The probabilistic fuzzy set (PFS) and the related probabilistic fuzzy logic system (PFLS) is designed for handling the uncertainties in both stochastic and nonstochastic nature. In this paper, a bell-shaped probabilistic fuzzy set is proposed and the related PFLS is constructed and applied to a modeling problem to study stochastic modeling capability. It clearly discloses that the bell-shaped PFS performs better than the previous PFS under certain stochastic circumstance. The bell-shaped

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... listic fuzzy set gives a more general model of fuzzy rules and improving the precision of probabilistic fuzzy logic system. The PFLS using bell-shaped probabilistic fuzzy set improves its potential application in engineering.