Uncertainty Measures in Fuzzy Set-Valued Information Systems Based on Fuzzy β-Neighborhood Similarity Relations

Uncertainty measures are instrumental in describing the classification abilities in information systems, and uncertain information has been measured and processed with granular computing theory. While the fuzzy set-valued information system is a generalization of fuzzy information systems, the relationship between the information granulation and the uncertainty in fuzzy set-valued information systems remains to be studied. This paper probes into uncertainty measures in fuzzy set-valued information systems based on the fuzzy [Formula: see text]-neighborhood and the idea of granulation. Specifically, the fuzzy [Formula: see text]-neighborhood similarity relation that reflects the similarity between two objects is defined in terms of the nearness degree. We propose the concepts of information granules and granular structures induced by fuzzy [Formula: see text]-neighborhood similarity relations, based on which we introduce the granularity measures and rough approximation measures of granular structures in fuzzy set-valued information systems. Given the situation of decision information systems, we propose the granularity-based rough approximation measures by combining granularity measures with rough approximation measures. Experiment results and effectiveness analysis show that the measures we proposed are reasonable and feasible.