Interval valued intuitionistic fuzzy sets
Fuzzy Sets and Systems
Operators over interval valued intuitionistic fuzzy sets
Fuzzy Sets and Systems
On the relationship between some extensions of fuzzy set theory
Fuzzy Sets and Systems - Theme: Basic notions
Interval-valued versus intuitionistic fuzzy sets: Isomorphism versus semantics
Pattern Recognition
Information Sciences: an International Journal
QoS-aware web services selection with intuitionistic fuzzy set under consumer's vague perception
Expert Systems with Applications: An International Journal
Some aspects of intuitionistic fuzzy sets
Fuzzy Optimization and Decision Making
A method based on distance measure for interval-valued intuitionistic fuzzy group decision making
Information Sciences: an International Journal
Fuzzy Sets and Systems
Toward a generalized theory of uncertainty (GTU)--an outline
Information Sciences: an International Journal
IEEE Transactions on Fuzzy Systems
Interval-valued fuzzy TOPSIS method with leniency reduction and an experimental analysis
Applied Soft Computing
Cuts of intuitionistic fuzzy sets respecting fuzzy connectives
Information Sciences: an International Journal
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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.