A hitchhiker's guide to poset ranking.

When ranking objects (like chemicals, geographical sites, river sections, etc.) by multicriteria analysis, it is in most cases controversial and difficult to find a common scale among the criteria of concern. Therefore, ideally, one should not resort to such artificial additional constraints. The theory of partially ordered sets (or posets for short) provides a solid formal framework for the ranking of objects without assigning a common scale and/or weights to the criteria, and therefore constitutes a valuable alternative to traditional approaches. In this paper, we aim to give a comprehensive literature review on the topic. First we formalize the problem of ranking objects according to some predefined criteria. In this theoretical framework, we focus on several algorithms and illustrate them on a toy example. To conclude, a more realistic real-world application shows the power of some of the algorithms considered in this paper.

New operations for informative combination of two partial order relations with illustrations on pollution data.

We discuss various ways in which to construct and process partial order relations or partially ordered sets (posets) in the context of ranking objects on the basis of multiple criteria. Oftentimes, it is undesirable or even impossible to devise a weighting scheme to compute a final score on the basis of the criteria. An alternative is then to restrict oneself to the information contained in the partial ordering of all objects implied by the criteria. We will consider some ways in which one can exploit partial order relations to determine a ranking of a collection of objects. More exactly, we will examine how to combine information coming from two sources, both for the case in which the sources are considered to be equally important, as well as for the case in which one source of information should take priority. We illustrate the concepts on pollution data coming from 59 regions in Baden-Württemberg.

Mining fatty acid databases for detection of novel compounds in aerobic bacteria.

This study examines how the discriminatory power of an automated bacterial whole-cell fatty acid identification system can be significantly enhanced by exploring the vast amounts of information accumulated during 15 years of routine gas chromatographic analysis of the fatty acid content of aerobic bacteria. Construction of a global peak occurrence histogram based upon a large fatty acid database is shown to serve as a highly informative tool for assessing the delineation of the naming windows used during the automatic recognition of fatty acid compounds. Along the lines of this data mining application, it is suggested that several naming windows of the Sherlock MIS TSBA50 peak naming method may need to be re-evaluated in order to fit more closely with the bulk of observed fatty acid profiles. At the same time, the global peak occurrence histogram has put forward the delineation of 32 new peak naming windows, accounting for a 26% increase in the total number of fatty acid features taken into account for bacterial identification. By scrutinizing the relationships between the newly delineated naming windows and the many taxonomic units covered within a proprietary fatty acid database, all new naming windows were proven to correspond with stable features of some specific groups of microorganisms. This latter analysis clearly underscores the impact of incorporating the new fatty acid compounds for improving the resolution of the bacterial identification system and endorses the applicability of knowledge discovery in databases within the field of microbiology.