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Fuzzy Sets and Fuzzy Logic-Based Methods in Multicriteria Decision Analysis

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Trends in Multiple Criteria Decision Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 142))

Abstract

In this chapter, we discuss some fuzzy sets and fuzzy logic-based methods for multicriteria decision aid. Alternatives are identified with score vectors x ∈ [0, 1]n, and thus they can be seen as fuzzy sets, too. After discussion of integral-based utility functions, we introduce a transformation of score x into fuzzy quantity U(x). Orderings on fuzzy quantities induce orderings on alternatives. A special attention is paid to defuzzification-based orderings, especially to mean of maxima method. Our approach allows an easy incorporation of importance of criteria. Finally, a fuzzy logic-based construction method to build complete preference structures over set of alternatives is given.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68, Bratislava, Slovakia

    Radko Mesiar & Lucia Vavríková

Authors
  1. Radko Mesiar
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  2. Lucia Vavríková
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Correspondence to Lucia Vavríková .

Editor information

Editors and Affiliations

  1. Dept. Engineering Science, University of Auckland, Auckland, New Zealand

    Matthias Ehrgott

  2. Depto. Engenharia e Gestao, Instituto Superior Tecnico, Av. Prof.Dr. Cavaco Silva, Porto Salvo, 2780-990, Portugal

    José Rui Figueira

  3. Faculty of Economics, University of Catania, Corso Italia 55, Catania, 95129, Italy

    Salvatore Greco

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Mesiar, R., Vavríková, L. (2010). Fuzzy Sets and Fuzzy Logic-Based Methods in Multicriteria Decision Analysis. In: Ehrgott, M., Figueira, J., Greco, S. (eds) Trends in Multiple Criteria Decision Analysis. International Series in Operations Research & Management Science, vol 142. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5904-1_6

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