Abstract
In rule optimization, some rule characteristics were extracted to describe the uncertainty correlations of fuzzy relations, but the concrete numbers cannot express correlations with uncertainty, such as “at least 0.1 and up to 0.5.” To solve this problem, a novel definition concerning interval information content of fuzzy relation has been proposed in this manuscript to realize the fuzziness measurement of the fuzzy relation. Also, its definition and expressions have also been constructed. Meanwhile based on the interval information content, the issues of fuzzy implication ranking and clustering were analyzed. Finally, utilizing the combination of possibility’s interval comparison equations and interval value’s similarity measure, the classifications of implication operators were proved to be realizable. The achievements in the presented work will provide a reasonable index to measure the fuzzy implication operators and lay a solid foundation for further research.
Highlights
Nowadays, we are in the midst of an information revolution, which is driving the development and deployment of new kinds of science and technology with ever-increasing depth and breadth
How to select and evaluate rules is the key issue to realize the control of fuzzy system, which can be summarized as rule optimization [6, 7]
For any fuzzy implication operator, after determining the best classification by extracting the interval information content characteristics, the final categories are confirmed by the similarity measure between the sample implication operators and the clustering centers of each category
Summary
We are in the midst of an information revolution, which is driving the development and deployment of new kinds of science and technology with ever-increasing depth and breadth. Many fuzzy implication operators can be constructed [20,21,22,23,24], and for them, the research on how to realize better control of fuzzy systems is still lacking To address these issues, a novel method has been proposed in the paper, utilizing which the interval information contents of fuzzy relations have been extracted to realize the ranking, clustering, and classification. The fuzzy relation of the interval information content was proposed, and five different expressions were developed, with which the ranking, clustering, and classification of fuzzy implication operators have been realized
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