From: Osher Doctorow, Ph.D. [log in to unmask], Sun. Oct. 1, 2000, 6:15AM
The paper "Soft computing based signal prediction, restoration, and
filtering" by E. Uchino and T. Yamakawa of Kyushu Institute of Technology,
Japan (CS and Control Engineering Dept.), in D. Ruan (Ed.) Intelligent
Hybrid Systems: Fuzzy Logic, Neural Networks, and Genetic Algorithms,
Kluwer: Boston, 1997, 331-351, is of considerable interest for evolutionary
computing. Ruan at the time of publication was with the Belgian Nuclear
Research Centre, SCK.CEN, Mol, Belgium. The discussion of neo-fuzzy neurons
is especially valuable, and several papers on this topic are cited to which
Yamakawa and Uchino contributed in 1992 and 1993.
I will only comment on one preliminary aspect here and hopefully continue
later. The same book has a paper, "Introduction to fuzzy systems, neural
networks, and genetic algorithms", pp. 3-33, by H. Takagi of Kyushu
Institute of Design, Fukuoka, Japan, where fuzzy reasoning and aggregation
are introduced. The consequents of the Takagi-Sugeno-Kang models are
expressed by linear combination of weighted input variables. Takagi gives
an example using the Product/Goguen t-norm which is just the algebraic
product xy.
My comment concerns logic-based probability (LBP), which I introduced in
1980, and which yields the Lukaciewicz t-norm x*y = max(0, x+y-1) and the
Lukaciewicz (fuzzy) many-valued implication x-->y = 1 - x + y for the
nontrivial case. A third t-norm is the Godel t-norm x*y = min(x,y). These
three fuzzy/many-valued implications and t-norms divide the continuous
t-norms among themselves essentially and any two of them have been proven to
yield the general case. Thus, Lukaciewicz t-norm and fuzzy implication
could just as well have been used. LBP goes a step further and directly
uses the Lukaciewicz (fuzzy) many-valued implication rather than the
corresponding t-norm for calculating each rule strength, although it could
be modified to use t-norms. The final system output in then obtained as in
Takagi by weighting every rule output by the rule strength calculated and
then Mamdani [University of London] fuzzy controllers defuzzify the combined
system output and obtain the final nonfuzzy control state.
The advantage of using LBP over Product/Goguen methods is somewhat
interesting. LBP yields a generalization of maximum entropy and even
generalized maximum-parameter-entropy results in that the results are
(generalized) maximum entropy for the fewest (next fewest, etc.) number of
unknown parameters. Thus, we obtain a tie-in with maximum parameter methods
of probability/statistics. Abstracts of 46 of my papers are on the internet
at http://www.logic.univie.ac.at, Institute for Logic at the University of
Vienna (select ABSTRACTS, then BY AUTHOR, then my name). It is difficult
for me to send full papers to all requesters because I am a private
consultant in mathematics/statistics/physics and do not obtain academic or
corporate discounts for sending post (I am also rather short in time), but I
will be glad to answer as many email inquiries as I can, and the abstracts
are unusually precise and concise summaries of the main ideas.
Osher Doctorow
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