Fuzzy measures and integrals in MCDA

Michel Grabisch and Christophe Labreuche ()
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Christophe Labreuche: Thales Research and Technology [Palaiseau] - THALES [France]

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Abstract: This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem ofmulticriteria decision making, and describes the various possible scales ofmeasurement (difference, ratio, and ordinal). Then a whole section is devotedto each case in detail: after introducing necessary concepts, the methodologyis described, and the problem of the practical identification of fuzzy measuresis given. The important concept of interaction between criteria, central inthis chapter, is explained in details. It is shown how it leads to k-additivefuzzy measures. The case of bipolar scales leads to thegeneral model based on bi-capacities, encompassing usual models based oncapacities. A general definition of interaction for bipolar scales isintroduced. The case of ordinal scales leads to the use of Sugeno integral, andits symmetrized version when one considers symmetric ordinal scales. Apractical methodology for the identification of fuzzy measures in this contextis given. Lastly, we give a short description of some practical applications.

Keywords: Choquet integral; fuzzy measure; interaction; bi-capacities (search for similar items in EconPapers)
Date: 2004
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00268985
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Citations: View citations in EconPapers (29)

Published in Multiple Criteria Decision Analysis, Kluwer Academic Publishers, pp.563-608, 2004

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Related works:
Chapter: Fuzzy Measures and Integrals in MCDA (2016)
Chapter: Fuzzy Measures and Integrals in MCDA (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00268985

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