In this paper we will treat a generalization of inner and outer approximations of fuzzy sets, which we will call R-inner and $R-outer approximations respectively (R being any finite set of rational numbers in [0,1]). In particular we will discuss the case of those fuzzy sets which are definable in the logic LP by means of step functions from the hypercube [0, 1]^k and taking value in an arbitrary (finite) subset of [0, 1] \cap Q$. Then, we will show that if a fuzzy set is definable as truth table of a formula of LP, then both its R-inner and R-outer approximation are definable as truth table of formulas of LP. Finally, we will introduce a generalization of abstract approximation spaces and compare out approach with the notion of fuzzy rough set.
Ciucci, D.E., & Flaminio, T. (2008). Generalized rough approximations in LP1/2. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 48(2), 544-558.
Citazione: | Ciucci, D.E., & Flaminio, T. (2008). Generalized rough approximations in LP1/2. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 48(2), 544-558. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Titolo: | Generalized rough approximations in LP1/2 |
Autori: | Ciucci, DE; Flaminio, T |
Autori: | |
Data di pubblicazione: | 2008 |
Lingua: | English |
Rivista: | INTERNATIONAL JOURNAL OF APPROXIMATE REASONING |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.ijar.2007.10.006 |
Appare nelle tipologie: | 01 - Articolo su rivista |
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