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Preferences and Decisions pp 261–279Cite as

Supporting Consensus Reaching Processes under Fuzzy Preferences and a Fuzzy Majority via Linguistic Summaries

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 257))

Abstract

We consider the classic approach to the evaluation of of degrees of consensus due to Kacprzyk and Fedrizzi [6], [7], [8] in which a soft degree of consensus has been introduced. Its idea is to find a degree to which, for instance, “most of the important individuals agree as to almost all of the relevant options”. The fuzzy majority, expressed as fuzzy linguistic quantifiers (most, almost all, ...) is handled via Zadeh’s [46] classic calculus of linguistically quantified propositions and Yager’s [44] OWA (ordered weighted average) operators. The soft degree of consensus is used for supporting the running of a moderated consensus reaching process along the lines of Fedrizzi, Kacprzyk and Zadrożny [3], Fedrizzi, Kacprzyk, Owsiński and Zadrożny [2], Kacprzyk and Zadrożny [22], and [24].

Linguistic data summaries in the sense of Yager [43], Kacprzyk and Yager [13], Kacprzyk, Yager and Zadrożny [14], in particular in its protoform based version proposed by Kacprzyk and Zadrożny [23], [25] are employed. These linguistic summaries indicate in a human consistent way some interesting relations between individuals and options to help the moderator identify crucial (pairs of) individuals and/options with whom/which there are difficulties with respect to consensus. An extension using ontologies representing both knowledge on the consensus reaching process and domain of the decision problem is indicated.

This work was supported by the Ministry of Science and Higher Education in Poland under Grant N N519 404734.

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Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447, Warsaw, Poland

    Janusz Kacprzyk & Sławomir Zadrożny

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  1. Janusz Kacprzyk
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  2. Sławomir Zadrożny
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Editor information

Editors and Affiliations

  1. Department of Economics and Quantitative Methods, University of Catania, Corso Italia 55, 95129, Catania, Italy

    Salvatore Greco

  2. Department of Computer and Management Sciences, University of Trento, Via Inama 5, 38122, Trento, Italy

    Ricardo Alberto Marques Pereira

  3. Department of Economical and Social Sciences, University of Sannio at Benevento, Via delle Puglie, 82100, Benevento, Italy

    Massimo Squillante

  4. Machine Intelligence Institute, Iona College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

  5. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447, Warsaw, Poland

    Janusz Kacprzyk

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Kacprzyk, J., Zadrożny, S. (2010). Supporting Consensus Reaching Processes under Fuzzy Preferences and a Fuzzy Majority via Linguistic Summaries. In: Greco, S., Marques Pereira, R.A., Squillante, M., Yager, R.R., Kacprzyk, J. (eds) Preferences and Decisions. Studies in Fuzziness and Soft Computing, vol 257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15976-3_15

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  • DOI: https://doi.org/10.1007/978-3-642-15976-3_15

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