At present time, theory of complex numbers is a very renowned subject area in Mathematics as well as various other fields of science and technology. In nineteenth century, different number systems had been introduced for examining algebra regarding multiple imaginary units. The notion of bicomplex numbers, perhaps, would be the most important among those. Later on, as an extension of this number system, generalized bicomplex number had been introduced. On the other hand, the concept of fuzzy logic has been considered to be significant in Mathematics to solve problems having imprecise spectrum of data. In this paper, our intension is to fuzzify generalized bicomplex number. For this purpose, here we first define generalized fuzzy bicomplex numbers from two alternative aspects and then, based upon these we propose some basic mathematical tools such as generalized fuzzy bicomplex norm, basic arithmetic operations etc. which help to study some fundamental properties in this regard.