Measures of uncertainty based on Gaussian kernel for a fully fuzzy information system

摘要

The uncertainty of information plays an important role in practical applications, so how to capture the uncertainty of information systems becomes more and more popular. Uncertainty measures can supply new viewpoints for processing information systems, and they can help us in disclosing the substantive characteristics of information. Fuzzy information systems are important research objects in artificial intelligence. As a special kind of fuzzy information system, fully fuzzy information system (FFIS) is worth studying. This article is devoted to search indicators for measuring uncertainty in a FFIS according to fuzzy information structures in view of Gaussian kernel, and the fuzzy information structures can be viewed as granular structures under granular computing. Firstly, by employing Gaussian kernel for calculating similarities among objects in a FFIS, the fuzzy Tcos-similarity relation is obtained. Then, based on this relation, fuzzy information structures in a FFIS are introduced. Next, according to the information structures, granulation measure of a given FFIS is advanced. Moreover, entropy measure is also considered for a given FFIS. Finally, two numerical experiments are conducted to interpret the realistic significance and potential applications for measuring uncertainty in a FFIS. Theoretical research, numerical experiments and validity analysis make clear that the proposed measures are efficacious and applicable for a FFIS.