Information Entropy and Co-entropy of Crisp and Fuzzy Granulations

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. y of Abstract Discrete Probability Distributions section we briefly discuss the abstract approach to information theory, involving suitable finite sequences of numbers from the real unit interval [0, 1], each of which can be interpreted as a probability of occurrence of something, without any reference to a concrete universe X. To be precise, a length N probability distribution is a vector p = (p1, p2, . . . , pN ) in which: (pd-1) every p1 ≥ 0 and (pd-2) n

• Type: Conference
• Year: 2007
• Where: WILF
• Authors: Daniela Bianucci, Gianpiero Cattaneo, Davide Ciucci
• Keywords: Artificial Intelligence, Corresponding Crisp Identity, Identity Resolutions, Probability Distribution, WILF 2007