TitleEvaluation of a greedy algorithm for Hierarchically Decomposable Fuzzy Measure Approximation
Publication TypeConference Paper
Year of Publication2002
AuthorsTorra V
Conference NameProc. of the Joint 1st Int. Conference on Soft Computing and Intelligent Systems and 3rd Int. Symposium on Advanced Intelligent Systems

The application of aggregation operators based on fuzzy measures, like Choquet and Sugeno integrals, is not an easy task due to the intrinsic difficulty of defining such measures (they require $2^{N}$ parameters where $N$ is the number of values to be aggregated). To overcome this difficulty there exist some families of fuzzy measures with reduced complexity (with less parameters). In this work we deal with the approximation of general and arbitrary fuzzy measures by hierarchically decomposable ones (HDFM): a family of reduced complexity. In particular, we present heuristic methods for this approximation. Computational results are also presented. The interest of the approach is twofold: (i) the method can be used for helping on the understanding of general fuzzy measures learned from examples; (ii) the method can be used to generate complete fuzzy measures from non-complete ones. In the former case, HDFM are used to have a better understanding of the original measure rather than replace it. In the latter case, the algorithm is to find all $2^N$ required values from a subset of them.