Uncertainty measures in rough algebra with applications to rough logic

The present paper is devoted to the measurement of uncertainty in rough algebra. Specifically, we employ the probability measure on the set of homomorphism of pre-rough algebra into $${\{0,\frac{1}{2},1\}}$${0,12,1} to present the graded version of rough truth value for elements in pre-rough algebra, which leads to the definition of rough (upper, lower) truth degree. These notions are subsequently used to introduce some other types of uncertainty measures including roughness degree, accuracy degree, rough inclusion degree, etc. A comparative study is conducted between these proposed uncertainty measures and the existing notions in rough logic and it is shown that the obtained results in She et al. (Fundam Inform 107:1–17, 2011) can be regarded as a special case of the present paper.

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