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A Review of Fuzzy Sets in Decision Sciences: Achievements, Limitations and Perspectives

  • Chapter
Multiple Criteria Decision Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 233))

Abstract

We try to provide a tentative assessment of the role of fuzzy sets in decision analysis. We discuss membership functions, aggregation operations, linguistic variables, fuzzy intervals and valued preference relations. The importance of the notion of bipolarity and the potential of qualitative evaluation methods are also pointed out. We take a critical standpoint on the state of the art, in order to highlight the actual achievements and try to better assess what is often considered debatable by decision scientists observing the fuzzy decision analysis literature.

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Notes

  1. 1.

    Indeed, the addition μ +ν is questionable on an ordinal scale. One may replace μ +ν ≤ 1 by μ ≤ n(ν), for a strong negation on L, but then μ ≤ n(ν) implies \(\varphi (\mu ) \leq \varphi (n(\nu ))\) while we need \(\varphi (\mu ) \leq n(\varphi (\nu )\).

  2. 2.

    For more details on the computation of the max-min closure of a fuzzy relation see [38].

  3. 3.

    In fact, one may even consider that the very question of determining how many more times a criterion is important than another one is meaningless.

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Acknowledgements

This paper is an extended version of a position paper written by the first author [40]. The latter is grateful to O. Pavlačka for pointing out a mistake in that paper, and to E. Huellermeier for suggestions on ranking fuzzy intervals stemming from fuzzy weighted averages.

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Authors and Affiliations

  1. IRIT, CNRS & Université de Toulouse, Toulouse, France

    Didier Dubois

  2. LIP6, Université P. et M. Curie, Paris, France

    Patrice Perny

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  1. Didier Dubois
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  2. Patrice Perny
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Correspondence to Didier Dubois .

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Editors and Affiliations

  1. Department of Economics and Business; Portsmouth Business School, Operations & Systems Management, University of Catania; University of Portsmouth, Catania; Portsmouth, Italy

    Salvatore Greco

  2. Department of Management Science, Lancaster University, Lancaster, United Kingdom

    Matthias Ehrgott

  3. Universidade de Lisboa, CEG-IST, Instituto Superior Técnico, Lisboa, Portugal

    José Rui Figueira

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© 2016 Springer Science+Business Media New York

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Dubois, D., Perny, P. (2016). A Review of Fuzzy Sets in Decision Sciences: Achievements, Limitations and Perspectives. In: Greco, S., Ehrgott, M., Figueira, J. (eds) Multiple Criteria Decision Analysis. International Series in Operations Research & Management Science, vol 233. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3094-4_16

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