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Fuzzy Measures and Integrals in MCDA

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Multiple Criteria Decision Analysis: State of the Art Surveys

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 78))

Abstract

This chapter aims at a unified presentation of various methods of MCDA based on fuzzy measures (capacity) and fuzzy integrals, essentially the Choquet and Sugeno integral. A first section sets the position of the problem of multicriteria decision making, and describes the various possible scales of measurement (cardinal unipolar and bipolar, and ordinal). Then a whole section is devoted to each case in detail: after introducing necessary concepts, the methodology is described, and the problem of the practical identification of fuzzy measures is given. The important concept of interaction between criteria, central in this chapter, is explained in detail. It is shown how it leads to fuzzy measures. The case of bipolar scales leads to the general model based on bi-capacities, encompassing usual models based on capacities. A general definition of interaction for bipolar scales is introduced. The case of ordinal scales leads to the use of Sugeno integral, and its symmetrized version when one considers symmetric ordinal scales. A practical methodology for the identification of fuzzy measures in this context is given.

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  1. Université Paris I — Panthéon-Sorbonne, LIP6, 8 rue du Capitaine Scott, 75015, Paris, France

    Michel Grabisch

  2. Thales Research & Technology Domaine de Corbeville, 91404, Orsay Cedex, France

    Christophe Labreuche

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  1. Michel Grabisch
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Grabisch, M., Labreuche, C. (2005). Fuzzy Measures and Integrals in MCDA. In: Multiple Criteria Decision Analysis: State of the Art Surveys. International Series in Operations Research & Management Science, vol 78. Springer, New York, NY. https://doi.org/10.1007/0-387-23081-5_14

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