Further exploration on relationship between crisp sets and fuzzy sets

Author

Wang, Zhao-xia ; Wang, Quan ; Bai, Ming ; Chen, Zeng-qiang ; Sun, Zhen

Author_Institution

Sch. of Electron. Inf. Eng., Tianjin Univ. of Technol., Tianjin, China

Volume

2

fYear

2010

fDate

26-28 Feb. 2010

Firstpage

609

Lastpage

613

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

fuzzy set theory; crisp sets; fuzzify upgrade operator; higher order fuzzy sets; theory analysis; type-1 fuzzy sets; type-2 fuzzy sets; Automation; Drives; Function approximation; Fuzzy control; Fuzzy reasoning; Fuzzy set theory; Fuzzy sets; Gaussian processes; Humans; Uncertainty; Fuzzify upgrade operator; crisp set; type-1 fuzzy set; type-2 fuzzy set;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer and Automation Engineering (ICCAE), 2010 The 2nd International Conference on

Conference_Location

Singapore

Print_ISBN

978-1-4244-5585-0

Electronic_ISBN

978-1-4244-5586-7

Type

conf

DOI

10.1109/ICCAE.2010.5451688

Filename

5451688