Continuous Fuzzy Transform as Integral Operator

نویسندگان

چکیده

The fuzzy transform (F-transform) is ubiquitous in different research fields and applications, such as image data compression, mining, knowledge discovery, the analysis of linguistic expressions. As a generalization F-transform, this article, we introduce continuous F-transform its inverse, an integral operator induced by kernel function. Through relation between membership functions kernels, show that main properties (e.g., continuity symmetry) are inherited F-transform. Then, operators used to data-driven which encodes intrinsic information structure, geometry, sampling density) about input data. In way, avoid coarse partitions, group into large clusters do not adapt their local behavior, or too dense partition, generally has cells covered data, thus being redundant resulting higher computational cost. To end, defined properly filtering spectrum Laplace–Beltrami associated with Finally, space F-transforms, useful for comparison F-transforms efficient computation.

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ژورنال

عنوان ژورنال: IEEE Transactions on Fuzzy Systems

سال: 2021

ISSN: ['1063-6706', '1941-0034']

DOI: https://doi.org/10.1109/tfuzz.2020.3012764