Abstract
Non-standard fuzzy sets play a significant role in uncertainty modeling. In addition to membership and non-membership degree, how to handle the hesitant degree is the key issue in the uncertain information process. In this paper, we model the Pythagorean fuzzy set (PFS) under the belief structure and measure its uncertainty based on fractal-based belief (FB) entropy. A novel fuzzy entropy for PFS called belief structure-based Pythagorean fuzzy (BSPF) entropy is proposed, whose effectiveness and advantages are proven based on mathematical analysis and numerical examples. A comparative analysis between BSPF entropy and other methods shows that BSPF entropy can obtain more reasonable results. Besides, a BSPF entropy-based multi-criteria decision-making (MCDM) method and a classification method are designed to solve practical problems. The experimental results demonstrate the effectiveness of these two proposed methods in solving real-world problems of decision-making and classification.
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