Soft Computing

, Volume 22, Issue 6, pp 1777–1789 | Cite as

Redefinition of the concept of fuzzy set based on vague partition from the perspective of axiomatization

  • Xiaodong Pan
  • Yang Xu


Based on the in-depth analysis of the essence and key features of vague phenomena, this paper focuses on establishing the axiomatical foundation of membership degree theory using for modeling vague phenomena, presents an axiomatic system to govern membership degrees and their interconnections. The concept of vague partition is introduced, on this basis, the concept of fuzzy set in Zadeh’s sense is redefined based on vague partition from the perspective of axiomatization. The thesis defended in this paper is that the mutual constraint relationship among vague attribute values in a vague partition should be the starting point to recognize and model vague phenomena by the quantitative analysis method.


Vagueness Axiom Vague membership space Vague partition Fuzzy set 



The authors would like to express my warm thanks to Prof. P. Eklund and Prof. D.W. Pei for valuable discussions on some of the problems considered here, and are very grateful to the Editors and the anonymous reviewers for their insightful and constructive comments and suggestions that have led to an improved version of this paper. This work was partially funded by the National Natural Science Foundation of China (Grant Nos. 61305074, 61673320).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

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

Informed consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of MathematicsSouthwest Jiaotong UniversityChengduPeople’s Republic of China

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