Please use this identifier to cite or link to this item: https://doi.org/10.1109/ICCAE.2010.5451688
Title: Further exploration on relationship between crisp sets and fuzzy sets
Authors: Wang, Z.-X. 
Wang, Q.
Bai, M.
Chen, Z.-Q.
Sun, Z.
Keywords: Crisp set
Fuzzify upgrade operator
Type-1 fuzzy set
Type-2 fuzzy set
Issue Date: 2010
Source: Wang, Z.-X., Wang, Q., Bai, M., Chen, Z.-Q., Sun, Z. (2010). Further exploration on relationship between crisp sets and fuzzy sets. 2010 The 2nd International Conference on Computer and Automation Engineering, ICCAE 2010 2 : 609-613. ScholarBank@NUS Repository. https://doi.org/10.1109/ICCAE.2010.5451688
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. ©2010 IEEE.
Source Title: 2010 The 2nd International Conference on Computer and Automation Engineering, ICCAE 2010
URI: http://scholarbank.nus.edu.sg/handle/10635/70400
ISBN: 9781424455850
DOI: 10.1109/ICCAE.2010.5451688
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