Rough approximation quality revisited
نویسندگان
چکیده
In rough set theory, the approximation quality γ is the traditional measure to evaluate the classification success of attributes in terms of a numerical evaluation of the dependency properties generated by these attributes. In this paper we re-interpret the classical γ in terms of a classic measure based on sets, the Marczewski–Steinhaus metric, and also in terms of “proportional reduction of errors” (PRE) measures. We also exhibit infinitely many possibilities to define γ -like statistics which are meaningful in situations different from the classical one, and provide tools to ascertain the statistical significance of the proposed measures, which are valid for any kind of sample. 2001 Published by Elsevier Science B.V.
منابع مشابه
ROUGH SET OVER DUAL-UNIVERSES IN FUZZY APPROXIMATION SPACE
To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy approximation space by means of cut set. Then, we discuss properties of rough se...
متن کاملTopological structure on generalized approximation space related to n-arry relation
Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...
متن کاملRough approximation operators based on quantale-valued fuzzy generalized neighborhood systems
Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system...
متن کاملT-Rough Sets Based on the Lattices
The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...
متن کاملOn $L$-double fuzzy rough sets
ur aim of this paper is to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined and the basic properties of them are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Artif. Intell.
دوره 132 شماره
صفحات -
تاریخ انتشار 2001