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## Publications

Publications (341)

Evaluation by ranking/rating of data based on a multitude of indicators typically calls for multi-criteria decision analyses (MCDA) methods. MCDA methods often, in addition to indicator values, require further information, typically subjective. This paper presents a partial-order methodology as an alternative to analyze multi-indicator systems (MIS...

This paper aims to identify the major determinants of the structural differences in gender equality for EU countries, using tools from partial order theory on a system of 6 indicators, pertaining to the Sustainable Development Goal 5 “Achieve gender equality and empower all women and girls”. The paper analyzes the gender equality partial orders, am...

Computer crime is a matter of increasing concern, and worldwide action is required if the proper responses to it are to be found. One of the tools that can be deployed here is the Global cybersecurity index (GCI), a control and feedback mechanism based on a composite indicator. The GCI is based on a hierarchy of sub-indicators. The indicators used...

Hasse diagram technique, based on partial ordering is an advantageous method to analyse complex systems of data such as objects characterized by multi-indicator systems. Beside ordered sequences of objects the theory may reveal the impact of each indicator for the set of order relations, which in general is of high interest. A method to measure the...

The inequality between genders is a problem virtually in all countries. A comparison among 28 nations of the European Union together with a data set corresponding to a population weighted average of all European Union nations is performed for the years 2006, 2010 and 2017, respectively. In order to compare the nations mutually, six indicators out o...

Stakeholders decisions often are based on the construction of an indicative quantity (a composite indicator), which can be obtained by an aggregation process of a series of single indicators. This aggregation process combines single indicators to one quantity, the composite indicator. In the most simple aggregation technique a weighted sum is appli...

The United Nations’ 17 sustainable development goals (SDGs) were adopted in 2015. Following a 2020 status report of the status and development for 102 countries, for which data for all 17 SDGs for the years 2010, 2015 and 2019 were studied. The analyses were carried out applying partial ordering methodology. Four sets of analyses are reported: 1) a...

The inequality within the 27 European member states has been studied. Six indicators proclaimed by Eurostat to be the main indicators charactere the countries: (i) the relative median at-risk-of-poverty gap, (ii) the income distribution, (iii) the income share of the bottom 40% of the population, (iv) the purchasing power adjusted GDP per capita, (...

We introduce a new method for ranked set sampling with multiple criteria. The method relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, units are ranked in sets based on linear extensions in partially order set theory with considering all variables simultaneously. Results will b...

Measured data are a challenge for partial order theory, because a priori partial order does only know the

Many decisions in environmental chemistry are based on a set of indicators. The task is, how to extract from them (i.e.in our study: from the resulting data matrix of sites vs metals/metalloids) a composite indicator, also called a synthetic indicator. From the composite indicator in turn a ranking may be derived and decisions can be obtained based...

Partial orders can be a useful interim step, when decisions are to be found within the framework of a Multi-Indicator system. However, the concept of partial order comes to its limit when, due to conflicting values in the data matrix certain the objects can no longer be compared with each other. Alternatively the concept of weighted sums is very of...

The challenge for the development of a sustainability assessment for management purposes is that many boundary conditions are to be considered (Koplin, Nachhaltigkeit im Beschaffungsmanagement. Ein Konzept zur Integration von Umwelt- und Sozialstandards. Dissertation. Universität Oldenburg, Oldenburg. Wirtschaftswissenschaften, 2006; Wilkens, Multi...

Partial order, the leading concept in this book, is not studied because of its mathematical secrets, but because this mathematical concept is helpful in ranking studies and therefore in many decision situations. Although the mathematical treatment is not difficult, the manual handling is tedious and error-prone. Therefore, software was and is devel...

The partial order theoretical treatment of measured data leads to a set of implications. Each implication is evaluated by a truth-value, a value in the range between 0 and 1. Conventional statistical tools such as correlation measures can also be used as a basis to formulate implications. Therefore, it is needed to compare the partial order approac...

Indicators play an increasing role in characterizing complex systems and – to some degree – in decision problems, when a ranking is thought of as an intermediate step for a selection of optimal – or depending on external constraints – suboptimal options. When ranking is the aim, we cannot usually describe it by a single indicator. We need a set of...

