Title: Fuzzy logic system with evolutionary variables rules
Abstract: The fuzzy logic system of the present invention creates fuzzy rules in real-time and updates the fuzzy rules dynamically. This is accomplished by continually optimizing the features, qualifiers, cases, and operators of the fuzzy rules. The fuzzy logic system may be utilized in applications requiring constantly-updated fuzzy rules and also in applications where fuzzy rules are difficult to pre-define due to a large quantity of input data, such as, for example, stock market forecasting.
Patent Number: 6,853,991 Issued on 02/08/2005 to Kermani
| Inventors:
|
Kermani; Bahram Ghaffarzadeh (Whitehall, PA)
|
| Assignee:
|
Agere Systems Inc. (Allentown, PA)
|
| Appl. No.:
|
427802 |
| Filed:
|
October 27, 1999 |
| Current U.S. Class: |
706/52; 13/3 |
| Intern'l Class: |
G06F 009//44; G06N 007//02; G06N 007//06 |
| Field of Search: |
706/52,13,3
|
References Cited [Referenced By]
U.S. Patent Documents
| 4875184 | Oct., 1989 | Yamakawa | 706/3.
|
| 5193144 | Mar., 1993 | Tsutsumi et al. | 706/60.
|
| 5335314 | Aug., 1994 | Tsutsumi et al. | 706/1.
|
| 5604842 | Feb., 1997 | Nishidai | 706/52.
|
| 5727130 | Mar., 1998 | Hung | 382/155.
|
| 6324529 | Nov., 2001 | Kamihira et al. | 706/13.
|
Other References
N. K. Chidambaran et al; Adapting Black-Scholes to a Non-Black-Scholes
Environment Via Genetic Programming; 1998; IEEE; 98.sup.TH 8367; 197-211.*
G. B. Sheble; Market Based Operation and Planning Simulation and Analysis;
1999; IEEE; INSPEC 6282787; 6/1-6/15.*
"Prognosis with MS Excel," http://www.fuzzytech.com/e_ft4bs2.htm.
"Fuzzy Application Library/Business and Finance
Applications/Knowledge-BasedPrognosis,"
http://www.fuzzytech.com/e/e_ft4bb7.html.
"Other Business Applications," http://www.fuzzytech.com/e_ft4bb8.htm.
"Introduction to Genetic Algorithms," pp. 3-5,
http://www.kneehighs.com/intro.html.
"What is Fuzzy Logic?,"
http://www.emsl.pnl.gov:2080/proj/neuron/fuzzy/what.html.
James F. Brule, "Fuzzy Systems--A Tutorial,"
http://www.austinlinks.com/Fuzzy/tutorial.html.
"Fuzzy InferenceSystems," pp. 2-19 to 2-27.
Jerry M. Mendel, "Fuzzy Logic Systems and Qualitative Knowledge,"Part III:
Articles, pp. 410-413.
David L. Carroll, "A Genetic What?," in: What is a Genetic Algorithm?,
http://www.diemme.it/.about.luigi/ga.html.
Steven D. Kaehler, "Fuzzy Logic--An Introduction," Part 1,
http://www.seattlerobotics.org/encoder/mar98/fuz/fl_part1.html.
Steven D. Kaehler, "Fuzzy Logic--An Introduction," Part 2,
http://www.seattlerobotics.org/encoder/mar98/fuz/fl_part2.html.
Steven D. Kaehler, "Fuzzy Logic--An Introduction," Part 3
http://www.seattlerobotics.org/encoder/mar98/fuz/fl_part3.html.
Steven D. Kaehler, "Fuzzy Logic--An Introduction," Part 4,
http://www.seattlerobotics.org/encoder/mar98/fuz/fl_part4.html.
Steven D. Kaehler, "Fuzzy Logic--An Introduction," Part 5,
http://www.seattlerobotics.org/encoder/mar98/fuz/fl_part5.html.
Steven D. Kaehler, "Fuzzy Logic--An Introduction," Part 6,
http://www.seattlerobotics.org/encoder/mar98/fuz/fl_part6.html.
"Example Illustrations,"
http://www.seattlerobotics.org/encoder/mar98/fuz/flcases.html.
