Abstract
The classification problem in the real-world applications always involves uncertainties in both stochastic and fuzzy nature. This paper proposes a classification framework based on the unified probabilistic fuzzy configuration for data with uncertainties in both stochastic and fuzzy nature. The design and tuning procedures are also developed in terms of probability-based performance measure for working in the complex environment. A theoretical analysis is conducted to derive its quantificational model and disclose the interesting features. In addition to a superior performance than the traditional fuzzy method, the proposed method generates probabilistic fuzzy rules that can help users to better understand how the classifier works. This explainable characteristic is crucial for the decision making. Finally, the effectiveness of the proposed classifier will be demonstrated on its application to the Pima Indians Diabetes data and low back pain diagnosis. The satisfactory classification and the explainable characteristic disclose its potential in classification of data with uncertainties.