Upper and Lower Approximations of Fuzzy Sets

Abstract

The upper and lower approximations of a f u n y subset with respect to an indistinguishability opcrator are studied. Their relations with f u u y rough sets are also investigated.

On the relationship among F-transform, fuzzy rough set and fuzzy topology

“…In literature [5,15,22], several generalizations of rough sets have been made by replacing the equivalence relation by an arbitrary relation. After Dubois and Prade [3] introduced a fuzzy rough set, which is a generalization of a rough set, the relationship between fuzzy rough sets and fuzzy topological spaces were studied [1,14,20,21].…”

Comparison of Different Algorithms of Approximation by Extensional Fuzzy Subsets

“…From a topological viewpoint these operators can be seen as closure and interior operators on the set [0, 1] X [11]. It is remarkable that these operators also appear in a natural way in fields such as fuzzy rough sets [20], fuzzy modal logic [6], [5], fuzzy mathematical morphology [8] and fuzzy contexts [3] among many others.…”

Approximating Arbitrary Fuzzy Subsets by Extensional Ones

“…In the literature this problem has not been faced but indirectly and the main results found on this topic have been the construction of two operators φ E [11] and ψ E [5] that given a fuzzy subset µ provide the lowest extensional fuzzy subset containing µ and the biggest extensional fuzzy subset that contains µ respectively. However, in general there is no guarantee that there are no extensional sets "in between" that approximate µ better.…”