Alexander Schatten, "Genetic
Algorithms,"http://qspr03.tuwein.ac.at/.about.aschatt/info/ga/genetic.
html.
Bahram Ghaffarzadeh Kermani, "Using Neural Networks and Genetic Algorithms
to Enhance Performance in an Electronic Nose," IEEE Transactions on
Biomedical Engineering, vol. 46, No. 4, Apr. 1999.
Karr et al., "Computer Modelling of Mineral Processing Equipment Using
Fuzzy Mathematics," Minerals Engineering, V. 9, No. 2, p. 183-194 (Feb.
1996).
|
Primary Examiner: Knight; Anthony
Assistant Examiner: Hirl; Joseph P.
Claims
I claim:
1. A method for deriving an optimized rule set for a fuzzy logic system,
said method comprising the steps of:
generating a pool of random rules having a fitness function and storing
said random rules;
evolving said random rules using a genetic algorithm to improve the fitness
function of said rules in said random rule set until the overall fitness
function of said rules plateaus, thereby generating an optimized rule; and
storing said optimized rule in an optimized rule storage area, said rules
stored in said optimized rule storage area comprising said optimized rule
set.
2. A method as set forth in claim 1, wherein said generating step includes
the steps of:
checking said optimized rule storage area to determine if it contains any
optimized rules; and
using any optimized rules contained in said optimized rule storage area
when generating said pool of random rules.
3. A method is set forth in claim 1, wherein said evolving step comprises
evolving the features of said random rules.
4. A method is set forth in claim 1, wherein said evolving step comprises
evolving the qualifiers of said random rules.
5. A method is set forth in claim 1, wherein said evolving step comprises
evolving the operators of said random rules.
6. A method is set forth in claim 1, wherein said evolving step comprises
evolving the features, cases, qualifiers, and operators of said random
rules.
7. A method as set forth in claim 1, wherein said generating, evolving, and
storing steps are repeated until a predetermined number of optimized rules
are stored as said optimized rule set.
8. A method as set forth in claim 7, wherein said repeating of said steps
occurs on a real-time basis.
9. At method for deriving an optimized rule set for a fuzzy logic system
for use in stock market analysis, said method comprising the steps of:
generating a pool of random rules having a fitness function and storing
said random rule;
evolving said random rules using a genetic algorithm to improve the fitness
function of said rules in said random rule set until the overall fitness
function of said rules plateaus, thereby generating an optimized rule;
storing said optimized rule in an optimized rule storage area, said rules
stored in said optimized rule storage area comprising said optimized rule
set;
applying a stock market data set to said optimized rule set; and
outputting a stock market analysis result based on the application of said
stock market data set to said optimized rule set.
10. A method is set forth in claim 9, wherein said evolving step comprises
evolving the features of said random rules.
11. A method is set forth in claim 9, wherein said evolving step comprises
evolving the qualifiers of said random rules.
12. A method is set forth in claim 9, wherein said evolving step comprises
evolving the operators of said random rules.
13. A method is set forth in claim 9, wherein said evolving step comprises
evolving the features, cases, qualifiers, and operators of said random
rules.
14. A method as set forth in claim 9, wherein said generating, evolving,
and storing steps are repeated until a predetermined number of optimized
rules are stored as said optimized rule set.
15. A method as set forth in claim 14, wherein said repeating of said steps
occurs on a real-time basis.
16. A method as set forth in claim 9, wherein said stock market data set
comprises data regarding a particular stock choice.
17. A method as set forth in claim 9, wherein said stock market data set
comprises data regarding a particular stock market.
18. A method as set forth in claim 9, wherein said stock market data set
comprises data regarding comprising a particular segment of stocks.
19. A method as set forth in claim 9, wherein said stock market data set
comprises data regarding comprising mutual funds.
20. A method as set forth in claim 9, wherein said stock market data set
comprises data regarding comprising futures.
Description
FIELD OF THE INVENTION
The present invention generally relates to fuzzy logic systems for
conducting a fuzzy inference. In particular, the invention relates to a
fuzzy reasoning process and the generation of fuzzy rules using a genetic
algorithm which are utilized by the fuzzy logic systems in applications
requiring frequent updating, such as stock market forecasting.
