An axiomatic approach of fuzzy rough sets based on residuated lattices
Yanhong She,Guo-Jun Wang +1 more
TLDR
An operator-oriented characterization of L- fuzzy rough sets is presented, that is, L-fuzzy approximation operators are defined by axioms, and the relationship between L-magnitude rough sets and L-topological spaces is obtained.Abstract:
Rough set theory was developed by Pawlak as a formal tool for approximate reasoning about data Various fuzzy generalizations of rough approximations have been proposed in the literature As a further generalization of the notion of rough sets, L-fuzzy rough sets were proposed by Radzikowska and Kerre In this paper, we present an operator-oriented characterization of L-fuzzy rough sets, that is, L-fuzzy approximation operators are defined by axioms The methods of axiomatization of L-fuzzy upper and L-fuzzy lower set-theoretic operators guarantee the existence of corresponding L-fuzzy relations which produce the operators Moreover, the relationship between L-fuzzy rough sets and L-topological spaces is obtained The sufficient and necessary condition for the conjecture that an L-fuzzy interior (closure) operator derived from an L-fuzzy topological space can associate with an L-fuzzy reflexive and transitive relation such that the corresponding L-fuzzy lower (upper) approximation operator is the L-fuzzy interior (closure) operator is examinedread more
Citations
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On some types of fuzzy covering-based rough sets
Bin Yang,Bao Qing Hu +1 more
TL;DR: Three new types of fuzzy covering-based rough set models are proposed by introducing a new notion of a fuzzy complementary -neighborhood by introducing some new definitions of fuzzy -covering approximation spaces.
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Topological and lattice structures of L-fuzzy rough sets determined by lower and upper sets
Zhen Ming Ma,Bao Qing Hu +1 more
TL;DR: It is proven that the set of all the lower (resp. upper) L-fuzzy approximation sets forms a complete lattice when the L-relation is reflexive.
Journal ArticleDOI
An information fusion approach by combining multigranulation rough sets and evidence theory
TL;DR: A two-grade fusion approach involved in the evidence theory and multigranulation rough set theory is proposed, which is based on a well-defined distance function among granulation structures and will be useful for pooling the uncertain data from different sources and significant for establishing a new direction of granular computing.
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On the union and intersection operations of rough sets based on various approximation spaces
TL;DR: It is proved that the union and intersection operations of rough fuzzy approximation pairs are closed and a bounded distributive lattice can be constructed.
Journal ArticleDOI
Constructive methods of rough approximation operators and multigranulation rough sets
TL;DR: Four kinds of constructive methods of rough approximation operators from existing rough sets are established, and the important conclusion is obtained: some rough set are essentially direct applications of these constructive methods.
References
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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.
Book
Metamathematics of Fuzzy Logic
TL;DR: This paper presents a meta-analysis of many-Valued Propositional Logic, focusing on the part of Lukasiewicz's Logic that deals with Complexity, Undecidability and Generalized Quantifiers and Modalities.
Journal ArticleDOI
Rough fuzzy sets and fuzzy rough sets
Didier Dubois,Henri Prade +1 more
TL;DR: It is argued that both notions of a rough set and a fuzzy set aim to different purposes, and it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems.