> Whether the underlying logic is classical, fuzzy, probabilistic, possibilistic, > bayesian, dempster/shafer or any other of the myriad variants and/or > combinations might change the semantics of computed degrees associated > with derived formulae, but it doesn't change in the least the general > ability of the system to deal with background knowledge.
Laszlo Koczy wrote (3.08.2001 11:36-comp.ai.fuzzy): "My favourite way of looking at fuzzy inferece/control methods is that they represent a compromise approach to approximation (in a rather user friendly way!), with a reasonable computational complexity side as well. The two are of course contradictory requirements and while one is optimal, the other might quite easily be not acceptable at all. Think about the statements on the universal approximation properties that have been proved by Wang, Kosko, later Nguyen and Kreinovich, even later by Castro and many others." (End of citation.) If we know relation R(x,y) we can approximate it using fuzzy relation R1(x,y). It could be done for any choice of s-norm and t-norm. Because of this I agree the following statement "myriad variants and/or combinations might change the semantics of computed degrees associated with derived formulae, but it doesn't change in the least the general ability of the system to deal with background knowledge."> So the question how well background knowledge is handeled is > completely unsuitable for distinguishing between probabilistic and > fuzzy logic.
In my work I don't know relation between input and output. This relation is a solution of some differential equations with uncertain parameters. I have to calculate this relation using given data. I can't compare each solution with experiments and after that choose the best "AND" and "OR" operators because this is too expensive. I can not approximate the relation R(x,y), because I don't know it. I have to predict the result without compression with experiments. (This is the aim of mathematical modelling.) In this kind of engineering problems I have to know the best "AND" and "OR" operators before calculation. Additionally I have to know what is physical interpretation of fuzzy arithmetic operation. From this discussion I came to the conclusion that using fuzzy logic we cannot predict behaviour of engineering systems. We can only approximate behaviour of the system which characteristics are known with other sources. The question "how well background knowledge is handled" (in fuzzy logic operations)" is fundamental in prediction of behaviour of engineering systems. Andrzej Pownuk --------------------------------------------- MSc. Andrzej Pownuk Chair of Theoretical Mechanics Silesian University of Technology E-mail: pownuk@zeus.polsl.gliwice.pl URL: http://zeus.polsl.gliwice.pl/~pownuk ---------------------------------------------