Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

2010

Research Collection School Of Computing and Information Systems

Operations Research, Systems Engineering and Industrial Engineering

Crisp set

Articles 1 - 1 of 1

Full-Text Articles in Physical Sciences and Mathematics

Further Exploration On Relationship Between Crisp Sets And Fuzzy Sets, Zhaoxia Wang, Quan Wang, Ming Bai, Chen Zeng-Qiang, Zhen Sun Feb 2010

Further Exploration On Relationship Between Crisp Sets And Fuzzy Sets, Zhaoxia Wang, Quan Wang, Ming Bai, Chen Zeng-Qiang, Zhen Sun

Research Collection School Of Computing and Information Systems

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 …