Indicators are more and more applied to describe and analyze complex systems. Typical examples: Innovation potential of nations, child-well being, Environmental health, poverty, chemical pollution, corruption of nations. The task is: How can a system of indicators be defined in order to fulfill the above expectations. One possibility is the applica...

In sampling theory, we are looking for efficient sampling designs to estimate the population parameters. Efficiency is mostly defined based on high precision and low cost. Such sampling designs are more achievable when auxiliary variables are available. Selecting many sampling units and rank them based on auxiliary variables before selecting the fi...

The environmental perception in 33 European countries is based on eight indicators: ‘Air Pollution,’ ‘Drinking Water Pollution and Inaccessibility,’ ‘Dissatisfaction with Garbage Disposal,’ ‘Dirty and Untidy,’ ‘Noise and Light Pollution,’ ‘Water Pollution,’ ‘Dissatisfaction to Spend Time in the City’ and ‘Dissatisfaction with Green and Parks in the...

This paper is going to introduce a new method for ranked set sampling with multiple criteria. The method is based on a version of ranked set sampling, introduced by Panahbehagh et al. (2017), which relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, elements are ranked in sets ba...

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...

Background
The theory of partial order is a branch of Discrete Mathematics and is often seen as pretty esoteric. However, depending on a suitable definition of an order relation, partial order theory has some statistical flavor. Here we introduce the application of partial order for environmental chemistry.
Objective
We showed that partial order i...

Land use and climate changes induce shifts in plant functional diversity and community structure.
Comparing the past, current, and potential future distribution of indicator species is important for detecting these biodiversity shifts. Therefore, a thorough understanding of the main factors affecting the distribution of those species is necessary....

Aim and objective:
In chemistry, there is a long tradition in classification. Usually, methods are adopted from the wide field of cluster analysis. The present study focusses on the application of partial ordering methodology for the classification of 21 alkyl substituted anilines.
Materials and methods:
The analyses are based on the concepts fr...

The project “Barrier-reduced Machines in Innovative Interaction” (iBaMs) was aimed at enabling employees with intellectual disabilities to extend their range of tasks and to increase their level of responsibility. This goal is to be achieved by an assistive accessible control panel for the operation of complex computer-controlled machines. Therefor...

Journal Social Indicators Research, 136(3), 1269-1285.
DOI: 10.1007/s11205-017-1666-5
Abstract: https://link.springer.com/article/10.1007/s11205-017-1666-5.

Urban air pollution with benzene, toluene, ethyl benzene and xylenes (BTEX) is a common phenomenon in major cities where the pollution mainly originates from traffic as well as from residential heating. An attempt to rank cities according to their BTEX air pollution is not necessarily straight forward as we are faced with several individual polluta...

Analysing order relationships among objects is central for decision making processes or for optimisation, which are also relevant in the field of chemistry. A mathematical tool to carry out ordering studies is the Hasse diagram technique, whose Hasse diagram summarises a large amount of order information. However, when the number of objects is larg...

The actual state of the development of PyHasse allows an ordinal analysis in the field of decision making, especially of performing rankings. The project iBaMs—Barriere-Reduced Machines in Innovative Interaction—aimed at promoting social inclusion for intellectually disabled people and their integration into labor markets and everyday activities. W...

The German core sustainability indicators are applied to determine the status of sustainable development (SD) of Germany’s federal states. As such processes depend on political measures, the chapter analyses the connection of the SD performance of federal states with the governing political parties using the Partial Order methodology. Based on the...

Classical measurements of performances are typically based on linear scales. However, in analytical chemistry one scale may be not sufficient to measure items appropriately. However, explorative statistics provide more factors, which all tell their own story about the analytical performance. Partial order methodology offers a possibility to evaluat...

Undoubtedly, the use of ethnobotanical and ethnopharmacological knowledge is of high priority worldwide, especially in fields such as drug development. Beginning in the 20th century, in the period of academic ethnobotany, the fields of ethnobotany and ethnopharmacology experienced a shift from the raw compilation of data to a greater methodological...

When a mutual ranking of a selection of objects is wanted, an initial step is the development of a multi-indicator system (MIS). Many MCDA concepts, e.g., members of the ELECTRE-family or of the different PROMETHEE versions, are available for obtaining rankings from an MIS. On the one side, a major disadvantage applying these models is the need for...

