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Rough Numbers and Rough Regression
2011In this article a new model of regression is defined. On the basis of the rough sets theory a notion of rough number is defined. Typical real numbers calculations do not keep the additional information like the uncertainty or the error of input data. Rough numbers remove this limitation.
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Using rough sets for rough classification
Proceedings of 7th International Conference and Workshop on Database and Expert Systems Applications: DEXA 96, 2002Rough sets theory is emerging as a powerful tool for knowledge discovery in databases. The author introduce a rough sets based method for learning classification rules. The author's method will not necessarily derive all the consistent classification rules from a database, nor will the rules derived be totally consistent with the database.
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Rough Group, Rough Subgroup and Their Properties
2005The theory of rough sets is an extension of the set theory, for the study of intelligent systems characterized by insufficient and incomplete information. Since proposed by Pawlak, rough sets have evoked a lot of research. Theoretic study has included algebra aspect of rough sets.
Duoqian Miao 0001 +3 more
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On Rough Equalities and Rough Equivalences of Sets
2008The different types of rough equalities [4,5,6] of sets deal with approximate equalities of sets which may not be equal in the usual sense of classical set theory. In this article, we make further study of the properties of rough equalities. A more general kind of equality of sets (we call it rough equivalence) shall be introduced, which captures ...
Bala Krushna Tripathy +2 more
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Information Sciences, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bijan Davvaz, M. Mahdavipour
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bijan Davvaz, M. Mahdavipour
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Communications of the ACM, 1995
Rough set theory, introduced by Zdzislaw Pawlak in the early 1980s [11, 12], is a new mathematical tool to deal with vagueness and uncertainty. 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 ...
Zdzislaw Pawlak +3 more
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Rough set theory, introduced by Zdzislaw Pawlak in the early 1980s [11, 12], is a new mathematical tool to deal with vagueness and uncertainty. 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 ...
Zdzislaw Pawlak +3 more
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Information Sciences, 2013
Rough set theory is a useful mathematical tool for dealing with the uncertainty and granularity in information systems. In this paper, rough approximations are introduced into quantales, a kind of partially ordered algebraic structure with an associative binary multiplication.
Lingyun Yang, Luoshan Xu
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Rough set theory is a useful mathematical tool for dealing with the uncertainty and granularity in information systems. In this paper, rough approximations are introduced into quantales, a kind of partially ordered algebraic structure with an associative binary multiplication.
Lingyun Yang, Luoshan Xu
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Information Sciences, 2004
Let \(I\) be an ideal of a ring \(R\). Let \(P(R)\) denote the power set of \(R\). Define \(\underline{Apr}_I\colon P(R)\to P(R)\) and \(\overline{Apr}_I\colon P(R)\to P(R)\) as follows: \(\forall X\in P(R)\), \(\underline{Apr}_I(X)=\{x\in R\mid x+I\subseteq X\}\) and \(\overline{Apr}_I(X)=\{x\in R\mid(x+I)\cap X\neq\emptyset\}\). Then \(\underline{Apr}
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Let \(I\) be an ideal of a ring \(R\). Let \(P(R)\) denote the power set of \(R\). Define \(\underline{Apr}_I\colon P(R)\to P(R)\) and \(\overline{Apr}_I\colon P(R)\to P(R)\) as follows: \(\forall X\in P(R)\), \(\underline{Apr}_I(X)=\{x\in R\mid x+I\subseteq X\}\) and \(\overline{Apr}_I(X)=\{x\in R\mid(x+I)\cap X\neq\emptyset\}\). Then \(\underline{Apr}
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2010 IEEE International Conference on Granular Computing, 2010
We introduced rough sets into lattices. The concepts of upper and lower approximations of a subset in a lattice are given. We discussed the properties of θ??(A)and θ_(A) when A is a sublattice, an ideal, a prime ideal and a convex sublattice of L.
Zuhua Liao, Lian Wu, Miaohan Hu
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We introduced rough sets into lattices. The concepts of upper and lower approximations of a subset in a lattice are given. We discussed the properties of θ??(A)and θ_(A) when A is a sublattice, an ideal, a prime ideal and a convex sublattice of L.
Zuhua Liao, Lian Wu, Miaohan Hu
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Scientific American, 2018
The article offers information on formation of rare diamonds. It mentions that when a meteorite containing graphite slams into the earth, the collision's heat and pressure can transform this form of carbon into a rare and extremely hard type of diamond. It presents the views of Yogendra Gupta, from Washington State University, on formation of hexagonal
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The article offers information on formation of rare diamonds. It mentions that when a meteorite containing graphite slams into the earth, the collision's heat and pressure can transform this form of carbon into a rare and extremely hard type of diamond. It presents the views of Yogendra Gupta, from Washington State University, on formation of hexagonal
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