Behavioral finance FAQ / Glossary (Fuzzy)
This is a separate page of the F section of the Glossary.
Dates of related message(s) in the
Behavioral-Finance group (*):
Year/month, d: developed / discussed,
01/5i,10i - 02/1i,7i,11i -
03/5i ,10i - 05/1i,3i + see soft
computing, probability, extreme,
range estimate aversion, stereotype,
uncertainty, narrow thinking,
mental myopia + bfdef3 + fuzzy
Thinking neither in black nor in white,
but in a variable shade of grey.
In other words, really thinking.
If we oversimplify - something that fuzzy logic precisely tries to avoid ;-) -
Fuzzy logic considers that
Most statements are neither fully true nor fully false.
They have some - approximate and variable -
shade or "degree" of truth (or trueness):
a high / low / higher / lower possibility to be true
To take a financial example, an asset can be considered as:
* When addressing its
Ultra risky, rather risky,
rather safe, ultra safe.
* When addressing its
Ultra high, rather high,
rather low, ultra low
* When addressing its
Ultra cheap, rather cheap,
rather / ultra expensive.
In each case with some margin of trust, as nothing
can be fully certain and the "cursor" is not fully stable
Challenging, is it not?
Fuzzy logic is an alternative tool to probabilities,
as it addresses uncertainties,
while probabilities address measurable risks (see uncertainty, risk).
Some traits of FL:
Approximation, possibilities, imprecision, uncertainty,
=> No 0 nor 1, but a degree in between,
that crawls on a cursor.
FL is often called the theory of approximations and possibilities.
Something we use it half-consciously when moving our shower
handle (well, unless the thermostat does the job automatically) to
find an acceptable (approximatively optimum) temperature
between hot and cold, by testing intermediate positions such as
rather hot and rather cold, until reaching the quasi nirvana of
Rather, quasi, opproximate, acceptable, you get it ?
It applies to the - very frequent, practically universal -
situations that combine imprecision and uncertainty.
It is a non-Aristotelian / non-binary / approximate /
But what for?
An antidote to mental myopia.
Fuzzy logic takes into account that many realities are
not really clear-cut.
It considers that, not only many mental notions, but even many material
things (and even more, future prospects), are:
Not completely true or false, white or black,
known or unknown...
Not even fully consistent with their general
definition and categorization (see "stereotype /
Well, not a full discovery, everybody knows that ...to some degree!
But the preference for the feeling of comfort
brought by an illusion of certainty often overrides that
knowledge and distorts reasoning and decisions with
Exclusive / unbalanced / myopic / caricatural
representations and judgements
Therefore we have to be wary of:
* The pseudo-certainty of some - individual or collective -
beliefs or representations,
* Or the tempting, but error-prone, practicality of some
habits or heuristics / recipes.
So, in practice, what is it?
Fuzzy logic considers most statements, concepts, things,
categories ( ) as "approximately" ( )
X % true ( ) and (100 - X) % false.
Categories are here called "fuzzy sets"
Even opposite categories can in fact intertwine
in a "Yin-yang" way
And temporarily, depending on circumstances
X can be any number (multivalence) between 0 and
100 (or 1 and 99)
But to describe the degree of truth, fuzzy logic might
use soft criteria, instead of too precise numbers,
"low", "average", "high".
"ultra low", "ultra high".
In practice, does it freezes decisions?
Or does it make it more conscious?
Fuzzy reasoning is not a tool for indecision, far from it, it gives just a
courageous and conscious way to make decisions, accepting that
they are bets and thus admitting uncertainty.
Conscious, courageous, responsible and independent
choices accept uncertainty in their outcomes.
Why this flexible / non-binary
approach of realities?
Is the World so foggy?
Most philosophers who deride fuzzy logic still consider as the "true" (*)
logic the formal binary logic (BL) , which is based on
reductive postulates such as "one cause -one effect" or "things are
either true or false".
(*) the true / false syndrome at its best.
That formal binary screening / sorting method can be useful in a first
approach or for some clear-cut phenomena, as it avoids some confusion,
imprecision and fallacies (see that word).
But BL should not be venerated: it is a rather primitive, narrow and
simplistic form of thinking (see narrow thinking).
It can help (like most heuristics, see that word) as an hypothesis before
digging further as it tends to be disconnected from the realities of a
complex and highly changing world (see also dynamical systems).
Fuzzy logic on the other hand, does not renounce to the quest for
truth,on the contrary, but it sees it differently as it takes into account
that, as detailed below.
