Generalized Rough Sets via Quantum Implications on Quantum Logic

This paper introduces some new concepts of rough approximations via five quantum implications satisfying Birkhoff–von Neumann condition. We first establish rough approximations via Sasaki implication and show the equivalence between distributivity of multiplication over join and some properties of rough approximations. We further establish rough approximations via other four quantum implication and examine their properties.

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Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system

Information Sciences ◽

10.1016/j.ins.2012.03.023 ◽

2012 ◽

Vol 207 ◽

pp. 66-78 ◽

Cited By ~ 34

Author(s):

Lijuan Wang ◽

Xibei Yang ◽

Jingyu Yang ◽

Chen Wu

Keyword(s):

Rough Sets ◽

Neighborhood System ◽

Generalized Rough Sets

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Transition from regular to Mach reflection of shock waves Part 2. The steady-flow criterion

Journal of Fluid Mechanics ◽

10.1017/s0022112082003000 ◽

1982 ◽

Vol 123 ◽

pp. 155-164 ◽

Cited By ~ 98

Author(s):

H. G. Hornung ◽

M. L. Robinson

Keyword(s):

Shock Waves ◽

Steady Flow ◽

Mach Reflection ◽

Strong Shock ◽

Hysteresis Effect ◽

Neumann Condition ◽

Flow Transition ◽

Von Neumann ◽

Mach Numbers ◽

Flow Criterion

It is shown experimentally that, in steady flow, transition to Mach reflection occurs at the von Neumann condition in the strong shock range (Mach numbers from 2.8 to 5). This criterion applies with both increasing and decreasing shock angle, so that the hysteresis effect predicted by Hornung, Oertel & Sandeman (1979) could not be observed. However, evidence of the effect is shown to be displayed in an unsteady experiment of Henderson & Lozzi (1979).

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Algebraic Properties of Generalized Rough Sets

Fundamenta Informaticae ◽

10.3233/fi-2009-116 ◽

2009 ◽

Vol 94 (1) ◽

pp. 41-48

Author(s):

Michiro Kondo

Keyword(s):

Rough Sets ◽

Algebraic Properties ◽

Generalized Rough Sets

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Generalized rough sets based feature selection

Intelligent Data Analysis ◽

10.3233/ida-2000-4102 ◽

2000 ◽

Vol 4 (1) ◽

pp. 3-17 ◽

Cited By ~ 10

Author(s):

Mohamed Quafafou ◽

Moussa Boussouf

Keyword(s):

Feature Selection ◽

Rough Sets ◽

Generalized Rough Sets

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On the correctness of partial differential operators and the von Neumann condition for stability of finite difference operators

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1963-0156484-7 ◽

1963 ◽

Vol 14 (6) ◽

pp. 948-948 ◽

Cited By ~ 4

Author(s):

D. G. Aronson

Keyword(s):

Finite Difference ◽

Differential Operators ◽

Difference Operators ◽

Neumann Condition ◽

Partial Differential ◽

Von Neumann ◽

Partial Differential Operators

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Reduction of Neighborhood-Based Generalized Rough Sets

Journal of Applied Mathematics ◽

10.1155/2011/409181 ◽

2011 ◽

Vol 2011 ◽

pp. 1-22 ◽

Cited By ~ 3

Author(s):

Zhaohao Wang ◽

Lan Shu ◽

Xiuyong Ding

Keyword(s):

Information Systems ◽

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Open Problems ◽

The Third ◽

Generalized Rough Sets

Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. This paper discusses five types of existing neighborhood-based generalized rough sets. The concepts of minimal neighborhood description and maximal neighborhood description of an element are defined, and by means of the two concepts, the properties and structures of the third and the fourth types of neighborhood-based rough sets are deeply explored. Furthermore, we systematically study the covering reduction of the third and the fourth types of neighborhood-based rough sets in terms of the two concepts. Finally, two open problems proposed by Yun et al. (2011) are solved.

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