Problems of solvability and choice of algorithms for decision making by precedence

A wide range of practical and theoretical problems are reduced to decision making, which is interpreted rather ambiguously from the viewpoint of its statement. This is mainly related to the fact that the concept of decision cannot be formalized. From the methodological point of view, decision making is a process whose result is a decision. Even if the concept of decision is not defined, such a methodological view of the problem highlights its key points in a different way. In this case, the problem is transformed into a sequence of clearer and unambiguously defined problems. In this sequence, there certainly exists the problem of calculating the property of objects, and the decision itself can be associated with such a property [21]. Then, the problem of decision making can be reduced to calculating (determining) the properties of the information analyzed. This is undoubtedly one version of the problem of decision making, which is based on the problem of determining the above properties. Decision making allows one to easily find out if all property determination problems have a common nature and to reduce them to a single statement on a formal level. What problems are meant by the determination of properties? These are well-studied problems of sentential calculus and predicate calculus [1, 2]; problems of logical diagnostics [3, 4], which are less studied but have a larger number of practical interpretations; and, finally, just poorly formalized problems in pattern recognition theory (PRT) [5, 9]. It is obvious that, formally, all the above problems contain sets divided into subsets. Each subset is characterized by a certain property. The problem consists in calculating this property for each element of the original set.