Poverty can be seen as a multidimensional phenomenon. A one-dimensional measure of poverty serving as a ranking index can be obtained by aggregating the different poverty aspects into a single scalar. Ranking indexes are thought of as supporting political decisions. We propose an alternative view based on simple concepts of partial order theory and...

The resilience of savanna ecosystems to climate and land-use changes is an important ecological and management question. The term ‘resilience’ is used to refer to the ability of a tree species to survive in a specific location, even under changing environmental conditions. In this study, vectors of functional traits of selected savanna tree species...

Partial order methodologies appear as advantageous tools to disclose evaluative trends and developments for time series as, e.g., the fragile states index (FSI). The present study focuses on the variations in the 12 individual indicators of the FSI over the years 2011–2015. The FSI includes in total 178 states and the present study analyzes both th...

Uranium contamination is of global concern and several approaches have been applied to cleanse U-contaminated ecosystems. Among them, biotechnological techniques using microorganisms have proven to be eco-friendly. However, knowing which of them behave better for U trapping is still an open question. In this study, a general and a detailed comparis...

According to the World Health Organization, the safety of herbal medicines has become a major concern to both national health authorities and the general public. Here, using partial order analysis, we explore the reported undesirable effects of medicinal herbal substances, in their traditional/ethnopharmacological use. Data were retrieved from the...

Given two sets A and B, often the question arises how far objects a of A and b of B can be combined to a pair (a,b), fulfilling certain requirements. A first example is the marriage problem, another, the successful assignment of scientific projects to the needs of small or medium sized enterprises. A third example, which motivated this study, arise...

Risk assessment of chemicals consists of eight steps: ‘hazard identification, effects assessment, exposure assessment, risk characterization, risk classification, risk–benefit analysis, risk reduction, and monitoring’. The present study deals with the following steps: exposure assessment, effects assessment, risk characterization, and risk reductio...

The role of data noise is analyzed for a pair of objects and m indicators (m > 1) with respect to order relations. A general probability scheme is developed and by specifying a noise-model and a distribution for noisy values explicit expressions are derived. These expressions allow an a priori estimation at which noise level effects the order relat...

This book illustrates recent advances in applications of partial order theory and Hasse diagram techniques to data analysis, mainly in the socio-economic and environmental sciences. For years, partial order theory has been considered a fundamental branch of mathematics of only theoretical interest. In recent years, its effectiveness as a tool for d...

Poverty can be seen as a multidimensional phenomenon described by a set of indicators, the poverty components. A one-dimensional measure of poverty serving as a ranking index can be obtained by combining the component indicators via aggregation techniques. Ranking indices are thought of as supporting political decisions. This paper proposes an alte...

Classical measurements of performances are typically based on linear scales. However, in analytical chemistry a simple scale may be not sufficient to analyze the analytical performance appropriately. Here partial order methodology can be helpful. Within the context described here, partial order analysis can be seen as an ordinal analysis of data ma...

We discuss some property-property relationships (PPRs) for the estimation of vapour pressure with regard to their predictive power in terms of accuracy and applicability. Seven different PPRs mostly based on the Clausius-Clapeyron equation are analysed, including for example the method of Mackay or those of Fishtine/Vetere. A data set of 375 compou...

Decision making is to an increasing extent supported by multi-criteria decision analysis (MCDA) software. Especially when a ranking of objects (chemicals, geographical units, nations, strategies etc) is wanted, an initial step is the development of a multi-indicator system (MIS). One of the famous MCDA concepts to obtain a ranking from MIS is reali...

We continue [5] by generalizing the indicator-driven evaluation. The mathematical basis is now a general complete lattice L. We show that this allows a problem-orientation by choosing a suitable set theory and logic. It leads, for example, to a problem-oriented subsethood degree relation that generalizes Kosko's subsethood degree applied in [5]. In...

A priori in partial ordering methodology the input data are understood as exact and true values, which is denoted as the "original data matrix". As such even minor differences between values are regarded as real. However, in real life data are typically associated with a certain portion of noise or uncertainty. Hence, introducing noise may cause ch...

Simple elements of partial order theory appear helpful for a causal analysis in the context of ranking. The Hasse diagrams may seem as a confusing system of lines and a high number of incomparabilities. Thus, they indicate that metric information may be lost, but, on the other side partial order tools offer a wide variety of additional information...

