References 2018

Beycan, T., B. P. Vani, R. Bruggemann, and C. Suter. 2018.
Ranking Karnataka Districts by the Multidimensional Poverty Indes (MPI) and Applying Simple Elements of Partial Order Theory. Social Indicators
Abstract:
This study focuses on the Multidimensional Poverty Index (MPI) ranking. The standard ranking process of the MPI produces a single total (linear) rank of units by simply ordering them from the best to the worst (or the inverse) as a function of their MPI score. However, units are not necessarily comparable regarding all 10 indicators simultaneously on which the MPI is based. We use the 2012/13 India District Level Household Survey wave four with a special focus on the State of Karnataka. By using partial order theory (i.e. the Hass Diagram technique and the software package PyHasse), we found that, in Karnataka, the number of incomparabilities greatly exceeds the number of comparabilities. This indicates that the aggregation process leading to the MPI hides the individual role of indicators. We utilized a number of tools in partial order theory to analyze the comparabilities and incomparabilities.
This included local partial order, antichain, and average height analysis. In contrast with the standard MPI ranking, partial order theory provides average height which does not only account for comparable districts, but also considers to what extent incomparable districts influence the position of a district in the ranking. We found that the results of partial order ranking deviate considerably from those of the MPI ranking. Given the extent of incomparabilities, for most of our sample, the MPI ranking does not provide an adequate ranking. The Hasse Diagram technique, can therefore be seen as a synthetic ranking tool or a robustness tool that complements the standard ranking process of the MPI. 
Bruggemann, R. and A. Kerber. 2018.
Fuzzy Logic and Partial Order;
First Attempts with the new PyHasseProgram L_eval. Comm.in math.and in comp.chemistry (match) 80:745768.
Abstract:
Logic for sets by introduction of tnorms. When residual tnorms exist they represent a logic, i.e. a truth value for a hold relation. Obect x may hold attribute q(j) with the truth value tv.Implications can be analyzed in dependence on tnorm, object subset and a user defined premise about attribute subsets. 
Bruggemann, R. and L. Carlsen. 2018.
Partial Order and Inclusion of Stakeholder's Knowledge. Comm.in math.and in comp.chemistry (match) 80:769791.
Abstract:
Stakeholders may have a qualitative knowledge about objects to be prioritized. Weights for a weighted sum of indicator values may therefore found in intervals instead of having sharp values. From this fact a new poset about a series of composite indicators can be obtained. The development of incomparability as a function of weightuncertainty is introduced and discussed. 
Carlsen, L. and R. Bruggemann. 2018.
Assessing and Grouping Chemicals Applying Partial Ordering, Alkyl Anilines as IllustrativeExample.
Combinatorial Chemistry & High Throughput Screening 21:349357.
Abstract:
Alkyl Anilines are grouped by applying chemical hazard indicators (accumulation, persistence, mobility,..). Crucial is the orientation of the indicators. It seems as if PO can be applied for grouping without the weaknesses of statistical classification methods. 
Carlsen, L. and R. Bruggemann. 2018.
Environmental perception in 33 European countries: an analysis based on partial order. Environment, Development and Sustainability
Abstract:
objects: 33 european nations, indicators 8 describing public perception of urban quality and environmental issues. Three data sets: pressure indicators (5 indicators) urban quality (3 indicators) and the complete set of indicators. Role of incomparability, Concepts of severity (number of indicator pairs, describing the incomparability of two objects) Discrepancy, taking care of numerical differences of conflicting indicators. So to say: First an purely ordinal measure, than a measure appliable if data are allowing to look for numerical differences.A little bit algebra of combination of indicators. Relative impact of indicators Squared Euclidian distance. A brief subsection about software, PyHasse. ACM: row / columnsum. Similarity. 
Carlsen, L. 2018.
Happiness as a sustainability factor. The world happiness index: a posetic  based data analysis.
Sustainability Science 13:549571.
Abstract:
7 indicators. Relative importance of the indicators. Role of peculiar countries. 157 countries. Average heights. 
Quintero, N. Y., R. Bruggemann, and G. Restrepo. 2018.
Mapping Posets Into Low Dimensional Spaces: The case of Uranium Trappers. Comm.in math.and in comp.chemistry (match) 80:793820.
Abstract:
Three indicators evaluate the suitable of bioorganisms to sorb Uranium and Thorium. The poset is complex.
By use of posetic coordinates lower dimensions can be found and the corresponding posets are better understandable.
The LPOMprocedures are here seen as an ultimate reduction too a 1 dimensional poset, i.e. to a weak order. 
Schoch, D. 2018.
Centrality without indices: Partial rankings and rank probabilities in networks. Social Networks 54:5060.
Abstract:
Social networks. Many centrality indices.Instead of empirical combining the centrality indices to a composite indicator, partial order is applied. Nodessubsetrelations.