1) Complete void or fullness (or perfection) is
practically never seen in the real world, whether a
human society or the Universe,
2) Truth vs. falsehood is a moving target in a dynamical,
evolving, uncertain world,
3) Classifying things in clear-cut categories, stereotypes
(and definitive words), however practical, can be illusive.
4) There is rarely "one cause one effect" but a conjunction of
factors and events.
1) The fuzzy approach can give a better picture of the world
than the "true vs. false" binary / reductive logic (*).
(*) We see the same binary illusions in the fanatical / caricatural
political search for "purity", "integrity", "identity", or similar
human (or inhuman?) concepts.
Truth is located in some movable position of the
cursor / thermometer, let us say - fuzzily -
between 1% and 99% .
Whence the name "multi-value logic" given sometimes to
this approach, to differentiate it from black or white / yes or
no / true or false bivalence.
Also factors that oppose each others can also intermingle
and complement each other (see yin-yang asset valuation...).
For example a bitten apple is neither an apple nor a non-
apple, but it has some degree of "appleness".
A car with a breakdown is not exactly a car or a non-car, its
degree of "carness" depends on the importance of the
There is a tipping point, not too easy to decide, here binary logic
is at loss and hard criteria are arbitrary, when it becomes more a
clunker than a car.
Another thing is quantic mathematics that admit a superposition
of different cases. A quantic computer would use three logical
positions (0 - 1 - Others) instead of just 0 -1 in classical computer
2) To spot truth vs. falsehood is a moving target.
Have you truly seen the truth passing by?
In the real world, not only things and situations
are rarely fully clear-cut, but they also tend to
be uncertain and to vary with circumstances.
The world is made of evolutionary systems
(see dynamical system).
A stable equilibrium (see that word) is never fully reached.
We have unstable equilibriums.
3) Fuzzy logic avoids too clear-cut categories,
verging on stereotypes (see that word).
Hard to store square concepts in round cans.
It makes for a better understanding of categories of things or
concepts with fuzzy borders with other categories, and are thus
This acceptance of fuzzy categories moderates
the tendency to think in terms of generalization,
stereotypes and dogmas.
Beware for example of what is hidden behind everyday
Their definitions are usually less simple and more ambiguous than
they seem, and everybody makes its own representation of what
When buying strawberry jam, look at the prints to see if plenty of
other stuffs do not override strawberries!
Well, maybe that is the true meaning of "jam".
and difference with probabilities
Those too neat statistical frequencies might be misleading.
As the position of the cursor is not only imprecise but ever-changing, the
degree of trueness / truth and its consequences, for example in a market
pricing model, are hard to state.
In most case, the only way is to make a vague
(fuzzy), tentative, iterative (higher / lower),
or temporary estimate.
Some people confuse
fuzzy logic with probabilities ,
although the approach is different:
For fuzzy logic: approximations and graduations,
For probabilities: odds, usually taken from frequencies
shown in historical statistics.
Also, extreme events, which are too scarce for being seen in distribution
statistics, can be dealt which fuzzy logic (here there are no limits for the cursor).
The fact that fuzzy logic allows for iterative adaptation makes it somewhat
close to Bayesian probabilities (see that phrase), but it cannot be confused
with them as it is more ..."fuzzy", approximate.
What is it used for?
What about finance as a fuzzy playground?
Fuzzy logic is used in automatic regulating systems and in some decision
models that strive to obtain "artificial intelligence" or at least self-adaptation.
It can be also applied to finance, where some trading systems
use it. This is based on the facts that:
Financial markets are neither fully efficient nor
completely inefficient, but have a variable "degree
of efficiency" (see "efficient")
Economic and financial previsions cannot rely
fully on probabilities,
In those fields, the scenarios and their odds can only rest on
approximations, without an overreliance on past occurrences.
Probabilities deal with measurable risks and random laws, while
those fields of activities rest largely on non measurable
uncertainty. This is because:
Economics and finance rest on human /
social reactions, which are not fully predictable.
Some are persistent and reproducible, others can change or
differ completely even in situations that look alike.
They are not only multi-faced but also "dynamical systems"
with specific behaviors (bifurcation, chaos, percolation,
What is called "value" (see that word) is a fuzzy
concept, based on a cocktail of objective / subjective
criteria if not on pure preferences.
This is one of their differences with "price", which is a tangible
See Paul Victor Birke's contribution about the
See also above, under the fuzzy logic definition, how
the FL "cursor" can be included in financial reasoning
and models, in a way similar to Bayesian
probabilities (see that phrase), only even more
Fuzziness is helpful for asset valuations that deliver
value brackets, corresponding to
potential price evolutions, instead of just one
Here again we use a "multi-value" logic.
In this respect, fuzzy logic is an antidote to the
range estimate aversion (see that phrase).
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