Rough Sets and Rule Induction from Indiscernibility Relations Based on Possible World Semantics in Incomplete Information Systems with Continuous Domains

2020 ◽  
pp. 3-23
Author(s):  
Michinori Nakata ◽  
Hiroshi Sakai ◽  
Keitarou Hara
Keyword(s):  
Information Systems ◽  
Incomplete Information ◽  
Rough Sets ◽  
Rule Induction ◽  
Possible World ◽  
Possible World Semantics ◽  
Continuous Domains ◽  
Incomplete Information Systems

Generalized neighborhood systems-based pessimistic rough sets and their applications in incomplete information systems

2021 ◽  
pp. 1-13
Author(s):  
Jing Pang ◽  
Bingxue Yao ◽  
Lingqiang Li
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Rough Set ◽  
Rough Sets ◽  
Decision Model ◽  
Incomplete Information System ◽  
Basic Properties ◽  
Model Based ◽  
Incomplete Information Systems

In this paper, we point out that Lin’s general neighborhood systems-based rough set model is an extension of Qian’s optimistic rough set model, and thus called optimistic general neighborhood systmes-based rough set model. Then we present a new rough set model based on general neighborhood systems, and prove that it is an extension of Qian’s pessimistic rough set model. Later, we study the basic properties of the proposed pessimistic rough sets, and define the serial, reflexive, symmetric, transitive and Euclidean conditions for general neighborhood systems, and explore the further properties of related rough sets. Furthermore, we apply the pessimistic general neighborhood systems-based rough set model in the research of incomplete information system, and build a three-way decision model based on it. A simple practical example to show the effectiveness of our model is also presented.

UNCERTAINTY MEASURE OF ROUGH SETS BASED ON A KNOWLEDGE GRANULATION FOR INCOMPLETE INFORMATION SYSTEMS

2008 ◽  
Vol 16 (02) ◽  
pp. 233-244 ◽  
Author(s):  
JUNHONG WANG ◽  
JIYE LIANG ◽  
YUHUA QIAN ◽  
CHUANGYIN DANG
Keyword(s):  
Information Systems ◽  
Incomplete Information ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Computer Applications ◽  
Mathematical Tool ◽  
Uncertainty Measure ◽  
Definition Of ◽  
Incomplete Information Systems

Rough set theory is a relatively new mathematical tool for computer applications in circumstances characterized by vagueness and uncertainty. In this paper, we address uncertainty of rough sets for incomplete information systems. An axiom definition of knowledge granulation for incomplete information systems is obtained, under which a measure of uncertainty of a rough set is proposed. This measure has some nice properties such as equivalence, maximum and minimum. Furthermore, we prove that the uncertainty measure is effective and suitable for measuring roughness and accuracy of rough sets for incomplete information systems.

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