BACKGROUND OF THE INVENTION
The concept of "fuzzy theory" was introduced by Lofti Zadeh in the 1960's
to allow imprecise decision-making and problem-solving tasks, such as
medical diagnosis, to be understood quantitatively. Fuzzy theory is
specifically designed to mathematically represent uncertainty and
vagueness and provide formalized tools for dealing with the imprecision
intrinsic to many problems. Unlike traditional computing which relies on
precision, fuzzy theory resembles human reasoning in its use of
approximate information and uncertainty to generate a decision.
Fuzzy theory implements classes or groups of data with boundaries that are
not sharply defined (i.e. they are fuzzy). Any methodology or theory
implementing "crisp" (precise) definitions such as classical set theory,
arithmetic and programming may be "fuzzified" by generalizing the concept
of a "crisp set" to a "fuzzy set" with blurred boundaries. For example, if
it is assumed that a vehicle made in the United States is a "domestic"
vehicle and a vehicle made elsewhere is a "foreign" vehicle, and if it is
assumed that the set "U" is the set of all automobiles in Los Angeles, and
it is desired to classify specific cars within the set "U" as being
foreign or domestic, using crisp-set theory, this could be accomplished by
simply examining the brand name (e.g. rules are set defining a Toyota as
"foreign" and a Ford as "domestic") of each automobile in the set "U".
However, consider a situation where a Toyota is manufactured in the United
States using some parts made in Japan and others made in the United
States. In fuzzy theory a rule could be set to define the percentage of
parts for a specific car made in United States and to assign a degree of
similarity to what is perceived to be a domestic or foreign car. For
example, if 25% of the car parts for a Ford are made in the United States
then the car could be considered similar to a domestic car to the degree
of 0.25 and similar to a foreign car to degree of 0.75. In such a case,
the fuzzy system could conclude, assuming the existence of appropriate
rules, that the car is "foreign". Thus, in fuzzy theory an element can
reside with degrees of similarity.
Fuzzy theory utilizes linguistic variables whose values are not necessarily
numbers, but could also be words and sentences. These linguistic variables
are often characterized by membership functions. A membership function
provides a measure of the degree of similarity (degree of membership) and
the grade of the membership function is typically expressed by numerical
values in the region of 0.0 to 1.0, and varies within this range.
Fuzzy logic systems encompassing principles of fuzzy theory emerged into
the mainstream of information technology in the late 1980's and early
1990's. Currently most of the prior art fuzzy logic systems use
pre-defined fuzzy rules. The fuzzy rules may be provided by experts in the
field of use of the fuzzy logic system (e.g., by physicians for a medical
diagnosis system) or they may be extracted from numerical data. In either
case, the fuzzy rules allow the fuzzy logic systems to handle approximate
information in a systematic way.
Fuzzy logic systems are helpful for controlling nonlinear systems and
modeling complex systems where an inexact (ambiguous or vague) model
exists. Today, fuzzy logic systems are found in a variety of control
applications including chemical process control, manufacturing, and
consumer products such as washing machines, video cameras, and
automobiles. Typical examples of prior art fuzzy logic systems are
described in U.S. Pat. No. 4,875,184 (Yamakawa); U.S. Pat. No. 5,193,144
(Tsutsumi et al.); U.S. Pat. No. 5,335,314 (Tsutsumi et al.); and U.S.
Pat. No. 5,604,842 (Nishidi), all of which are incorporated herein by
reference.
A traditional fuzzy logic system typically consists of a rule based
membership function, and an inference procedure. The predetermined rules
of the system are represented in a linguistic format e.g. "If x is A and
(y is B and z is not C), then w is D."
Here the "IF" is referred to as an "antecedent" and the "THEN" is referred
to as a "consequent". x, y, and z are input variables of the antecedent,
and A, B, and C are membership functions thereof. w is a variable of the
consequent and D is a membership function thereof. Typically, the
membership functions, such as A, B, C, and D, are items of vague
linguistic information such as "positive", "negative", "large", "medium",
or "small".
FIG. 6 depicts a typical prior art fuzzy logic system 10 that is widely
used in control and signal processing applications. It contains four
components: a fuzzy memory 20, a fuzzifier 30, a fuzzy inference engine 40
connected to the fuzzifier 30, and a defuzzifier 50 connected to the fuzzy
inference engine 40.
