Formalization of indicator requirements in multidimensional evaluation of objects

The development of a multidimensional evaluation model for an object involves meeting specific requirements for each assessed indicator. The complexity of this process is proportional to the number of indicators. The requirements for an indicator are divided into quantitative and qualitative ones. Quantitative requirements are formalized as a set of logical constraints on indicators values. These constraints are modeled using first-order predicate logic. Qualitative requirements account for the decision maker’s inclination or disinclination toward risk in tasks involving the selection of a preferred option and in axiomatic classification problems. When information about risk preferences is unavailable, and the boundaries between adjacent classes are vague, qualitative requirements are modeled using monotonic or nonmonotonic linear and piecewise-linear functions defined over the indicator’s scale. The propensity to take risks is represented by a value or utility function that changes slowly at the lower end of the scale and more rapidly toward the upper end. Conversely, risk aversion is modeled by a function with the opposite behavior. To reflect the fuzziness of class boundaries, evaluation functions with varying rates of transition across class borders are employed. The paper proposes a minimum set of features that distinguish all possible approaches to modeling both quantitative and qualitative requirements for indicator values. The sets of features for solving the problems of ordering and classifying objects differ only quantitatively due to the need to specify requirements for each class. This information is entered into the "Features / Indicators" table of the spreadsheet processor; once imported into the system, an assessment model for each indicator is automatically generated based on the specified requirements.