Axiomatic approaches to rough approximation operators on complete completely distributive lattices

2016 ◽  
Vol 348 ◽  
pp. 227-242 ◽  
Author(s):  
Ning Lin Zhou ◽  
Bao Qing Hu
Keyword(s):  
Distributive Lattices ◽  
Completely Distributive ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Axiomatic Approaches

Aximatics for Rough Set Model Based on Vague Relations

2011 ◽  
Vol 282-283 ◽  
pp. 283-286
Author(s):  
Hai Dong Zhang ◽  
Yan Ping He
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
General Framework ◽  
Axiomatic Approach ◽  
Constructive Approach ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Axiomatic Approaches ◽  
Set Approximation

This paper presents a general framework for the study of rough set approximation operators in vague environment in which both constructive and axiomatic approaches are used. In constructive approach, by means of a vague relation defined by us, a new pair of vague rough approximation operators is first defined. Also some properties about the approximation operators are then discussed. In axiomatic approach, an operator-oriented characterization of vague rough sets is proposed, that is, vague rough approximation operators are defined by axioms.

Approximation operators on complete completely distributive lattices

2013 ◽  
Vol 247 ◽  
pp. 123-130 ◽  
Author(s):  
Keyun Qin ◽  
Zheng Pei ◽  
Jilin Yang ◽  
Yang Xu
Keyword(s):  
Distributive Lattices ◽  
Completely Distributive ◽  
Approximation Operators

scholarly journals Rough Approximation Operators on a Complete Orthomodular Lattice

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 164
Author(s):  
Songsong Dai
Keyword(s):  
Boolean Algebra ◽  
Orthomodular Lattice ◽  
Orthomodular Lattices ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Distributive Law ◽  
Complete Orthomodular Lattice ◽  
The Relationship

This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.

scholarly journals Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 417 ◽  
Author(s):  
Hu Zhao ◽  
Hong-Ying Zhang
Keyword(s):  
Algebraic Structure ◽  
Rough Sets ◽  
Lattice Structure ◽  
Single Domain ◽  
One Dimensional ◽  
Basic Properties ◽  
Approximation Operators ◽  
Rough Approximation ◽  
The One ◽  
Comprehensive Study

As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied. However, they did not do a comprehensive study on the algebraic structure of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators. In the present paper, we will provide the lattice structure of the pessimistic multigranulation neutrosophic rough approximation operators. In particular, in the one-dimensional case, for special neutrosophic relations, the completely lattice isomorphic relationship between upper neutrosophic rough approximation operators and lower neutrosophic rough approximation operators is proved.

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