Extension principles for interval-valued intuitionistic fuzzy sets and algebraic operations |
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Authors: | Deng-Feng Li |
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Institution: | 1. School of Management, Fuzhou University, No. 2, Xueyuan Road, Daxue New District, Fuzhou District, Fuzhou, Fujian, 350108, China
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Abstract: | The Atanassov’s intuitionistic fuzzy (IF) set theory has become a popular topic of investigation in the fuzzy set community.
However, there is less investigation on the representation of level sets and extension principles for interval-valued intuitionistic
fuzzy (IVIF) sets as well as algebraic operations. In this paper, firstly the representation theorem of IVIF sets is proposed
by using the concept of level sets. Then, the extension principles of IVIF sets are developed based on the representation
theorem. Finally, the addition, subtraction, multiplication and division operations over IVIF sets are defined based on the
extension principle. The representation theorem and extension principles as well as algebraic operations form an important
part of Atanassov’s IF set theory. |
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