An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria

By Jean-Luc Marichal. IEEE transactions on fuzzy systems, 2000

423 citations recorded by the source corpus.

The most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean. However, in many problems the criteria considered interact and a substitute to the weighted arithmetic mean has to be adopted. We show that, under rather natural conditions, the discrete Choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by taking into consideration of the interaction among criteria. The axiomatic that supports the Choquet integral is presented and an intuitive approach is proposed as well.

Subfields: Control and Systems Engineering, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d973c763ac10e09d688a7522d9dff50f334e28d9

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Citations in the corpus

A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package (2008, methodology): “An axiomatic characterization of the Choquet integral as an aggregation operator can be found in [10].”
Decomposition-integral: unifying Choquet and the concave integrals (2014, methodology): “Marichal (2000) uses the Choquet integral as a tool to aggregate interacting criteria.”
An analysis of DEMATEL approaches for criteria interaction handling within ANP (2016, neutral): “Interest-137 ingly enough, the Choquet (Grabisch & Labreuche, 2010; Marichal,138 2004; Marichal, 2000) and Sugeno integrals (Dubois, Marichal, Prade,139 Roubens, & Sabaadin, 2001; Sugeno, 1974, 1977; Torra & Narukawa,140 2006), also known as the members of non-additive integrals or fuzzy141…”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, background): “The Lovász extension [135], which is often referred to as the Choquet integral in decision theory [46, 146], allows the extension of a set-function defined on the vertices of the hypercube {0, 1}p, to the full hypercube [0, 1]p (and in fact also to the entire space Rp).”
Preferences for multi-attributed alternatives: Traces, dominance, and numerical representations (2004, neutral): “• the specialization of our results in order to study particular functional forms for F such as min, max, Sugeno or Choquet integrals (see Grabisch, 1996; Marichal, 2000a, 2000b ).”
Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices (2006, methodology): “In this context, it is used to appraise the overall interaction among criteria [8, 9, 15, 20, 21, 22, 24], thereby giving more insight into the decision problem.”
Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making (2010, methodology): “As an aggregation operator, the Choquet integral has been proposed by many authors as an adequate substitute to the weighted arithmetic mean or OWA operator to aggregate interacting criteria (Grabisch, 1995; Grabisch, Murofushi, & Sugeno, 2000; Labreuche & Grabisch, 2003; Marichal, 2000).”