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This study defines various degrees of intuitionistic fuzzy functions, revealing their classifications and implications for fuzzy relation types.
In this paper, we explore the concept of degree of the intuitionistic fuzzy functions. In [4], Demirci studied gradations of fuzzy functionhood. There, for a fuzzy relation f on X×Y considering the fuzzy equalities E_X on X and E_Y on Y the degree of f of being a fuzzy fuction, being surjective, being injective and being bijective is defined. We extend this study to intuitionistic fuzzy functions. In this paper, we use intuitionistic fuzzy functions and their types defined by Lim, Choi and Hur [7] by using intuitionistic fuzzy equalities. Since an intuitionistic fuzzy function is a (µA(x, y), νA(x, y)) ordered pair, we define its degree of being (α) and the degree of non-being (β) by using (α, β) ∈ L∗. For an intuitionistic fuzzy relation f from X×Y to I^2, considering the intuitionistic fuzzy equalities E_X on X and E_Y on Y, we define the degree to which f is an intuitionistic fuzzy function, the degree of it being surjective, injective and bijective, respectively. We especially analyze the degrees of some types of intuitionistic fuzzy functions. We prove some theorems using these definitions
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Deniz et al. (2025) studied this question.
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