The standard approach to information entropy applied to partitions of a universe is equivalently formulated as the entropy of the corresponding crisp identity resolutions, interpreted as crisp granulations, by the corresponding characteristic functionals. Moreover, in this crisp context the co–entropy notion is introduced. The extension to the case of fuzzy identity resolutions, a particular case of fuzzy granulation, is studied.
Bianucci, D., Cattaneo, G., Ciucci, D. (2007). Information entropy and co-entropy of crisp and fuzzy granulations. In WILF 2007 (pp.9-19). Springer [10.1007/978-3-540-73400-0_2].
Information entropy and co-entropy of crisp and fuzzy granulations
CATTANEO, GIANPIERO;CIUCCI, DAVIDE ELIO
2007
Abstract
The standard approach to information entropy applied to partitions of a universe is equivalently formulated as the entropy of the corresponding crisp identity resolutions, interpreted as crisp granulations, by the corresponding characteristic functionals. Moreover, in this crisp context the co–entropy notion is introduced. The extension to the case of fuzzy identity resolutions, a particular case of fuzzy granulation, is studied.
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