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RSKT 2010: Rough Set and Knowledge Technology pp 195-203

# Qualitative Approximations of Fuzzy Sets and Non-classical Three-Valued Logics (I)

• Xiaohong Zhang
• Yiyu Yao
• Yan Zhao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6401)

## Abstract

(0,1)-Qualitative approximations of fuzzy sets are studied by using the core and support of a fuzzy set. This setting naturally leads to three disjoint regions and an analysis based on a three-valued logic. This study combines both an algebra view and a logic view. From the algebra view, the mathematical definition of a (0,1)-approximation of fuzzy sets are given, and algebraic operations based on various t-norms and fuzzy implications are established. From the logic view, a non-classical three-valued logic is introduced. Corresponding to this new non-classical three-valued logic, the related origins of t-norms and fuzzy implications are examined.

## Keywords

Fuzzy set (0 and 1)-approximation non-truth functional logic three-valued logic

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## Copyright information

© Springer-Verlag Berlin Heidelberg 2010

## Authors and Affiliations

• Xiaohong Zhang
• 1
• Yiyu Yao
• 2
• Yan Zhao
• 2
1. 1.Department of MathematicsNingbo UniversityNingboP.R. China
2. 2.Department of Computer ScienceUniversity of ReginaRegina, SaskatchewanCanada