What is chochoquet integral?

Choquet Integral is an aggregation function defined with respect to the fuzzy measure. A fuzzy measure is a set function, acting on the domain of all possible combinations of a set of criteria. The complexity is therefore exponential of 2 n subsets, where n is the number of criteria.

How do you find the Choquet integral from a fuzzy measure?

The Choquet Integral computed from the general fuzzy measure is given by: (9.3) C v(x) = n ∑ i = 1[x i − x i − 1]v(H i). where x0 = 0 by convention, and Hi = { i, …, n } is the subsets of indexes of the n − i + 1 largest components of x.

What is the Lovász extension of the Choquet integral?

We recognize here the Lovász extension of v (see (6) ), which shows clearly the link between the set function and the Choquet integral: the latter is an extension of the former, which means that for any S ⊂ N, if fs is defined as f Si = 1 whenever i ∈ S, and 0 otherwise, then C v(f S) = v(S).