Justification and Classification of Evaluation Fused in Rating Methods of Multi-criteria Choice

Abstract

The recommendations on the application of methods of multidimensional estimation (MDE) of objects, proposed in the paper Velasquez M., Hester P.T. «An Analysis of Multi-Criteria Decision Making Methods», are analyzed. The weak substantiation of these recommendations, resulting from the superficial systematization of MDE methods, is noted. The recommendations are focused not on the classes of MDE methods, but on various areas of activity. However, in each area of activity there is a wide range of tasks for evaluating objects of various nature. In this regard, the urgency of a more thorough systematization of MDE methods is recognized.
 Taking into account the diversity of MDE methods, it was decided to limit ourselves to the systematization of methods that use evaluation functions (EF), and on this basis to offer general recommendations for their application.
 The review of MDE methods from a unified position required clarification of the terminology used in them. On the basis of the formal model of the criterion, the relationship between the concepts of "preference", "criterion" and "indicator" is established. To highlight the methods that use evaluation functions, the concept of the target value of the indicator is introduced. Regarding its location on the indicator scale, the concepts of ideal and real goals are introduced. The criteria corresponding to these goals are divided into target and restrictive ones. Using the proposed terminology, a review of the most well-known MDE methods was carried out. Of these, a group of methods using evaluation functions is distinguished.
 Variants of evaluation functions created on the basis of the criterion and postulates of the theory of value and utility are considered. On the basis of the similarity of the domains of definition and the meanings of EFs, the relationship between them is established. Regarding the target value of the indicator, they are divided into the functions of achieving the goal and functions of deviation from the goal. The mutual complementarity of these functions is shown. A group of functions of deviation from the goal is highlighted, which allows us to order objects separately according to penalties and rewards in relation to achieving a real goal. The concept of norm is introduced for the correspondence relation. On the example of medical analyzes, the practical application of deviation functions from the norm is shown using both the minimax and the weighted average generalizing function to establish a rating on a set of objects.
 The similarities and differences of the EFs revealed in the course of the study form the basis for the classification of the MDE methods that use them. The difference in EFs in terms of the complexity of creation is reflected in the proposed methodology for their application.