Four New Operators over Intuitionistic Fuzzy Sets

Over the object intuitionistic fuzzy set (IFS) [1, 2] has been defined different operators: , , Dα (α ∈ [0, 1]), Fα,β (α, β ∈ [0, 1]), Gα,β (α, β ∈ [0, 1]), and others (see [1-4]). Here, by analogy with the operators Dα, Fα,β and Gα,β , we shall define four other operators for a given IFS A and for given numbers α, β ∈ [0, 1]:* Hα,β (A) = {〈x, α.μA(x), νA(x) + β.πA(x)〉 | x ∈ E}, , ( ) H A α β = {〈x, α.μA(x), νA(x) + β.(1 – α.μA(x) – νA(x))〉 | x ∈ E}, Jα,β (A) = {〈x, μA(x) + α.πA(x), β.νA(x)〉 | x ∈ E}, , ( ) J A α β = {〈 x, μA(x) + α.(1 – μA(x) – β.νA(x)), β.νA(x)〉 | x ∈ E}.