Publication Type
Conference Proceeding Article
Version
publishedVersion
Publication Date
2-2010
Abstract
This paper employs the concept of fuzzify upgrade operator to describe the relationship between crisp sets, fuzzy sets and higher order fuzzy sets, such as type-2 fuzzy sets. Theory analysis and case studies demonstrate that a crisp set can be represented by a type-1 fuzzy set, a type-1 fuzzy set can be represented by a type-2 fuzzy set, and a type-n (n>=2) fuzzy set can be represented by a type-(n+1) (n>=2) fuzzy set. The fuzzify upgrade operator makes crisp sets, type-1 fuzzy sets, type-2 fuzzy sets and any fuzzy sets much more accessible to all readers. The relationship between crisp sets and fuzzy sets are explored.
Keywords
Crisp set, Fuzzify upgrade operator, Type-1 fuzzy set, Type-2 fuzzy set
Discipline
Numerical Analysis and Scientific Computing | Operations Research, Systems Engineering and Industrial Engineering
Research Areas
Intelligent Systems and Optimization
Publication
Proceedings of the 2010 2nd International Conference on Computer and Automation Engineering (ICCAE) Singapore, February 26-28
First Page
609
Last Page
613
ISBN
9781424455850
Identifier
10.1109/ICCAE.2010.5451688
Publisher
IEEE
City or Country
New York
Citation
WANG, Zhaoxia; WANG, Quan; BAI, Ming; CHEN Zeng-qiang; and SUN, Zhen.
Further exploration on relationship between crisp sets and fuzzy sets. (2010). Proceedings of the 2010 2nd International Conference on Computer and Automation Engineering (ICCAE) Singapore, February 26-28. 609-613.
Available at: https://ink.library.smu.edu.sg/sis_research/6729
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1109/ICCAE.2010.5451688
Included in
Numerical Analysis and Scientific Computing Commons, Operations Research, Systems Engineering and Industrial Engineering Commons