Intuitionistic fuzzy generators Application to intuitionistic fuzzy complementation

Abstract In this paper from the definition of intuitionistic fuzzy sets we analyze the complementation in these sets. We begin by defining the intuitionistic fuzzy generators and the particular cases for which this definition coincides with the fuzzy complementation. Afterwards, we study the existence of the equilibrium points, dual points and we present different characterization theorems of intuitionistic fuzzy generators. By means of these theorems we can generate an unlimited number of intuitionistic fuzzy generators. Lastly, we present a way of constructing intuitionistic fuzzy sets from a fuzzy set and the intuitionistic fuzzy generators. The definition of intuitionistic fuzzy generator and the method of construction presented leads us in a natural way to define (ϕ 1 ,ϕ 2 ) -intuitionistic fuzzy sets obtaining from them, as a particular case, intuitionistic fuzzy sets. We conclude defining the intuitionistic fuzzy complementations and seeing how these recover the fuzzy complementations. We also study the complementary of an intuitionistic fuzzy set from the intuitionistic fuzzy generators.

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