Information granulation and rough set approximation

By Yiyu Yao. International Journal of Intelligent Systems, 2001

556 citations recorded by the source corpus.

Information granulation and concept approximation are some of the fundamental issues of granular computing. Granulation of a universe involves grouping of similar elements into granules to form coarse‐grained views of the universe. Approximation of concepts, represented by subsets of the universe, deals with the descriptions of concepts using granules. In the context of rough set theory, this paper examines the two related issues. The granulation structures used by standard rough set theory and the corresponding approximation structures are reviewed. Hierarchical granulation and approximation structures are studied, which results in stratified rough set approximations. A nested sequence of granulations induced by a set of nested equivalence relations leads to a nested sequence of rough set approximations. A multi‐level granulation, characterized by a special class of equivalence relations, leads to a more general approximation structure. The notion of neighborhood systems is also explored. © 2001 John Wiley & Sons, Inc.

View Paper: https://www.semanticscholar.org/paper/06870066a57b7c75811e808dd71e9e64297cb1c5

How researchers see this paper

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

1. Y. Qian
2. Qinghua Hu
3. Yiyu Yao
4. Daren Yu
5. Jiye Liang
6. Zongxia Xie
7. Weizhi Wu
8. Chuangyin Dang

Citations in the corpus

• Fuzzy probabilistic approximation spaces and their information measures (2006, methodology): “Rough set methodology presents a novel paradigm to deal with uncertainty and has been applied to feature selection [1], [2], knowledge reduction [3], [36], [38], rule extraction [4]–[6], uncertainty reasoning [7], [8] and granulation computing [9], [33], [34], [42].”
• Probabilistic approaches to rough sets (2003, background): “For every x, compute the conditional risk R(ai|x) for i = 1,...,m defined by equation ( 26 ), and then select the action for which the conditional risk is the minimum.”
• MGRS: A multi-granulation rough set (2010, methodology): “Yao [38] connected rough set approximation with a classic distance measure based on sets, called Marczewski–Steinhaus metric (MZ), which is defined by MZðX;YÞ 1⁄4 jX [ Y j jX \ Y j jX [ Yj : Gediga and Düntsch [3] redefined the measures a; c and p using MZ, which discovers the relationships between ”
• Perspectives of granular computing (2005, background): “establishing a holistic, whole, and integrated view of granular computing [37], [38], [39], [40], [41], [42], [43], [44], [45], [46].”
• A Partition Model of Granular Computing (2004, background): “Both processes lead naturally to a hierarchical organization of granules and granulations [22, 61].”
• Incomplete Multigranulation Rough Set (2010, methodology): “Rough-set methodology presents a novel paradigm to deal with uncertainty and has been applied to feature selection [18], [48], [49], knowledge reduction [9], [16], [51], rule extraction [1], [8], [35], [50], [59], uncertainty reasoning [20], [25], [31], decision evaluation [36]–[38], and granular co”
• Positive approximation: An accelerator for attribute reduction in rough set theory (2010, background): “Each equivalence class [x]R may be viewed as an information granule consisting of indistinguishable elements [59].”
• Rudiments of rough sets (2007, unknown): “, [8,37,60,39,40,72,46,48,59,66,67,96,128,103, 127,134,136,139,148,149,157,189–196,207,208,216,219,229,230,232,236,244,245,251,265,188,279,281,286,288, 295,299,302,317,318,321–324,326,327,329,358–363,365,368]).”
• Granular Computing and Knowledge Reduction in Formal Contexts (2009, background): “Rough set theory is one of the most advanced areas popularizing GrC [19], [28], [30], [42], [56], [57], [58], [67].”
• Probabilistic rough set approximations (2008, background): “Each equivalence class is considered as a whole granule instead of many individuals [51].”
• Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation (2007, background): “Fuzzy information granulation and granular computing are important concepts in fuzzy set and rough set theories in recent years [31,32].”