Extraction of fuzzy rules from support vector machines

Fuzzy Inference System for Data Processing in Industrial Applications

“…Another typology of FSVM regards the extraction of fuzzy rules from the trained SVM model and a lot of works were been proposed (Chiang & Hao, 2004;Chen & Wang, 2003;Chaves et al, 2005;Castro et al, 2007).…”

On the usefulness of fuzzy SVMs and the extraction of fuzzy rules from SVMs

“…Approximating ( [28]. The clue here is that every SV corresponds to a fuzzy clause "distance between the SV and x" in the antecedent.…”

The theoretical foundations of statistical learning theory based on fuzzy number samples

“…Based on fuzzy set theory [9,10] and the statistics with vague data [11], a lot of scholars have studied SLT and SVM to deal with fuzzy samples [12][13][14][15][16][17][18][19][20][21][22][23]. Most of them mainly studied the SVM with fuzzy samples, for example, Lin and Wang [12] established SVM based on fuzzy samples, Jin et al [13] discussed SVM with genetic fuzzy feature transformation for biomedical data classification, and Castro et al [14] studied the extraction of fuzzy rules from SVM, and so on.…”

“…Most of them mainly studied the SVM with fuzzy samples, for example, Lin and Wang [12] established SVM based on fuzzy samples, Jin et al [13] discussed SVM with genetic fuzzy feature transformation for biomedical data classification, and Castro et al [14] studied the extraction of fuzzy rules from SVM, and so on. However, some scholars have also studied SLT to deal with fuzzy samples [20][21][22] recently, and they transferred samples from random ones to fuzzy ones, and defined fuzzy expected risk functional, fuzzy empirical risk functional and fuzzy empirical risk minimization (FERM) principle.…”

“…Based on the key theorem, the bounds show the relationship between fuzzy empirical risk and fuzzy expected risk. Utilizing the FERM principle, the bounds research the generalization ability of fuzzy learning machine, and provide the theoretical basis for the applied research of Fuzzy SVM [12][13][14][15][16][17]. Therefore, in this paper, as a series of theoretical foundations of statistical learning theory based on fuzzy number samples, we will discuss the bounds on the rate of convergence of learning processes based on fuzzy number samples by using the theory of fuzzy numbers.…”