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The probabilistic fuzzy set (PFS) is designed for handling uncertainties with both fuzzy and stochastic nature, so the probabilistic fuzzy logic system (PFLS) has the ability to handle more complex uncertainties in process. In this paper, the general probabilistic fuzzy set is proposed, and the convergence analyses of its secondary probability density function (PDF) are conducted. It discloses the distribution regularity of membership degree in general PFS, which improves the information and interpretability of PFS. Then, according to convergence, a new method to tuning parameters for PFLS is proposed. This method avoids the parameters into local inefficiency, and also reduces the number of learning parameters in PFLS. Last, the new tuning method is applied to the electromyography (EMG) robots modeling problem. The comparison shows that the probabilistic fuzzy logic system based on general PFS (GPFLS) can achieve a simple modeling process, and also, it improves the learning speed compared to PFLS. The work presented will improve the potential application of probabilistic fuzzy logic system. [ABSTRACT FROM AUTHOR]

Highlights: [•] We propose the concept of the distance between probabilistic fuzzy sets. [•] The corresponding proofs of the proposed distance measure are conducted. [•] We propose PFS-based distance classifier. [•] The PFS-based distance classifier is applied to classification problems. [Copyright &y& Elsevier]