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International Journal of Computer & Information Sciences, 1982
Summary: We investigate in this paper approximate operations on sets, approximate equality of sets, and approximate inclusion of sets. The presented approach may be considered as an alternative to fuzzy set theory and tolerance theory. Some applications are outlined.
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Summary: We investigate in this paper approximate operations on sets, approximate equality of sets, and approximate inclusion of sets. The presented approach may be considered as an alternative to fuzzy set theory and tolerance theory. Some applications are outlined.
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Soft Computing, 2016
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Rajab Ali Borzooei +2 more
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Rajab Ali Borzooei +2 more
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Roughness bounds in rough set operations
Information Sciences, 2006Roughness indicates the significance of the uncertain elements of a rough set. This paper presents some bounds for rough set operations. The bounds obtained for the union as well as for the difference of rough sets depend on their operand's roughnesses.
Yingjie Yang, Robert I. John
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Information Sciences, 2011
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Young Bae Jun, Feng Feng
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Young Bae Jun, Feng Feng
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2007
The subject-matter of the consideration touches the problem of vagueness. The notion of the rough set, originated by Zdzislaw Pawlak, was constructed under the influence of vague information and methods of shaping systems of notions leading to conceptualization and representation of vague knowledge, so also systems of their scopes as some vague sets ...
Zbigniew Bonikowski +1 more
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The subject-matter of the consideration touches the problem of vagueness. The notion of the rough set, originated by Zdzislaw Pawlak, was constructed under the influence of vague information and methods of shaping systems of notions leading to conceptualization and representation of vague knowledge, so also systems of their scopes as some vague sets ...
Zbigniew Bonikowski +1 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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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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Information Sciences, 1996
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Mohua Banerjee, Sankar K. Pal
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Mohua Banerjee, Sankar K. Pal
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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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2012
There are multiple kinds of data in information systems, e.g., categorical data, numerical data, set-valued data, interval-valued data and missing data. Such information systems are called as composite information systems in this paper. To process such data, composite rough sets are introduced, composite relation is defined and composite classes are ...
Junbo Zhang 0004 +2 more
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There are multiple kinds of data in information systems, e.g., categorical data, numerical data, set-valued data, interval-valued data and missing data. Such information systems are called as composite information systems in this paper. To process such data, composite rough sets are introduced, composite relation is defined and composite classes are ...
Junbo Zhang 0004 +2 more
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