Conference paper

FIEDOR Jan and MAZUREK Jiří. The Evaluation of the Entropy of Decision Makers' Preferences in Ordinal Consensus Ranking Problem. In: Proceedings of the 29th International Conference on Mathematical Methods in Economics 2011. Praha 4: Professional Publishing, 2011, pp. 157-162. ISBN 978-80-7431-059-1.
Publication language:english
Original title:The Evaluation of the Entropy of Decision Makers' Preferences in Ordinal Consensus Ranking Problem
Title (cs):Výpočet entropie preferencí rozhodovatelů v problému s ordinálním hodnocením alternativ
Pages:157-162
Proceedings:Proceedings of the 29th International Conference on Mathematical Methods in Economics 2011
Conference:29th International Conference on Mathematical Methods in Economics
Place:Praha 4, CZ
Year:2011
ISBN:978-80-7431-059-1
Publisher:Professional Publishing
Keywords
entropy, group decision analysis, ordinal consensus ranking problem, preferences, uncertainty
Annotation
The aim of the article is to introduce Shannon entropy and the relative entropy into ordinal consensus ranking problem (OCRP) context as a measure of uncertainty of preferences within a group of decision makers (DMs). An existence of a consensus in the OCRP crucially depends on initial decision makers' preferences: rankings of n objects from the 1st to the nth place. When those rankings are markedly different, there is high entropy (uncertainty) associated with DMs' preferences and a unique consensus within a group is unlikely to be achieved. However, when DMs' rankings are similar, the entropy is small and a consensus is much more likely to be obtained. In the article a relationship between the relative entropy of DMs preferences and an agreement among four classic methods' for OCRP solutions is discussed on several examples. Moreover, experimental evaluation of the relationship is performed and our results indicate that there is a negative relation between the relative entropy and the agreement among methods' solutions, e.g. the higher is the relative entropy, the lower is the methods' agreement. The question remains whether a theoretical relation connecting the entropy and a solution existence (or agreement among methods' solutions) to OCRP can be derived in general.
BibTeX:
@INPROCEEDINGS{
   author = {Jan Fiedor and Ji{\v{r}}{\'{i}} Mazurek},
   title = {The Evaluation of the Entropy of Decision Makers'
	Preferences in Ordinal Consensus Ranking Problem},
   pages = {157--162},
   booktitle = {Proceedings of the 29th International Conference on
	Mathematical Methods in Economics 2011},
   year = {2011},
   location = {Praha 4, CZ},
   publisher = {Professional Publishing},
   ISBN = {978-80-7431-059-1},
   language = {english},
   url = {http://www.fit.vutbr.cz/research/view_pub.php.en.iso-8859-2?id=9846}
}

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