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Contributions to the Theory of Rough Sets
Fundamenta Informaticae, 1999We study properties of rough sets, that is, approximations to sets of records in a database or, more formally, to subsets of the universe of an information system. A rough set is a pair 〈L, U〉 such that L, U are definable in the information system and L ⊆ U. In the paper, we introduce a language, called the language of inclusion-exclusion, to describe
Marek, V. Wiktor +1 more
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Rough Approximate Operators: Axiomatic Rough Set Theory
1994In rough set theory, the upper and lower approximations are defined in terms of equivalence relation. In this paper, the reverse problem is considered. Let H and L are two abstract operators acting on the power set of U, the universe of discourse. If the two operators satisfy six axioms, then there is an equivalence relation defined on U such that H(X)
T. Y. Lin, Qing Liu
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Rough set theory applied to lattice theory
Information Sciences, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Estaji, A. A. +2 more
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A new rough set theory: rough soft hemirings
Journal of Intelligent & Fuzzy Systems, 2015The aim of this paper is to introduce the notion of a rough soft hemiring, which is an extended notion of a rough hemiring and a soft hemiring. We study roughness in soft hemirings with respect to Pawlak approximation spaces. Some new rough soft operations are explored. In particular, lower and upper rough soft hemirings and (k-idealistic, h-idealistic,
Zhan, Jianming, Liu, Qi, Davvaz, Bijan
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Decision systems in rough set theory: A set operatorial perspective
Journal of Algebra and Its Applications, 2019In rough set theory (RST), the notion of decision table plays a fundamental role. In this paper, we develop a purely mathematical investigation of this notion to show that several basic aspects of RST can be of interest also for mathematicians who work with algebraic and discrete methods.In this abstract perspective, we call decision system a sextuple [
CHIASELOTTI GIAMPIERO +2 more
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A Rough Set Paradigm for Unifying Rough Set Theory and Fuzzy Set Theory
2007In this plenary address, we would like to discuss rough inclusions defined in Rough Mereology, a joint idea with A. Skowron, as a basis for common models for rough as well as fuzzy set theories. We would like to justify the point of view that tolerance (or, similarity) is the leading motif common to both theories and in this area paths between the two ...
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Research on rough set theory extension and rough reasoning
2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04CH37583), 2005Rough set theory is a new soft computing tool to deal with vagueness and uncertainty. It has attracted much attention of many researchers and practitioners all over the world, and has been applied to many fields successfully such as knowledge discovery, decision support, pattern recognition, machine learning, etc. Though the rough set theory is founded
null Yunliang Jiang +3 more
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The rough set theory and applications
Engineering Computations, 2004This paper presents a comprehensive review of the available literature on applications of the rough set theory. Concepts of the rough set theory are discussed for approximation, dependence and reduction of attributes, decision tables and decision rules.
Wu, Chengdong +3 more
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2019
This chapter overviews rough set theory. First, we give preliminaries of rough set theory. Second, we give an exposition of algebras for rough set theory. Third, connections of modal logic and rough sets are described. Fourth, rough set logics are introduced. We also consider logics for reasoning about knowledge and logics for knowledge representation.
Seiki Akama, Yasuo Kudo, Tetsuya Murai
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This chapter overviews rough set theory. First, we give preliminaries of rough set theory. Second, we give an exposition of algebras for rough set theory. Third, connections of modal logic and rough sets are described. Fourth, rough set logics are introduced. We also consider logics for reasoning about knowledge and logics for knowledge representation.
Seiki Akama, Yasuo Kudo, Tetsuya Murai
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Supervaluationism and rough set theory
2012 IEEE International Conference on Granular Computing, 2012In this paper, I want to propose a revised version to supervaluationists' strategy on vagueness by rough set theory. The main reason to my work is due to the very intuition about all the boundaries of vague terms must be obviously vague, i.e. not only the boundary of positive and negative extension but also the boundaries of positive or negative ...
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