A FUZZY APPROACH TO MODELING AND SOLVING ORDERING AND SELECTING PROBLEMS

Abstract

The ordering and selecting of objects arise in various fields of human activity. In cases where information about the characteristics of objects obtained from experts is used, fuzzy problem models are proposed that take into account various types of uncertainty and more logically reflect real situations. Special attention is drawn to the adequacy problems or homomorphism of empirical and mathematical models in problems with different types of data measured on different scales, namely, on ratio, order, intervals, and absolute scales. In such cases, according to the positions of the representative measurement theory, it is necessary to ensure the invariance of the calculation results in the presence of both quantitative and qualitative data. The paper considers the theoretical substantiation and development of an invariant procedure for solving the problems of ordering and selecting applicants for vacant positions in the enterprise based on the assessment of their competitiveness, taking into account various types of information that can be obtained on the basis of expert assessments. The solution of the problem is based on a separate comparison of the characteristics of the applicants with the corresponding best characteristics in relation to the position or profession (standard) based on the use of the linguistic correlation coefficient, which is used to determine a fuzzy similarity measure of the standard and the applicants. Theorems about the invariance of such similarity measure when measuring characteristics in different scales are proved. An example of solving one selection problem regarding the appointment of the best candidates from the applicants, who submitted relevant documents for vacant positions in the enterprise, while determining their characteristics according to order and absolute scales, is presented.