Hasse Diagram Technique

Bruggemann, R., J. Schwaiger, and R.D. Negele. 1995. Applying Hasse diagram technique for the evaluation of toxicological fish tests. Chemosphere 30 1767-1780. 

In this section the multivariate point of view is the central topic. The partial order to be analyzed is a result of a characterisation of objects, e g., of chemicals by different attributes. Especially the Hasse Diagram Technique (abbreviation HDT), which plays a central role in this and in the next three sections is devoted to derive and to draw information out of graphs, based on the <-relation among each single attribute. 

The concept of partial order is described in the chapter of El-Basil, p. 3. Therefore we concentrate ourselves on the specific order relation we are using here, which is known as "Hasse Diagram Technique". In this technique we specifically consider any component of a sequence separately, as it bears its own valuable information with respect to the evaluation. Techniques, motivated by the work of Muirhead 1900, 1906 and Karamata, see... 

The concept of order preserving maps plays an important role in applications of Hasse Diagram Technique (HDT). For an introduction, this concept will be exemplified by the so-called level construction (see Fig. 6). 

A combination of Hasse Diagram Techniques and explorative statistical methods could be a very promising approach to future tasks in environmental sciences. Approaches in this respect were followed on the pollution of regions in Germany with heavy metals, cf. Briiggemann et al. 1999b) and on the contents of environmental databases, cf. Voigt et al. 2004. 

Randic M (2002) On Use of Partial Ordering in Chemical Applications. In Voigt K and Welzl G (Ed.) Order Theoretical Tools in Environmental Sciences -Order Theory (Hasse Diagram Technique) Meets Multivariate Statistics. Shaker-Verlag, Aachen, pp 55-64... 

Lerche DB, Briiggemann R, Sorensen PB, Carlsen L, Nielsen OJ (2002) Comparison of Hasse Diagram Technique with three multicriteria analysis for ranking chemical substances. J Chem Inf Comput Sci 42 1086-1098... 

Partial ranking method Hasse diagram technique... 

The Hasse diagram technique is a very useful tool to perform partial order ranking (POR). It has been introduced in environmental sciences by Halfon. (Halfon et al. 1986 Halfon 1989 Halfon et al. 1998) and refined by... 

A partial order ranking is easily developed by the Hasse diagram technique comparing each pair of elements and storing this information in the Hasse matrix which is a (n x n) antisymmetric matrix for each pair of elements s and t the entry hst of this matrix is ... 

Hasse Diagram Technique and the concept of antagonistic indicators... 

An alternative to time-consuming risk assessments of chemical substances could be more reliable and advanced priority setting methods. Hasse Diagram Technique (HDT) and/or Multi-Criteria Analysis (MCA) provide an elaboration of the simple scoring methods. The present chapter evaluates HDT relative to two MCA techniques. The main methodological step in the comparison is the use of probability concepts based on mathematical tools such as linear extensions of partially ordered sets and Monte Carlo simulations. A data set consisting of 12 High Production Volume Chemicals (HPVCs) is used for illustration. 

It is a paradigm in this investigation to claim that the need of external input (often subjective weightings of criteria) should be minimized and that the transparency should be maximized in any multicriteria prioritisation. This study illustrates that the Hasse Diagram Technique (HDT) needs least external input, is most transparent and is therefore the least subjective... 

Hasse Diagram Technique (HDT) is based on partial order theory (see this book, chapter by El-Basil, p. 3 and Bruggemann et al. 2001). The HDT appears as a simple method, which a priori includes < as only mathematical relation. As the HDT is explained in chapter by Bruggemann and Carlsen, p. 61, we establish here only the main notation ... 

The partial order approach Evaluation of ESB data with the Hasse diagram technique... 

It is most important to note that the lattice of concepts given obviously allows reconstructing the context of Fig. 1. In fact, also in the general case, the lattice of concepts, better say the Hasse diagram of the lattice of concepts perfectly reflects and visualizes the information contained in the context in question For example, we can easily read off from the above diagram, that fire is supposed to be warm and dry (and neither humid nor cold). This is why Hasse Diagram Technique (HDT) is so helpful and important. 

Briiggemann R, Zelles L, Bai QY, Hartmann A (1995) Use of Hasse Diagram Technique for Evaluation of Phospholipid Fatty Acids Distribution in Selected Soils. Chemosphere 30(7) 1209-1228... 

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