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This paper investigates the behavior of the fuzzy sets in the antecedents of the Takagi Sugeno fuzzy model in identification of nonlinear and time variant systems. The methods applied are data-driven techniques, by considering that measurement data are available. The principal question to solve in this paper is related with the representation of this kind of systems applying the concept of interval-valued fuzzy set. An overall model includes explicitly the nonlinear or time variant behavior of the system being identified by means of this concept using Takagi Sugeno fuzzy models. The determination of the nonlinear parameters of the antecedent is a central point in this modeling for time variant and nonlinear systems, because of the characteristics of these parameters. An illustrative experiment on a hybrid-tank system is conducted to present the benefits of the proposed approach.