BK has published, in several places, an example of a FCM based on
an editorial about changes in the South African economy that would
result from foreign investment. It's on p. 153-54 of Neural Networks &
Fuzzy Systems, p. 227 of Fuzzy Thinking, and p. 380 of "Hidden
Patterns in Combined and Adaptive Knowledge Networks," Int'l Journal
of Approximate Reasoning, 1988, 2:379-380. Apparently the author
feels this is a strong example of FCM.
I re-analyzed BK's connection matrix using particle swarm optimization.
Kosko clamps on the first concept node and estimates thresholded values
for the other eight nodes, to demonstrate how investment (concept #1)
affects the other variables in the system.
He reports that the system settles on this vector of concepts:
(1 1 1 1 0 0 0 1 1)
The alternative optimization method, however, resulted in this vector:
(1 0 0 1 1 1 1 0 0)
As can be seen, these results are nearly opposite. The PSO solution
suggests that foreign investment in South Africa will reduce (Kosko said
increase) mining and Black employment, increase white racist radicalism
(the two solutions agree on that), increase job reservation laws, Black
tribal unity, and apartheid (Kosko says these will decrease), and
strengthen the government and National Party constituency (Kosko says
they will weaken).
I would appreciate if readers of this newsgroup would please check these
results, and if possible explain to me why Kosko's results are better.
If I get email, I will gladly post comments. FCM is a potentially exciting
technique for modeling experts' beliefs, but I am concerned about its
weaknesses.
Jim Kennedy