Models and Metrics for Information Technologies Based on Visual Ternary Comparisons

A new tool for identifying preferences in conditions of target and criterion uncertainty is proposed — lifts of preferences in the form of three sliders with adjustable discreteness. By moving these sliders on the screen of a laptop, tablet, or mobile phone, decision makers apply quick intuitive thinking and visualize their preferences for three alternatives. Visual, numerical, mathematical and symbolic models of visual ternary comparisons are considered and researched. New metrics are proposed for the numerical interpretation of visual ternary comparisons in order to more accurately and reliably calculate the resultant (overall or summarizing) cardinal rankings: the additive metric of sliders height differences and the multiplicative Z-metric. The joint application of both of these metrics showed the coincidence of the ordinal rankings and the closeness of the corresponding values of the resulting normalized and centered cardinal rankings. New metrics are proposed for the logical interpretation of visual ternary comparisons in order to identify the characteristic features of decision-makers (passivity, extremity of assessments, inconsistency of judgments and incompetence). All cases of the generation of binary three-level comparisons were considered and analyzed, and the concept of distance between them was defined, which can be considered a measure of the intransitivity of preferences, that is, the inconsistency of judgments of decision-makers. A new adaptive metric for distinguishing relations of preference and strong preference is proposed, which takes into account individual features of visual ternary comparisons performed by decision-makers. An example of practical implementation of the proposed models and metrics is considered. It is planned to further research the toolkit for identifying preferences based on visual ternary comparisons and improving the information technologies developed by the authors for effective, reliable and visual organization of collective online expertise.