Elicitating Sugeno Integrals: Methodology and a Case Study

Sugeno integrals are aggregation functions that return a global evaluation that is between the minimum and the maximum of the combined evaluations. The paper addresses the problem of the elicitation of (families of) Sugeno integrals agreeing with a set of data, made of tuples gathering the partial evaluations according to the different evaluation criteria together with the corresponding global evaluation. The situation where there is no Sugeno integral that is compatible with a whole set of data is especially studied. The representation of mental workload data is used as an illustrative example, where several distinct families of Sugeno integrals are necessary for covering the set of data (since the way mental workload depends on its evaluation criteria may vary with contexts). Apart this case study illustration, the contributions of the paper are an analytical characterization of the set of Sugeno integrals compatible with a set of data, the expression of conditions ensuring that pieces of data are compatible with a representation by a common Sugeno integral, and a simulated annealing optimization algorithm for computing a minimal number of families of Sugeno integrals sufficient for covering a set of data.