Environmental aspects often are in conflict with the criteria for a best/optimal behavior under technical aspects only. In these cases, common methods to compare different options and to come to a decision show methodological disadvantages. In this situation, this chapter intends to demonstrate the situation firstly by giving a typical example, sec...

Lichens and mosses have extensively been used in multielemental large-scale biomonitoring studies of atmospheric metal pollution. Despite its high importance in the assessment of cumulative risk and the communication with risk managers, the presentation and interpretation of biomonitoring results have only been partially the center of interest for...

When newer compilations of decision support methods are examined, partial order methods as a central methodological aspect are rarely found. This is strange, since the role of multi-indicator systems is worldwide increasing. Multi-indicator systems induce in a natural manner partial orders. Why is partial order not seen as that important tool? The...

Human health and the health of the environment have entwined. In this paper we underpin this position by presenting a modeling approach named CombiSimilarity, which has been developed by the first author in the software tool PyHasse comprising a wide variety of partial ordering tools. A case study of 18 Organochlorine Pesticides (OCPs) detected in...

Often from multi-indicator system (MIS), a composite indicator is derived by applying weighted sums of the single indicators. The eventual ranking being based on composite indicator yields a total (linear) ranking. In contrast, partial order ranking constitutes an alternative approach where assumptions about linearity or distribution of the indicat...

The role of indicators to measure trends in every area of interest is increasing. Especially in the field of politics and sociology, where modeling based on multiple indicators typically is difficult, multi-indicator systems call for attention. Multi-indicator systems are most often the first step to derive a ranking indicator. Correspondingly ther...

In this chapter we evaluate the data of 18 Organochlorine pesticides (OCPs) found in breast milk samples from 44 mothers in the Taurus Mountains in Turkey. In this approach the association of concentration levels in breast milk samples with the two confounding factors: smoking habit and habit of taking medication is the goal. For all data evaluatio...

Ranking of chemicals is an important step in risk assessments. The hazard of chemicals exerted on human or on environments is not directly measurable, instead a set of indicators serve as proxy for this purpose. This so-called multi-indicator system is of high scientific value because it contains specific knowledge about chemicals. Often a ranking...

When partial orders are applied on data matrices in order to perform a ranking then incomparabilities may appear, i.e., directed graphs have vertices, which are not connected and therefore not in a mutual ranking relation. Consequently, often partial order is not considered as a decision support system but rather as an analytical tool to explore da...

Douglas Jay Klein and other researchers have seen that there is a great potential in applying partial
order in the field of QSAR. The basic idea is to deduce from order relations among chemicals, properties
of the ordered chemicals. Despite the satisfactory results found by Klein’s methods, we think it is
worth exploring another feature of the pose...

"Multi-indicator Systems and Modelling in Partial Order" contains the newest theoretical concepts as well as new applications or even applications, where standard multivariate statistics fail. Some of the presentations have their counterpart in the book; however, there are many contributions, which are completely new in the field of applied partial...

Ideal formulation of a multi-indicator system (MIS) would be to define, design, and acquire the entire construct with complete consensus among all concerned. However, such would be an extreme rarity in actuality. Experts have differing views. Factors may not express monotonically, as when either extreme is unfavorable. The entirety cannot be assess...

The software PyHasse is an elaborated “experimental” software for ordinal analysis of data matrices. PyHasse is based on the interpreter programming language Python. A brief introduction to the programming language Python is given and the general principles behind PyHasse are outlined. An actual overview about PyHasse (status, April 2013) is provid...

Studies on fate and toxicity are important aspects in environmental impact assessments of chemicals. In order to elucidate “what is worst” a ranking of the chemicals under investigation is of significant interest, which obviously constitutes a multi-indicator system (MIS). Partial order methodologies turn out to be advantageous tools for analyses o...

Sustainable/Green Chemistry is a chemical philosophy encouraging the design of products and processes that reduce or eliminate the use and generation of hazardous substances. In this respect, metrical scientific disciplines like Chemometrics are important, because they indicate criteria for chemicals being hazardous or not. We demonstrated that sus...

