Comparative Knowledge Discovery with Partial Orders and Composite Indicators: Multi-indicator Systemic Ranking, Advocacy, and Reconciliation

In many decision-making situations, ranking of objects with related tasks is a fundamentally important issue. In these situations, a number of objects are ranked on the basis of measurements on a set of several indicators. A prevalent approach is to form a composite index from these several measurements using weights of relative importance for the selected indicators determined by experts and/or stakeholders. An entirely different approach for ranking uses the theory of partially ordered sets (posets). In classical poset ranking derived by average ranks (AR) method, unequal indicator weights of any kind do not play any part in the computation of ranking based on a given data matrix. Here we present a novel method of poset ranking that involves stochastic order of weighted indicator cumulative rank frequency (CRF) distributions. We then investigate how this data-validated evidence-based ranking can be used to construct a composite index reproducing an identical ranking. We further seek reconciliation between databased weighted poset CRF ranking and ranking induced by an arbitrary subjective composite index. This investigation acquires particular importance today in view of issues of trade-offs among indicators, implicit in the apparent advocacy involved in the choice of weights of the composite index. This chapter is based on research conducted in the spirit of start small even for big data. The concept of databased weighted poset ranking introduced here may open doors to still other ways of weighting schemes and other reconciliation approaches for comparative knowledge discovery using partial orders and composite indicators. Meaningful ability to deal with big data is an urgent need of comparative knowledge discovery with partial orders and composite indicators in this infometrical computer science and software engineering age of statistical information science and technology. This chapter is prepared in the spirit of a concept paper for digital age infometrics and comparative knowledge discovery critical in several fields, such as document discovery, drug discovery, gene discovery, chemical discovery, criminal discovery, geospatial critical area discovery, etc. The ranking, prioritization, and selection of objects and indicators carrying a variety of names in a variety of contemporary issues of societal and scientific importance based on relevant evidence embodied in data matrices provide insightful leads in these substantive investigations involving variously big data.