Development of Mathematical Models of Group Decision Synthesis for Structuring the Rough Data and Expert Knowledge

Abstract

Context. The problem of aggregating the decision table attributes values formed out of group expert assessments as the classification problem was solved in the context of structurally rough set notation. The object of study is the process of the mathematical models synthesis for structuring and managing the expert knowledge that are formed and processed under incompleteness and inaccuracy (roughness). Objective. The goal of the work is to develop a set of mathematical models for group expert assessments structuring for classification inaccuracy problem solving. Method. A set of mathematical models for structuring the group expert assessments based on the methods of the theory of evidence has been proposed. This techniques allow to correctly manipulate the initial data formed under vagueness, imperfection, and inconsistency (conflict). The problems of synthesis of group decisions has been examined for two cases: taking into account decision table existing data, only, and involving additional information, i.e. subjective expert assessments, in the process of the aggregation of the experts' judgments. Results. The outcomes gained can become a foundation for the methodology allowing to classify the groups of expert assessments with using the rough sets theory. This make it possible to form the structures modeling the relationship between the classification attributes of the evaluated objects, the values of which are formed out of the individual expert assessments and their belonging to the certain classes. Conclusions. Models and methods of the synthesis of group decisions in context of structuring decision table data have been further developed. Three main tasks of structuring decision table data gained through the expert survey has been considered: the aggregation of expert judgments of the values of the decision attributes in the context of modeling of the relationship between the universe element and certain class; the aggregation of expert judgments of the values of the condition attributes; the synthesis of a group decision regarding the belonging of an object to a certain class, provided that the values of the condition attributes are also formed through the expert survey. The proposed techniques of structuring group expert assessments are the theoretical foundation for the synthesis of information technologies for the solution of the problems of the statistical and intellectual (classification, clustering, ranking and aggregation) data analysis in order to prepare the information and make the reasonable and effective decisions under incompleteness, uncertainty, inconsistency, inaccuracy and their possible combinations.