FORMAL METHODS FOR CLASSIFICATION OF COMPLEX SITUATIONS

By classification of complex situations, we shall understand the procedure of discriminating to what category a given situation belongs. By formal methods, we understand such methods, which can be realized by computers. If the symptoms used for classification correspond to those on which the classification of situation is based, the actual classification simply consists of determining the truth (or falsity) of a statement that can be represented as a logical (Boolean) function, and the task of discrimination becomes trivial. Much more complicated are cases in which classificatory symptoms cannot be used (if, for instance, they are not yet established, or if they have not yet niade themselves known), and such a classification must be made on the basis of indirect (i.e., nonclassificatory) symptoms. Tasks of this kind appear rather frequently in engineering, medicine, economics, sociology, and in many other areas of contemporary life. Until recently, such tasks were either solved intuitively, on the basis of the experience of experts, o r remained unsolved. But even when the opinion of experts made it possible to assign a given situation t o a given category, the reliability of the decision still left much to be desired. The number of wrong classifications used to be (one may say, still is) too great, with serious consequences: people died, engineering systems failed, and resources or efforts were wasted. I n recent years, however, outlines of formalized classification procedures have begun to appear that promise to bring a more effective solution to the problem of classification of complex situations than was possible in the past. In many cases, such formalized procedures enable us to considerably enhance the reliability of classification and also to classify situations to which intuitive classification was not applicable. The frequency of such tasks in engineering is rather high. They occur in the classification of phenomena associated with an engineering project, that is, performance pattern, proper or defective operation, quality of design, and so on. The tasks of engineering diagnostics include, for instance, checking the performance of an engine by its sound, checking a computer by testing, and establishing the presence of mineral ores on the basis :of a set of geophysical and geologic data. The tasks of medical diagnostics (which is also a classification problem) consist of determining the state of a n animal or human organism o n the basis of accumulated anamnestic and clinical data. The important point is to establish the presence of a disease, type of disease, its stage, pathologic changes in relation to the normal situation, pregnancy, sex of the fetus, and so on. The need for the classification of situations appears in many other fields as well. Although the tasks of classification of complex situations on the basis of the complete set of symptoms are difficult,