Mathemathical modeling seeks to describe in a formal way a phenomenom but we can encounter two inconveniences, namely, the complexity and the uncertainty by vagueness. In order to take vagueness into consideration, the fuzzy set theory formalized by Zadeh in 1965 intends to give a mathematical treatment to the subjective topics. Additionally, it is considered as an important tool for getting a better understanding of some real situations. This is why we are motivated to give in this paper some of the basics notions of this branch of mathematics which has been in a continuous development for the latest fifty years.