Often a ranking based on a multi-indicator system is performed by construction of a composite indicator, which is generally computed as a weighted average of the indicators. The set of weight-tuples is introduced: the g-space. Each point of this space represents a tuple of weight values, which lead together with the indicators of an object to a cer...

Multi-indicator systems are of increasing importance in every field of science, corresponding to the complexity of objects to be ranked. Here we apply multi-indicator systems in order to describe and characterize the pollution in the South-West of Germany by the metals Lead, Pb, Cadmium, Cd, Zinc, Zn and Sulfur, S. We demonstrate the need of a prep...

Monte Carlo simulations are well known within risk assessments; similarly there is some interest in applying simple elements of partial order theory in the field of decision analysis, ranking and evaluation. Much criticism concerning the application of partial order to data matrices originates from the translation of even small numerical difference...

A special application of global sensitivity analysis is that on partially ordered sets – posets – that are sets of objects endowed by a binary order relation. In a partial order two objects can be in relation with each other, and are said to be comparable, or not, then they are said to be incomparable. Comparability and incomparability relations be...

Exposure data to organochlorine pesticides (OCPs) of mothers' breast milk samples were measured in different locations in the Taurus Mountains/Turkey. Villages at five altitudes were looked upon. The data analysis method applied is the Hasse diagram technique, based on Discrete Mathematics. For each of the five regions, one Hasse diagram was calcul...

The paper of Huang, Keisler and Linkov (HKL) (Huang et al., 2011) has motivated us to this note about the relation between ranking procedures and Multi-Criteria Decision Analysis (MCDA) tools. The key concept in the HKL-paper is in our eyes the 'trade-off'. A 'trade-off' seems necessary, when conflicting indicator values are present. HKL stress tha...

This study assesses the predictability of future livelihood strategies of transhumant pastoralists in semi-arid Morocco. A decrease in precipitation due to climate change will likely threaten their traditional livelihood strategy. We examine whether the pastoralists explicitly prefer certain alternative strategies or if their reactions will be cont...

Ranking chemicals according to their potential environmental hazard is a well accepted preparatory step in risk assessment. A study of Halfon et al. ranked pesticides by applying simple tools on the partially ordered set (poset) induced by chemical properties as proxies for their groundwater contamination hazard. In this contribution, we present so...

Simple elements of partial order theory turned out to be useful tools when rankings are needed. Here we show, how a subset of objects, mutually incomparable (called an antichain) can be further analyzed. There is a surprising relation to extremal graph theory, namely an application of the famous theorem of Turan. As example, we analyze the partiall...

Sustainable chemistry is a chemical philosophy encouraging the design of products and processes that reduce or eliminate the use and generation of hazardous substances. In this respect, metrical scientific disciplines like Chemometrics, Environmetrics, Biometrics, Chemoinformatics, Environmental Informatics, etc. support this principle. The effects...

The complexity of the present data-centric world finds its expression in the increasing number of multi-indicator systems. This has led to the development of multicriteria ranking systems based on partial order. Partial order theory helps reveal why an object of interest holds a certain ranking position and how much it is subject to change if a com...

Seawater desalination is a rising technology intended to overcome water scarcity and is increasingly being used for the production of drinking water. A good quality pretreatment process is prominent to the successful operation of a Seawater Reverse Osmosis (SWRO) plant. The tasks of the intake and the pretreatment modules are to prevent fouling and...

Partial order tools can be used in multiple criteria analysis to prioritize and rank a set of objects. In this setting the starting point is generally a matrix Mnxk of k observed indicators on n objects. Given that indicators are measured at least at the ordinal level, from matrix M its corresponding partially ordered set - poset - is set up to for...

There are at least two significant applications of partial order theory in chemistry: Ranking methods and substances' properties prediction. In both cases, a set of objects is endowed with a partial order relation e.g. "more polluting than", "can be obtained from", "more reactive than" etc. The couple of set and partial order relation is known in m...

Seawater desalination is a rising technology to overcome water scarcity and is increasingly being used for the production of drinking water. A good quality pretreatment process is prominent in the successful operation of a seawater reverse osmosis (SWRO) plant. The tasks of the intake and the pretreatment modules are to prevent fouling and to exten...

In Chapter 6, we have shown as to how we can obtain simpler Hasse diagrams from messy ones. We transformed the data matrix
so that incomparabilities or comparabilities disappear because objects become equivalent.