Traditionally, *fuzzy* methods (i.e., methods that use truth values
intermediate between 0 and 1) are mainly used in the situations with
*incomplete* information, i.e., in the situations when we have
uncertainty and fuzziness. However, such methods can also be useful in
solving situations with *complete* information, as a means of
formalizing informal experts' heuristics.
In 1981, S. Maslov from Russia used this idea to design a new
method of solving propositional satisfiability problem, a problem
whose particular cases involve expert systems and that
is known to be, in the general case, computationally intractable
(NP-hard). Maslov's iterative method, in which truth values between 0
and 1 are allowed on the intermediate stages, turned out to be very
efficient in comparison with previously known methods in which only
the truth values 0 (= false) and 1 (= true) were used.
It also turned out Maslov's iterative formulas can be interpreted
in several other terms, e.g., in terms of neural networks, or
in terms of chemical computing.
This edited book describes the foundations, modifications, and
successes of Maslov's iterative method. In particular, the
relationship between this method, neural networks, fuzzy logic,
chemical computing, traditional numerical optimization techniques,
and a (reasonably formalized) freedom of choice is summarized in
the book's last chapter.
Detailed bibliographic information:
"Problems of Reducing the Exhaustive Search"
(edited by V. Kreinovich, University of Texas at El Paso, and G. Mints,
Stanford University), American Mathematical Society (AMS), Providence, RI,
1997, 189 pp., hardcover, List: $79,
Institutional AMS Member: $63, Individual AMS Member: $47, code TRANS2/178
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