Aggregation of interacting criteria by means of the discrete Choquet integral
By Jean-Luc Marichal. 2002
154 citations recorded by the source corpus.
The most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean. In many problems however, the criteria considered interact, and a substitute to the weighted arithmetic mean has to be adopted. Under rather natural conditions, the discrete Choquet integral is proved to be an adequate aggregation operator that extends the weighted arithmetic mean by the taking into consideration of the interaction among criteria. The axiomatic that supports the Choquet integral is presented and some subfamilies are studied.
Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/53ecb0a7ef90b6ec864d498048be37f49f86170a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Michel Grabisch
- Gleb Beliakov
- Tomasa Calvo
- Ana Pradera
- Christophe Labreuche
- Chunqiao Tan
- Xiao-hong Chen
- Jean-Luc Marichal
In Management Science and Operations Research
- Michel Grabisch
- Chunqiao Tan
- Xiao-hong Chen
- Gleb Beliakov
- Ana Pradera
- Tomasa Calvo
- Christophe Labreuche
- Jean-Luc Marichal
In Statistics and Probability
- Michel Grabisch
- Chunqiao Tan
- Xiao-hong Chen
- Christophe Labreuche
- Gleb Beliakov
- Ana Pradera
- Tomasa Calvo
- Jean-Luc Marichal
Citations in the corpus
- A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS (2011, unknown): “The proof is similar to that of Proposition 4.1 in Marichal (2002).”
- A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid (2008, background): “The fact that the so-called Lovász extension is the Choquet integral was observed by Marichal (1998, 2002).”
- Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making (2010, background): “According to Definitions 4 and 7, the proof of the proposition is similar to that of Corollary 4 in Grabisch (1995) or that of Proposition 1 in Marichal (2002).”
- Behavioral analysis of aggregation in multicriteria decision aid (2000, background): “In the weighted arithmetic mean model, each criterion i ∈ N is given a weight ωi ∈ [0, 1] representing the importance of this criterion in the decision.”
- Aggregation Functions: A Guide for Practitioners (2007, methodology): “The uses of Choquet integrals as aggregation functions are documented in [106, 110, 111, 163, 165].”