Multi-dimensional fuzzy transform and projection

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• 作者：Jean-Franç ; ois Crouzet ; ^{jean-francois.crouzet@univ-montp2.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fuzzy transform ; Fuzzy projection ; Signal representation ; Image representation ; Stability ; Robustness
• 刊名：Fuzzy Sets and Systems
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：307
• 期：Complete
• 页码：83-98
• 全文大小：660 K

文摘

Fuzzy and inverse fuzzy transforms, introduced by I. Perfilieva, is an important tool for signal and image fuzzy representation. It led to several variants, as the natural least-squares minimization named fuzzy projection. We deal with this transform, proposing first to show its simplicity and its easy numerical implementation in any dimension of space. Secondly, we point out that a key parameter permits to control its numerical robustness. Thirdly, we show that this parameter also governs the stability of the representation by fuzzy projection, when choosing different partitions of the space. We conclude in discussing linear representation; especially triangular representation for signals and pyramidal representation for images.