Generalized rough approximations in LΠ1/2
Generalized rough approximations in LΠ1/2
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DOI：
10.1016/j.ijar.2007.10.006
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发表时间：
2008-06-01
影响因子：
3.9
通讯作者：
Flaminio, Tommaso
中科院分区：
文献类型：
--
作者：
Ciucci, Davide;Flaminio, Tommaso
在这篇文章中，我们将讨论模糊集的内逼近和外逼近的一个推广，我们将它们分别称为R-内逼近和R-外逼近(R是[0，1]中任何有理数的有限集合)。特别地，我们将讨论那些可由超立方体[0，1](K)的阶跃函数在[0，1]布尔和Q的任意(有限)子集中取值的模糊集在L派1/2中可定义的情形.然后，我们将证明：如果一个模糊集可定义为L派1/2公式的真值表，则它的R-内逼近和R-外逼近都可定义为L派1/2公式的真值表.最后，我们将介绍抽象逼近空间的一个推广，并将我们的方法与模糊粗糙集的概念进行比较.(C)2007 Elsevier Inc.保留所有权利。
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 L Pi 1/2 by means of step functions from the hypercube [0, 1](k) and taking value in an arbitrary (finite) subset of [0, 1] boolean AND Q. Then, we will show that if a fuzzy set is definable as truth table of a formula of L Pi 1/2, then both its R-inner and R-outer approximation are definable as truth table of formulas of L Pi 1/2. Finally, we will introduce a generalization of abstract approximation spaces and compare our approach with the notion of fuzzy rough set. (C) 2007 Elsevier Inc. All rights reserved.