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Brüggemann, R.* ; Restrepo, G.* ; Voigt, K. ; Annoni, P.*

Weighting intervals and ranking, exemplified by leaching potential of pesticides.

Match-Commun. Math. Comput. Chem. 69, 413-432 (2013)
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Often a ranking based on a multi-indicator systemis performed by construction of a compositeindicator, 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 certain value of the composite indicator. The composite indicator induces a weak or linear or der, when the associated space of an object set together with a data matrix is available. Each hypercube in the g-space, corresponding to intervals of the weights, can be represented by a partial order which is not necessarily a weak or even a linear order. Changing from one point of the hypercube to another will often not change the partial order. We have a freedom of changing weights according to the dimensionality of the g-space -1 (because of normalization). When other hypercubes are selected, then other partial orders can be found. The boundary between two hypercubes with different partial orders is a lower dimensional sphere, with fewer degrees of freedom. In the current paper we treat these two points: (i) how to use weight intervals to determine the resulting partial orders and (ii) if the number of indicators is not too large and if the focus is on a pair of objects instead on th e whole set, then equations are given which can be helpful. As example pesticides are taken, for which three attributes are available. These pesticides are a subset of a set of 50 Italian pesticides, whose leaching potential to groundwater is investigated in Galassi et al.,1996.  
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Publication type Article: Journal article
Document type Scientific Article
Keywords Hasse Diagram Technique ; Partial Order ; Averaged Ranks ; Meteor ; Water ; Refrigerants ; Germany ; Lattice ; Poset ; Tool
ISSN (print) / ISBN 0340-6253
e-ISSN 0340-6253
Quellenangaben Volume: 69, Issue: 2, Pages: 413-432 Article Number: , Supplement: ,
Publisher University of Kragujevac
Publishing Place Kragujevac, Serbia
Reviewing status Peer reviewed