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., Flaminio, T. (2008). Generalized rough approximations in LP1/2. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 48(2), 544-558 [10.1016/j.ijar.2007.10.006].

### Generalized rough approximations in LP1/2

#### Abstract

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.
##### Scheda breve Scheda completa Scheda completa (DC)
Articolo in rivista - Articolo scientifico
Fuzzy sets; Rough approximations; Abstract approximation spaces; Fuzzy rough sets
English
2008
544
558
Ciucci, D., Flaminio, T. (2008). Generalized rough approximations in LP1/2. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 48(2), 544-558 [10.1016/j.ijar.2007.10.006].
File in questo prodotto:
File
IJAR-sito.pdf

accesso aperto

Dimensione 259.54 kB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/4702`