Fuzzy Measures and Integrals in MCDA

Michel Grabisch and Christophe Labreuche ()
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Christophe Labreuche: Thales Research & Technology

Chapter Chapter 14 in Multiple Criteria Decision Analysis, 2016, pp 553-603 from Springer

Abstract: 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 k-additive 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.

Keywords: Choquet integral; Fuzzy measure; Interaction; Bi-capacities (search for similar items in EconPapers)
Date: 2016
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Chapter: Fuzzy Measures and Integrals in MCDA (2005)
Working Paper: Fuzzy measures and integrals in MCDA (2004)
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DOI: 10.1007/978-1-4939-3094-4_14

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