Fuzzy measures and integrals in MCDA

Michel Grabisch (1) , Christophe Labreuche (2)

1 DECISION
2 Thales Research and Technology [Palaiseau]

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 (difference, ratio, 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 details. 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. Lastly, we give a short description of some practical applications.

Mots clés: Choquet integral; fuzzy measure; interaction; bi-capacities

Domaines: Economies et finances; Recherche opérationnelle [cs.RO]

Michel Grabisch, Christophe Labreuche. Fuzzy measures and integrals in MCDA. Multiple Criteria Decision Analysis, Kluwer Academic Publishers, pp.563-608, 2004. ⟨halshs-00268985⟩