R (u, j) ∈ U × J which is reduced to the sequence of sets

$$ \begin{gathered} D_u (j) \subset U, j = 1,2...,M, \hfill \\ D_u (j) = \{ u \in U: (u,j) \in R (u,j)\} . \hfill \\ \end{gathered} $$

Assume that as a result of the observation it is known that u ∈ D _u ⊂ U. The recognition problem may consist in finding the set of all possible indexes j, i.e. the set of all possible classes to which the object may belong [32,49].