Fuzziness and randomness are two distinct components of uncertainty. While fuzzy sets are a rigorous softening of random sets, many of the operations de ned in fuzzy logic lack a complete formalism, and are not strongly supported by experimental evidence. Causal Probabilistic Networks (CPN) or Bayesian networks provide an ultimately exible inference mechanism based on Bayesian probability princ...

The likelihood approach to statistics can be interpreted as a theory of fuzzy probability. This paper presents a generalization of credal networks obtained by generalizing imprecise probabilities to fuzzy probabilities; that is, by additionally considering the relative plausibility of different values in the probability intervals.

This paper presents an applicable health monitoring method for Li-ion batteries based on profust reliability theory. The word “profust” derives from “probability” and “fuzzy-state”, which means that the profust reliability theory is a kind of fuzzy reliability theory based on probability assumption and fuzzy-state assumption. It defines a concept of transition from fuzzy success to fuzzy failur...

In this paper, a computational model of fuzzy reliability focusing on solving the engineering problems with random general stress–fuzzy general strength is presented. The mathematical basis of this computational model is that the fuzzy probability can be computed with the computational method of conventional probability by use of a mathematical transition. Based on this computational model, a n...

Probabilistic fuzzy systems combine a linguistic description of the system behaviour with statistical properties of data. It was originally derived based on Zadeh’s concept of probability of a fuzzy event. Two possible and equivalent additive reasoning schemes were proposed, that lead to the estimation of the output’s conditional probability density. In this work we take a complementary approac...