Contrib. 2a/b:

Fuzzy Finance & Soft Computing

Here, we enter financial applications of advanced, nonlinear, mathematic
approaches used in self-regulation, neural networks, artificial intelligence, etc.

Fuzzy logic definition (see also the article in our glossary)

Fuzzy Logic (or logic of fuzzy sets) says that "black or white / right or false" math's, and
also probability "laws" (i.e. the "normal distribution") are only approximate representations
of the real world (RW).

In the RW, everything is true or false to a degree, never 0 % or 100 %.

An apple of which a chunk was bitten off is at the same time an apple ...and a non-apple.

It is something in between, an apple to a certain degree and/or a non-apple to a
certain degree.

Fuzzy logic considers therefore that

There is a "degree" of truth or falsehood in most things and most concepts, contrarily
    to what Aristotle's binary logic asserts.

This degree is an approximation, fuzzy logic works with such soft concepts as
    "multivalence" and "low" or high".



FL applies to "hard" sciences (such as physics) and even more to "soft" ones (psychology,
economics, finance).

Here, phenomena are more complex, hard to measure and "non linear".

To use a linear, probabilistic, monovalent model to find the "normal" price of an apple,
sorry, an asset, gives most of the time a result slightly, or widely, different from the
market price.
The real price is one inside a range of many possible ones (multivalence).
A realistic model would give such a bracket.

On the contrary, probabilistic models centered on standard deviations, tend to hide the
extreme values and the extreme risks (rare events). On the other hand, Bayesian
probabilities, based on initial hypotheses which are adjusted every time a new event
or information occurs, are closer to fuzzy logic, but can also miss the extreme occurrences.


Paul Victor Birke shows us there are fuzzy stock prices and fuzzy market expectations.

Doug Elias enlarges the concept via the "soft computing" approach, that selects and
uses "soft" tools available in fuzzy logic, neural nets, imprecise probabilities, genetic
algorithms, learning and belief theories, and others.

2a. Communication 20-21 Feb.. 2000 from Paul Victor Birke,
              P. Eng. NN Researcher in Guelph ON CANADA

There is a Fuzzy Price

The price quoted is only one of a possible number from a small interval set. 
Usually a Uniform Distribution defined by {PriceLOW, PriceHIGH}


Also there is another way using a sort of Trapezoid with

The Ultra values define the Trapezoid boundaries having zero membership value.

The Low and High define the limits of the membership = 1 Uniform Distribution.

The Mean may or may not be in the centre between Low and High.

This leads to ideas of Maximized Fuzzy Expectation.
You find the Optimal Price Interval* {Plow*,Phigh*} by Maximization of a Fuzzy

This would be the expected range of price that has the strong possibility to maximize
your return.

Thus when you use Fuzzy Expectation as some kind of Price * Possibility

you could see that both require some modeling considerations, as Possibility is likely
an UltraFuzzy Function representing issues within the given marketplace of application.

Fuzzy Finance is slow to come on. I found a guy at Michigan State about 4 years ago
doing a master on fuzzy accounting. It gives you the strong impression that Fuzzy
Financial applications are real.

Why is everyone so slow on the pickup here. Likely disturbs existing paradigms for
That is what I found!!  Too complicated for Management!!

I have also noticed that there exist this other methodology that of so-called "Rough
Set Theory".
It seems to use the ideas I have put forth--that of Ultra Low and High.  I.E. the
"hard boundaries of believability" for your modeled object, here price.

2b. Communication Sep 18, 2000 from Pr. Doug Elias,
              Cornell University's Graduate Business School's Director of Technology

The topic being Soft Computing in Fundamental and Technical Analysis,
here're first a couple of quotes lifted from:

The Soft Computing and Artificial Life website

Soft computing differs from conventional (hard) computing in that, unlike hard
computing, it is tolerant of imprecision, uncertainty and partial truth.

In effect, the role model for soft computing is the human mind.

The guiding principle of soft computing is: Exploit the tolerance for imprecision,
uncertainty and partial truth to achieve tractability, robustness and low solution

The BISC website

At this juncture, the principal constituents of soft computing (SC) are fuzzy logic
(FL), neural network theory (NN) and probabilistic reasoning (PR), with the
latter subsuming belief networks, genetic algorithms, chaos theory and parts of
learning theory.

What is important to note is that SC is not a mélange of FL, NN and PR. Rather,
it is a partnership in which each partner contributes a distinct methodology
for addressing problems in its domain. In this perspective, the principal
contributions of FL, NN and PR are complementary rather than competitive.

On the actual ways that things like fuzzy logic, neural nets, chaos theory, genetic
algorithms and the rest may be applicable to the work-a-day financial research world
(as opposed to the academic one), I have a few ideas of my own, sure, but I'd like
you to also participate, using the definitions above, and your own understanding of:

where uncertainty, ambiguity, imprecision and partial truth exist,
  and have to be dealt within the world of "I make my living in the Market"?

where Soft Computing can make a contribution.


Here's one: rating of analystsWho do you believe, who do you trust,
    when the analysts' forecasts on earnings come out, and why?

And those forecasts themselves, it's always in terms of pennies.
No error bounds, no confidence intervals ... and the reports that back them up.

All *kinds* of places where uncertainty, imprecision, ambiguity and partial truth
have to have been dealt with.

But you don't *see* any of that, you just get "Based on past experience, we feel..."
and "Given their previous track record, our reading is...".

Okay, here's another: annual reports. Sure, lots of financial statements and
balance sheets and projections, but also lots of wriggle-room and opportunity to,
well, "misreport" might be too strong, but "overly optimistic" isn't too far off the
mark in many cases

... check out the Beneish paper on the Parker Center research working papers
website ( for a real eye-opener
on how to filter for earnings manipulation characteristics.

But notice, too, that while there are certain excellent *indicators*, there's almost
always room to doubt. And how do you deal with that doubt?

One last one: market activity by investor class, and its relationship to information
   quality and timeliness

By "investor class" I'm not talking about "individual" vs. "mutual fund" vs.
But rather "consistency of earnings" from "constant winner" to "constant loser".

If you believe the Efficient Market Hypothesis (and there's another one), then
everyone has access to the same information at the same time, really (;-) I don't think so. I'm not talking conspiracy here, I'm talking about:

- the HUGE amount of information available,

- the total inability to deal with it *all*,

- the subsequent need to know just *what* information to focus on, and from
  *which* source.

- the fact that all of that has to be tempered with explicit recognition of

So the basic question is:

"Do 'constant winners' have similar information-type and -source characteristics,
and do they subsequently deal with that information in similar ways?"

See also glossary definition + economic yin-yang & cursor


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