Journal Article10.1016/S0020-0255(97)10046-9
Extensions and intentions in the rough set theory
593
TL;DR: The approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension, which makes it possible to formulate necessary and sufficient conditions for the existence of operations on rough sets, which are analogous to classical operations on sets.
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About: This article is published in Information Sciences. The article was published on 01 Jun 1998. The article focuses on the topics: Dominance-based rough set approach & Rough set.
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Citations
On Rough Sets under Generalized Equivalence Relations
TL;DR: Rough sets are generalized based on two different interpretations under two different situations: a cases when an equivalence relation is generalized to a similarity relation and a case when a partition is generalizedto a cover.
20
An Axiomatic Approach to the Roughness Measure of Rough Sets
TL;DR: In this article, the authors provided a unified construction of roughness measure, called strong Pawlak measure, and then explored the properties of this measure and introduced three more strong-pawlak roughness measures as well.
20
The first type of graded rough set based on rough membership function
Weihua Xu,Shihu Liu,Qiaorong Wang,Wen-Xiu Zhang +3 more
- 01 Aug 2010
TL;DR: The first type of graded rough set (FGRS) based on rough membership function is presented, and the concepts of k-regions, k-rough degree, etc., are proposed, and some of important properties are investigated in this rough set model.
Generalizations of Rough Sets: From Crisp to Fuzzy Cases
TL;DR: The relations among generalized crisp rough sets and fuzzy rough sets are clarified and two different directions of applications in rule extraction are suggested.
20
Attribute Reduction Based on Consistent Covering Rough Set and Its Application
TL;DR: It can be proved that the method is feasible and the reduction results are recognized by Least Squares Support Vector Machine and Relevance Vector Machine, and the recognition results are consistent with the actual test results of a gas well, which verifies the effectiveness and efficiency of the presented method.
References
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.
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On rough sets
TL;DR: The presented approach may be considered as an alternative to fuzzy sets theory and tolerance theory and some applications are outlined.
Restructuring lattice theory: an approach based on hierarchies of concepts
Rudolf Wille
- 12 May 2009
TL;DR: Restructuring lattice theory is an attempt to reinvigorate connections with the authors' general culture by interpreting the theory as concretely as possible, and in this way to promote better communication between lattice theorists and potential users of lattices theory.
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Information systems theoretical foundations
TL;DR: The presented approach leads to a new information systems organization and the implementation shows many advantages compared with other methods.
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Logical foundations of knowledge representation
Ewa Orłowska,Zdzisław Pawlak +1 more
- 01 Jan 1984
TL;DR: This paper presents a meta-analyses of the models used for estimating the response of the immune system to the attacks of radiation and shows clear patterns in response to known attacks.