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Fuzzy Sets and Systems, 1985
In this note we compare notions of rough set and fuzzy set, and we show that these two notions are different.
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In this note we compare notions of rough set and fuzzy set, and we show that these two notions are different.
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Roughness Bounds in Set-oriented Rough Set Operations
2006 IEEE International Conference on Fuzzy Systems, 2006Roughness is an important indicator for the uncertainty of a rough set. This paper analyses the roughness bounds for set-oriented rough set operations. A bound of the roughness of the union between two set-oriented rough sets could be determined by the roughness of the two operand set-oriented sets.
Robert John, Yingjie Yang
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Rough set theory applied to UP-algebras
Journal of Information and Optimization Sciences, 2019In this paper, rough set theory is applied to UP-algebras, proved some results and discussed the generalization of some notions of rough UP-subalgebras, rough UP-filters, rough UP-ideals and rough strongly UP-ideals.
Theeyarat Klinseesook +2 more
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2015
As quantitative generalizations of Pawlak rough sets, probabilistic rough sets consider degrees of overlap between equivalence classes and the set. An equivalence class is put into the lower approximation if the conditional probability of the set, given the equivalence class, is equal to or above one threshold; an equivalence class is put into the ...
Yao, Yiyu +2 more
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As quantitative generalizations of Pawlak rough sets, probabilistic rough sets consider degrees of overlap between equivalence classes and the set. An equivalence class is put into the lower approximation if the conditional probability of the set, given the equivalence class, is equal to or above one threshold; an equivalence class is put into the ...
Yao, Yiyu +2 more
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2015
This chapter reviews three formulations of rough set theory, i. e., element-based definition, granule-based definition, and subsystem-based definition. These formulations are adopted to generalize rough sets from three directions. The first direction is to use an arbitrary binary relation to generalize the equivalence relation in the element-based ...
Yao, J, CIUCCI, DAVIDE ELIO, Zhang, Y.
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This chapter reviews three formulations of rough set theory, i. e., element-based definition, granule-based definition, and subsystem-based definition. These formulations are adopted to generalize rough sets from three directions. The first direction is to use an arbitrary binary relation to generalize the equivalence relation in the element-based ...
Yao, J, CIUCCI, DAVIDE ELIO, Zhang, Y.
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2005
Rough set theory is a new mathematical approach to imperfect knowledge. The problem of imperfect knowledge, tackled for a long time by philosophers, logicians, and mathematicians, has become also a crucial issue for computer scientists, particularly in the area of artificial intelligence.
Zdzislaw Pawlak +2 more
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Rough set theory is a new mathematical approach to imperfect knowledge. The problem of imperfect knowledge, tackled for a long time by philosophers, logicians, and mathematicians, has become also a crucial issue for computer scientists, particularly in the area of artificial intelligence.
Zdzislaw Pawlak +2 more
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2009
Multiple attribute (or multiple criteria) decision support aims at giving the decision maker (DM) a recommendation concerning a set of objects A (also called alternatives, actions, acts, solutions, options, candidates, ...) evaluated from multiple points of view called attributes (also called features, variables, criteria, objectives, ...).
SLOWINSKI R +2 more
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Multiple attribute (or multiple criteria) decision support aims at giving the decision maker (DM) a recommendation concerning a set of objects A (also called alternatives, actions, acts, solutions, options, candidates, ...) evaluated from multiple points of view called attributes (also called features, variables, criteria, objectives, ...).
SLOWINSKI R +2 more
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Attribute Selection for Partially Labeled Categorical Data By Rough Set Approach
IEEE Transactions on Cybernetics, 2017Attribute selection is considered as the most characteristic result in rough set theory to distinguish itself to other theories. However, existing attribute selection approaches can not handle partially labeled data.
Jianhua Dai +4 more
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Transactions on Rough Sets XVI
2004Three-Valued Logics, Uncertainty Management and Rough Sets.- Standard Errors of Indices in Rough Set Data Analysis.- Proximity System: A Description-Based System for Quantifying the Nearness or Apartness of Visual Rough Sets.- Rough Sets and Matroids.- An Efficient Approach for Fuzzy Decision Reduct Computation.- Rough Sets in Economy and Finance ...
Andrzej Skowron, James F. Peters
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A kind of new rough set: Rough soft sets and rough soft rings
Journal of Intelligent & Fuzzy Systems, 2015The aim of this paper is to lay a foundation for providing a rough soft tool in considering many problems that contain uncertainties. We put forward the concepts of rough soft rings and rough idealistic soft rings. Some basic operations on rough soft rings are discussed. Some good examples are explored.
Jianming Zhan, Bijan Davvaz
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