Multivariate Extension Principle and Algebraic Operations of Intuitionistic Fuzzy Sets

Multivariate Extension Principle and Algebraic Operations of Intuitionistic Fuzzy Sets

Extension principles for interval-valued intuitionistic fuzzy sets and algebraic operations

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 ...

Some operations on intuitionistic fuzzy sets

In This paper, Author Discuss about some operations on Intuitionistic Fuzzy sets (or vague sets) we understand that the most important and potential generalization of Fuzzy sets came in the form of intuitionistic Fuzzy sets developed by Atnassove. It is justified by Bustince and Burillo[2] that intuitionistic fuzzy sets and vague sets are same. So in this paper the two terminologies vague sets ...

Operations on Generalized Intuitionistic Fuzzy Soft Sets

Generalized intuitionistic fuzzy soft set theory, proposed by Park et al. [Journal of Korean Institute of Intelligent Systems 21(3) (2011) 389-394], has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we prove that certain De Margan’s law hold in generalized intuitionistic fuzzy soft set theory with respect to union and intersection operations on gener...

Algebraic Properties of Intuitionistic Fuzzy Residuated Lattices

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the sam...