Soft Computing

, Volume 21, Issue 9, pp 2189–2199 | Cite as

A unified view of consistent functions



In order to compare the structures and properties of two generalized information systems, a class of special mappings, called consistent functions in some literature, have been extensively studied over the past years. Most recently, consistent functions have been unified and extended into the framework of neighborhood systems which have general binary relations, dominance relations, and coverings as instances. In this paper, we further extend and investigate the notion of consistent functions for fuzzy neighborhood systems. After introducing the definition of extended consistent functions and showing their relationships with related functions, we present some basic properties of the new consistent functions with respect to set-theoretic operations and fuzzy neighborhoods, respectively. As an application, we consider the attribute reduction based on consistent functions. In doing so, we contribute to a unified view of consistent functions and attempt to develop a general theory for investigating the invariant properties of fuzzy neighborhood systems under consistent functions.


Attribute reduction Consistent function Fuzzy neighborhood system Homomorphism Granular computing 


Compliance with ethical standards


This work was funded by the National Natural Science Foundation of China (Grant Numbers 61370053, 61370193, and 61572081).

Conflict of interest

Author Ping Zhu declares that she has no conflict of interest. Author Huiyang Xie declares that she has no conflict of interest. Author Qiaoyan Wen declares that she has 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 2016

Authors and Affiliations

  1. 1.School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.College of ScienceBeijing Forestry UniversityBeijingChina
  3. 3.State Key Laboratory of Networking and SwitchingBeijing University of Posts and TelecommunicationsBeijingChina

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