In standard particle swarm optimization (PSO), the best particle in each neighborhood exerts its influence over other particles in the neighborhood. In this paper, we propose fuzzy PSO, a generalization which differs from standard PSO in the following respect: charisma is defined to be a fuzzy variable, and more than one particle in each neighborhood can have a non-zero degree of charisma, and, consequently, is allowed to influence others to a degree that depends on its charisma. We evaluate our model on the weighted maximum satisfiability (maxsat) problem, comparing performance to standard PSO and to Walk-Sat.