On Approximate Equivalences of Multigranular Rough Sets and Approximate Reasoning
B. K. Tripathy,Anirban Mitra +1 more
TLDR
The concepts of multigranular rough equivalences are introduced and the replacement properties, which are obtained by interchanging the bottom equivalences with the top equivalences, have been established.Abstract:
The notion of rough sets introduced by Pawlak has been a successful model to capture impreciseness in data and has numerous applications. Since then it has been extended in several ways. The basic rough set introduced by Pawlak is a single granulation model from the granular computing point of view. Recently, this has been extended to two types of multigranular rough set models. Pawlak and Novotny introduced the notions of rough set equalities which is called approximate equalities. These notions of equalities use the user knowledge to decide the equality of sets and hence generate approximate reasoning. However, it was shown by Tripathy et al, even these notions have limited applicability to incorporate user knowledge. So the notion of rough equivalence was introduced by them. The notion of rough equalities in the multigranulation context was introduced and studied. In this article, we introduce the concepts of multigranular rough equivalences and establish their properties. Also, the replacement properties, which are obtained by interchanging the bottom equivalences with the top equivalences, have been established. We provide a real life example for both types of multigranulation, compare the rough multigranular equalities with the rough multigranular equivalences and illustrate the interpretation of the rough equivalences through the example.read more
Citations
More filters
Journal ArticleDOI
Rough computing — A review of abstraction, hybridization and extent of applications
D. P. Acharjya,Ajith Abraham +1 more
TL;DR: This paper identifies the conventionally used rough computing techniques and discusses their concepts, developments, abstraction, hybridization, and scope of applications.
Journal ArticleDOI
Approximate Reasoning through Multigranular Approximate Rough Equalities
TL;DR: The notion of approximate rough equalities for multigranulations and their properties are introduced and a real life example is used to illustrate the results in the paper and also to construct examples in support of some parts of the properties.
Book ChapterDOI
On Multigranular Approximate Rough Equivalence of Sets and Approximate Reasoning
TL;DR: This paper extends the last but the most general of these approximate equalities to the multigranular context and establishes several direct and replacement properties of this type of approximateequalities.
Book ChapterDOI
Multi-Granular Computing through Rough Sets
TL;DR: In this chapter, the authors discuss all topics on multigranular computing and suggest some problems for further study.
Posted Content
LRA: an accelerated rough set framework based on local redundancy of attribute for feature selection.
TL;DR: The theorem regarding the stability of attributes in a decision system is proposed and proved and the LRA framework for accelerating rough set algorithms is proposed, a general-purpose framework which can be applied to almost all rough set methods significantly.
References
More filters
Journal ArticleDOI
Rough sets
TL;DR: This approach seems to be of fundamental importance to artificial intelligence (AI) and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery from databases, expert systems, decision support systems, inductive reasoning, and pattern recognition.
Journal ArticleDOI
Rudiments of rough sets
Zdziasław Pawlak,Andrzej Skowron +1 more
TL;DR: The basic concepts of rough set theory are presented and some rough set-based research directions and applications are pointed out, indicating that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences.
Journal ArticleDOI
Rough sets: Some extensions
Zdzisław Pawlak,Andrzej Skowron +1 more
TL;DR: Some extensions of the rough set approach are presented and a challenge for the roughSet based research is outlined and it is outlined that the current rough set based research paradigms are unsustainable.
Proceedings ArticleDOI
Rough Set Method Based on Multi-Granulations
Yuhua Qian,Jiye Liang +1 more
TL;DR: It is shown that some properties of Pawlak rough set are special instances of MGRS, and approximation measure of set described by using multi-granulations is always better than by using single granulation, which is suitable for describing more accurately the concept and solving problem according to user requirement.