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An axiomatic approach of fuzzy rough sets based on residuated lattices [PDF]

Computers and Mathematics With Applications, 2009
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.
Guo-Jun Wang
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The Fuzziness Measure in Fuzzy Rough Sets

2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery, 2008
The paper studies the fuzziness measure in fuzzy rough sets. By making use of the support set of fuzzy sets, a rough membership function for fuzzy sets based on fuzzy relation is introduced. Simultaneously, a fuzziness measure of fuzzy rough sets from total mean fuzzy degree is proposed.
Yue-Jin Lv, Hongyun Zhang, Zhi-cheng Chen   +2 more
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Fuzzy Binary Rough Set

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2020
In this paper, we provide a definition of α-fuzzified lower and upper approximations for fuzzy sets based on the α-cut of fuzzy binary relations. We show that the definition is a proper generalization of the previous one for approximations of crisp sets and compare it with an existing definition in the context of fuzzy tolerance relation.
Yu-Ru Syau, En-Bing Lin, Churn-Jung Liau
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Probabilistic Rough Sets Characterized by Fuzzy Sets

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2004
Theories of fuzzy sets and rough sets have emerged as two major mathematical approaches for managing uncertainty that arises from inexact, noisy, or incomplete information. They are generalizations of classical set theory for modelling vagueness and uncertainty.
Li-Li Wei, Wen-Xiu Zhang
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An approach to roughness of fuzzy sets

2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542), 2005
In rough-set-based data analysis, the roughness of a set is traditionally used to express the degree of inexactness of the set arose due to incompleteness of available knowledge. Recently, an attempt of integration between the theories of fuzzy sets and rough sets has resulted in providing a roughness measure for fuzzy sets (Banerjee and Pal, 1996 ...
Van-Nam Huynh, Yoshiteru Nakamori
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On rough set and fuzzy sublattice

Information Sciences, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ali Akbar Estaji, Somayeh Khodaii, Solmaz Bahrami   +2 more
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Fuzzy rough sets are intuitionistic L-fuzzy sets

Fuzzy Sets and Systems, 1998
The concepts of intuitionistic \(L\)-fuzzy sets (IL-FS) [see \textit{K. Atanassov} and \textit{S. Stoeva}, ``Intuitionistic \(L\)-fuzzy sets'', in: R. Trappl (ed.), Cybernetics and systems research 2, 539-540 (1984; Zbl 0547.03030)], which are extensions of the IFSs [\textit{K. T. Atanassov}, ``Intuitionistic fuzzy sets'', Fuzzy Sets Syst.
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A roughness measure for fuzzy sets

Information Sciences, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Van-Nam Huynh, Yoshiteru Nakamori
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On generalized fuzzy rough sets

International Journal of General Systems, 2009
In this paper, a class of generalized fuzzy rough sets based on two universes are studied. Some new set-valued mappings and fuzzy set-valued mappings are introduced to discuss properties of the known model, and a new model for fuzzy rough sets is proposed which provides a new selection of interval structure for uncertainty reasoning using rough set ...
Daowu Pei, Taihe Fan
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The notion of roughness of a fuzzy set

Fuzzy Sets and Systems, 2014
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Inés Couso, Laura Garrido, Luciano Sánchez   +2 more
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