Committees of systems of linear inequalities

The conceptual issues of the theory of committee decision rules were considered, and its close relationship with the theory of substantiation of collective decision making and teaching neural networks was demonstrated. The problem of the minimum committee of an incompatible system of constraints, which arises at the stage of constructing the committee decision rule with a small number of elements, was discussed by itself. The problem of the minimum committee is known to be NP-hard. Results concerning estimation of the computational complexity of allied problems were obtained. To solve the problem of minimum committee of an incompatible system of linear inequalities, an effective approximate algorithm was suggested, its correctness was proved and computational complexity and guaranteed precision were estimated.