The environmental and chemical sciences are ever more reliant on computers. This dependence needs formalization, and the theory of algebraic relations is one possibility. Under algebraic relations, "order" turns out to be of special interest in many applicational fields. Internationally renowned authors explain the theory and practice of order relations in such a way, that no specific mathematical skill is needed to understand the advantages of this algebraization. As the order relations are very general and simple, they can be used quite universally. For example, the structure of chemicals and their properties; evaluation of waste disposal sites, decision support for river management; and the way to measure biodiversity are examples of the broadness of the concept.
This book is recommended to those, who are interested in the interface between sciences and management.

TThis 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 data analysis is increasingly being realized and many applications of partially ordered sets to real problems in statistics and applied sciences have appeared. Main examples pertain to the analysis of complex and multidimensional systems of ordinal data and to problems of multi-criteria decision making, so relevant in social and environmental sciences. Partial Order Concepts in Applied Sciences presents new theoretical and methodological developments in partial order for data analysis, together with a wide range of applications to different topics: multidimensional poverty, economic development, inequality measurement, ecology and pollution, and biology, to mention a few. The book is of interest for applied mathematicians, statisticians, social scientists, environmental scientists and all those aiming at keeping pace with innovation in this interesting, growing and promising research field.

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 application of the mathematical theory of partial order, especially when the indicator system shall be used for ranking purposes.

"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 order.

This book explains the theory and practice of order relations in such a way that no specific mathematical skill is needed to understand the advantages of this algebraization. It acts as a primer in a mathematical technique which is useful in many expanding disciplines, like genomics, techniques of decision support, and sustainability. This book is recommended to those who are interested in the interface between sciences and management.

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 application of the mathematical theory of partial order, especially when the indicator system shall be used for ranking purposes.

Als roter Faden dient dem Autor hier erstmals der Bewertungsgedanke. Die Ausbreitung von Chemikalien wird modelliert, um zu sehen wo Akkumulationen denkbar sind. Bewertet werden Chemikalien in der Umwelt und die Umwelt in ihren Belastungszustanden. Dazu werden Ausbreitungsmodelle, Methoden zur Abschatzung von Substanzeigenschaften (QSAR), Wirkungsmodelle mit okologischem Hintergrund und Bewertungsverfahren vorgestellt. Der notwendige mathematische Apparat wird dabei meist Schritt fur Schritt erlautert. Das Buch eignet sich fur alle, die sich einen Uberblick uber weite Bereiche der mathematischen Modellierung von Umweltchemikalien verschaffen wollen, sowie fur Spezialisten, die sich mit Bewertungsverfahren beschaftigen.

Die begleitende CD-ROM beinhaltet kleine Programme. Leser konnen damit in die Modellierung praktisch eingefuhrt werden und selbst einzelne Schwerpunkte zur Modellierung ausprobieren."

TThis 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 data analysis is increasingly being realized and many applications of partially ordered sets to real problems in statistics and applied sciences have appeared. Main examples pertain to the analysis of complex and multidimensional systems of ordinal data and to problems of multi-criteria decision making, so relevant in social and environmental sciences. Partial Order Concepts in Applied Sciences presents new theoretical and methodological developments in partial order for data analysis, together with a wide range of applications to different topics: multidimensional poverty, economic development, inequality measurement, ecology and pollution, and biology, to mention a few. The book is of interest for applied mathematicians, statisticians, social scientists, environmental scientists and all those aiming at keeping pace with innovation in this interesting, growing and promising research field.

This book provides axioms of partial order and some basic material, for example consequences of "criss-crossing" of data profiles, the role of aggregations of the indicators and the powerful method of formal concept analysis. The interested reader will learn how to apply fuzzy methods in partial order analysis and what 'antagonistic indicator' means.

Als roter Faden dient dem Autor hier erstmals der Bewertungsgedanke. Die Ausbreitung von Chemikalien wird modelliert, um zu sehen wo Akkumulationen denkbar sind. Bewertet werden Chemikalien in der Umwelt und die Umwelt in ihren Belastungszustanden. Dazu werden Ausbreitungsmodelle, Methoden zur Abschatzung von Substanzeigenschaften (QSAR), Wirkungsmodelle mit okologischem Hintergrund und Bewertungsverfahren vorgestellt. Der notwendige mathematische Apparat wird dabei meist Schritt fur Schritt erlautert. Das Buch eignet sich fur alle, die sich einen Uberblick uber weite Bereiche der mathematischen Modellierung von Umweltchemikalien verschaffen wollen, sowie fur Spezialisten, die sich mit Bewertungsverfahren beschaftigen.

Die begleitende CD-ROM beinhaltet kleine Programme. Leser konnen damit in die Modellierung praktisch eingefuhrt werden und selbst einzelne Schwerpunkte zur Modellierung ausprobieren."