We propose a novel modelization of the party formation process, in which citizens’ private opinions are described by means of continuous fuzzy profiles. Those citizens who show a high level of commitment become politicians, and create a public profile of political tolerance that extends their private profile. The main goal of this first paper is to describe how parties endogenously emerge from the matching mechanism of the private-and-public profiles of politicians. We provide an algorithm for the genesis of parties, and characterize newborn parties that behave as a single politician. Future work on this topic will be devoted to a description of parties’ dynamics and voting procedures by using the same fuzzy approach.