A Generalized Definition of Rough Approximations Based on Similarity

By R. Słowiński, Daniel Vanderpooten. IEEE Transactions on Knowledge and Data Engineering, 2000

999 citations recorded by the source corpus.

This paper proposes new definitions of lower and upper approximations, which are basic concepts of the rough set theory. These definitions follow naturally from the concept of ambiguity introduced in this paper. The new definitions are compared to the classical definitions and are shown to be more general, in the sense that they are the only ones which can be used for any type of indiscernibility or similarity relation.

Subfields: Computational Theory and Mathematics, Information Systems

View Paper: https://www.semanticscholar.org/paper/87470b11fe40fee6efd95e758df62753c5c2c87e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Qinghua Hu
2. Daren Yu
3. Feng Feng
4. Witold Pedrycz
5. William Zhu
6. Jinfu Liu
7. Xiaoyan Liu
8. Weizhi Wu

In Information Systems

1. Witold Pedrycz
2. Jinfu Liu
3. Weizhi Wu
4. Qinghua Hu
5. Daren Yu
6. Congxin Wu
7. Wenxiu Zhang
8. Feng Feng

Citations in the corpus

• Reduction and axiomization of covering generalized rough sets (2003, background): “To address this issue, several interesting and meaningful extensions to equivalent relation have been proposed in the past, such as tolerance relations [4,8], similarity relations [9], and others [10,13,14].”
• Maximal consistent block technique for rule acquisition in incomplete information systems (2003, methodology): “Though knowledge acquisition methodologies have mainly been developed for complete information systems over the years, some important results have recently been obtained for incomplete information systems [1–3,6,9,10], particularly on the theoretical analysis of rule acquisition [1,2,9].”
• Handbook of Granular Computing (2008, methodology): “The salient properties of this arithmetic, which is detailed in [16, 17, 34], are presented here.”
• Knowledge acquisition in incomplete information systems: A rough set approach (2006, background): “Pawlak s rough approximations may be generalized to nonequivalence relations (Greco et al., 2001; Slowinski and Vanderpooten, 1997, 2000; Wu and Zhang, 2002; Yao, 1998).”
• Incomplete Information Tables and Rough Classification (2001, background): “the concept of indiscernibility relation (see S ł owi´nski and Vanderpooten 1997, 2000).”
• Soft sets and soft rough sets (2011, background): “Equivalence relations can be replaced by tolerance relations [28], similarity relations [27], dominance relations [10], general binary relations [15,32,33,36], coverings of the universe of discourse [5,13,30,38] or neighborhood systems [29,34].”
• Modeling uncertainty in multi-criteria decision analysis (2012, background): “Replacing indiscernibility with a less-restrictive ‘similarity’ relation allows imprecision in assessments [116].”
• Constructive and axiomatic approaches of fuzzy approximation operators (2004, background): “This has lead to various other approximation operators [25,26,39,40,42,43].”