Od: "Dmitry A. Kazakov" Temat: Re: fuzzy inference Data: 10 września 2003 14:41 On 10 Sep 2003 04:14:22 -0700, mackinson@hotmail.com (Steve) wrote: >I have a question regarding fuzzy inference that I have not been able >to find the answer to on the internet, or books etc. > >Simply it is: Why is it that MIN-MAX and PRODUCT-SUM inference >options are the most commonly used? MIN-MAX corresponds to possibilities. PRODUCT-SUM does to probabilities (under some conditions). >Why doesn't anyone mention >MIN-SUM? >I have been doing some work where we tried applying MIN inference >(implication) with SUM composition (aggregation of output sets). It >provided a better result using centroid defuzzification, which allows >for the fact that the summed DoBs of the output sets can be greater >than 1. > >No-one ever seems to talk about MIN-SUM and PRODUCT-MAX inference! I >can see that there may be a problem with MAX-PRODUCT because it would >result in valleys in the output sets. What might be wrong with >MIN-SUM? It would break de Morgan's laws with NOT=1-x. I do not know whether it is possible to define NOT in a consistent way. Anyway, it also breaks AUA=A. >I would very much appreciate any ideas you have or pointers to texts/ >examples that could help? There is a large amount of papers devoted to the issue. A decision depends on which result of the crisp set theory have to be preserved. It is known that the biggest set is preserved by min/max/1-x. --- Regards, Dmitry Kazakov www.dmitry-kazakov.de