Detail publikace

The Evaluation of the Entropy of Decision Makers' Preferences in Ordinal Consensus Ranking Problem

Originální název

The Evaluation of the Entropy of Decision Makers' Preferences in Ordinal Consensus Ranking Problem

Anglický název

The Evaluation of the Entropy of Decision Makers' Preferences in Ordinal Consensus Ranking Problem

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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{BUT76498,
  author="Jan {Fiedor} and Jiří {Mazurek}",
  title="The Evaluation of the Entropy of Decision Makers' Preferences in Ordinal Consensus Ranking Problem",
  annote="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.",
  address="Professional Publishing",
  booktitle="Proceedings of the 29th International Conference on Mathematical Methods in Economics 2011",
  chapter="76498",
  edition="NEUVEDEN",
  howpublished="print",
  institution="Professional Publishing",
  year="2011",
  month="september",
  pages="157--162",
  publisher="Professional Publishing",
  type="conference paper"
}