Meanings of improper problems of classification and optimization

In this article we study the interpretation of the formalized Committee decisions and conflicting objectives recognition and also reliability of such solutions. Inconsistently corresponding logic is built. Also a necessary and sufficient condition for the building committees for the separation of hard-separable, but still disjoint finite sets is provided. The design close to the concept of the Committee, their interpretation and application are described. Special attention is paid to the use of the Committee structures in the area of optimization problems. It is noted that the applicability of these structures in solving applied problems is based not only on solving specific problems, but also confirmed by a rigorous mathematical justification, which is given in this article as theorems. Also it is concluded that in non-native tasks or there are no solutions, or violated the relation of duality.