RT Journal Article
T1 Calculating the interaction index of a fuzzy measure: A polynomial approach based on sampling
A1 Gutiérrez, Inmaculada
A1 Castro, Javier
A1 Gómez, Daniel
A1 Espínola Vílchez, María Rosario
AB In this paper we address the problem of fuzzy measures index calculation. On the basis of fuzzy sets, Murofushi and Soneda proposed an interaction index to deal with the relations between two individuals. This index was later extended in a common framework by Grabisch. Both indices are fundamental in the literature of fuzzy measures. Nevertheless, the corresponding calculation still presents a highly complex problem for which no approximation solution has been proposed yet. Then, using a representation of the Shapley based on orders, here we suggest an alternative calculation of the interaction index, both for the simple case of pairs of individuals, and for the more complex situation in which any set could be considered. This alternative representation facilitates the handling of these indices. Moreover, we draw on this representation to define two polynomial methods based on sampling to estimate the interaction index, as well as a method to approximate the generalized version of it. We provide some computational results to test the goodness of the proposed algorithms.
PB Elsevier
SN 01650114
YR 2022
FD 2022-12-20
LK https://hdl.handle.net/20.500.14352/72998
UL https://hdl.handle.net/20.500.14352/72998
LA eng
NO CRUE-CSIC (Acuerdos Transformativos 2022)
NO Government of Spain, Grant Plan Nacional de I+D+i
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 17 may 2024