Soft Computing

, Volume 22, Issue 7, pp 2329–2339 | Cite as

Axiomatic approaches to rough approximation operators via ideal on a complete completely distributive lattice

  • Ninghua Gao
  • Qingguo Li
  • Hongxia Han
  • Zhaowen Li
Methodologies and Application


In 2014, Zhou and Hu (Inf Sci 269:378–387, 2014) introduced a kind of rough sets on a complete completely distributive lattice (short for CCD lattice), which can be seen as a unified framework for the study of rough sets based on ordinary binary relations, rough fuzzy sets and interval-valued rough fuzzy sets. Han et al. (Soft Comput 20:1853–1861, 2016) introduced a new pair of rough approximation operators via ideal on a CCD lattice in 2016, which is more general and accurate than Zhou and Hu’s. In this paper, we further investigate its properties, and then the axiomatic approaches are studied. Through some of our axioms, the rough approximations via ideal on a complete atomic Boolean lattice can be viewed as special cases of rough approximation operators via ideal on a CCD lattice if the ideal is well given.


Axiomatic approaches Complete completely distributive lattice Complete sublattice ideal Galois connection Rough set 



The authors are enormously grateful to the editors and the anonymous reviews for their professional comments and valuable suggestions. This work is supported by the National Natural Science Foundation of China (Nos. 11371130, 11461005) and Research Fund for the Doctoral Program of Higher Education of China (No. 20120161110017).

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Ninghua Gao
    • 1
    • 2
  • Qingguo Li
    • 1
  • Hongxia Han
    • 1
    • 3
  • Zhaowen Li
    • 4
  1. 1.College of Mathematics and EconometricsHunan UniversityChangshaChina
  2. 2.School of ScienceZhejiang University of Science and TechnologyHangzhouChina
  3. 3.Department of Applied MathematicsYuncheng UniversityYunchengChina
  4. 4.College of ScienceGuangxi University for NationalitiesNanningChina

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