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5)). The density around cluster focal points can also be recursively updated E V O L V I N G T A K A G I - S U G E N O F U Z Z Y S Y S T E M S FR OM ST R E A M I N G D A T A ( e T S þ ) 26 (Angelov, 2004) by: Dt ðzi* Þ ¼ tÀ1 ; þm  nX 1 tÀ1 þ ðtÀ2Þ DtÀ1 ðzi* Þ À1 þ ðztj ÀzðtÀ1Þj Þ  j¼1 D1 ðzi* Þ ¼ 1; t ¼ 2; 3; . . ð2:7Þ where ià denotes the focal points of the ith fuzzy rule. , 2000). The latter aims to find natural groupings in such a way that the data points in a certain cluster are compact and clusters are well separable.

Using this notation we express our algorithm for modifying the source credibility as akÀ1 ðrk ÀCkÀ1 Þ Ck ðjÞ ¼ CkÀ1 ðjÞ þ Mjk l ðIIIÞ where  akÀ1 ¼ 1ÀakÀ1 and l 2 [0,1] is a base learning rate. We note that if Sj is not the source of the kth learning experience, then Mjk ¼ 0 and Ck(j) ¼ CkÀ1(j). Thus, in this case we do not make any changes in our credibility. If Mjk ¼ 1, then akÀ1 ðrk ÀCkÀ1 ðjÞÞ ¼ ð1ÀlakÀ1 ÞCkÀ1 ðjÞ þ lakÀ1 Þrk Ck ðjÞ ¼ CkÀ1 ðjÞ þ l Here we see l akÀ1 is an effective learning rate; it is the product of our base learning rate and the negation of the arousal level.

Horizontal and vertical evolution in eTS þ . 10. The idea (Angelov, 2006) for automatic input variable selection is based on the online monitoring and analysis of the consequents’ parameter values. If the values of the parameters aijlt ; i ¼ ½1; RŠ; l ¼ ½1; mŠ are negligibly small across the rules for a certain input (feature) j 2 {1,n} and certain output l 2 {1,m} for the data points seen so far, one can conclude that this particular input/feature j is not contributing significantly toward the overall output and this input variable (feature) is a candidate for removal.