The rules for the typical fuzzy logic system 10 are pre-defined and stored
in the fuzzy memory 20. These rules are expressed as a collection of
IF-THEN statements.
The fuzzifier 30 receives crisp inputs and generates a fuzzy input set. The
inference engine 40 receives the fuzzy input set from the fuzzifier 30 and
combines the fuzzy input set to the fuzzy rules received from the fuzzy
memory 20. It then performs a fuzzy inference in accordance with the
predefined rules and outputs a fuzzy output set to the defuzzifier 50. The
defuzzifier 50 in turn generates an output comprising crisp numbers.
Thus, in a conventional fuzzy logic system, the membership functions and
the fuzzy operators are the only variables that can change. The fuzzy
rules are predefined, and once defined they are typically not changed
because the time required to recalculate and change the rules is
prohibitive. As such, it is not practical to use conventional fuzzy logic
systems in applications in which fuzzy rules need to be frequently
changed, such as in stock market forecasting, because of the tremendous
time delays required in calculating and changing the fuzzy rules.
In general, a fuzzy logic rule includes the following variables: Features
(e.g., temperature and sky's condition); cases (e.g. cold, hot, cloudy,
sunny); operators (e.g., AND, OR, NOT); outputs (e.g. chance of rain); and
qualifiers (e.g., high, low, somewhat, medium, very, slightly, none).
Thus, for example, using the above examples in a weather prediction
program, a rule might read: IF the temperature is hot AND the sky is very
cloudy, then the chance of rain is somewhat high."
It is known to utilize a genetic algorithm (GA) for deriving the membership
functions and/or rules for a fuzzy logic system. See, for example, U.S.
Pat. No. 5,727,130 to Hung, incorporated herein by reference. Prior art
methods evolve the output and cases of fuzzy rules using GA's, but do not
evolve or modify variables such as features, qualifiers, and operators,
i.e., the features, qualifiers and operators of the prior art are
considered as fixed values and not variable once they are selected at the
beginning. Thus, it would be desirable to have a fuzzy logic system which
is not limited by pre-defined fuzzy rules and which has the capability to
automatically create and evolve fuzzy rules, features qualifiers, and
operators in real-time for use in, for example, stock market forecasting.
SUMMARY OF THE INVENTION
According to the present invention, the features, qualifiers, and operators
of rules, and the rules themselves, are continually generated and evolved
using genetic algorithms, based on real-time data. This invention is
especially useful in stock market forecasting and, in particular,
day-trading wherein the pertinent data may change many times over a short
period of time.
The method of the present invention is as follows: first, a random set of
rules (a population of chromosomes) is generated using a random selection
from each of the categories of operators, features, cases, and qualifiers.
Next, the population of chromosomes are evolved to improve their fitness
function in a known manner. The fitness function is a cost function that
penalizes the algorithm if it renders non-compliant results, i.e., results
that do not logically follow the trend of the input data. This evolution,
which involves computing the fitness function, is done using fuzzy logic.
The computation of the fitness function is accomplished by the fuzzy logic
process in a known manner. For example, the fitness function can be
computed by applying the fuzzy rules to the input data, e.g., data
corresponding to stock market activity.
Once the fitness function plateaus for the population (i.e., ceases to
improve) the resultant rule (a chromosome) is stored, e.g., in a bin,
thereby creating a storage location or "binning pool" in which "optimized"
rules are accumulated. The chromosomes then go through further generation
(initialization) and evolution to improve their overall fitness function.
This process is repeated until adding more chromosomes to the optimized
rule pool does not improve the overall fitness of the pool. At this point
the algorithm may be stopped and the best chromosomes then define the
rules of the system. For example, if it is presumed that a optimized
chromosome pool population can contain 15 chromosomes, then once 16
chromosomes have been established, an evaluation is made and the 15
fittest chromosomes are kept while the worst of the 16 is deleted.
Thus, the fuzzy logic system of the present invention creates fuzzy rules
in real-time and updates the fuzzy rules dynamically. This is accomplished
by continually optimizing the features, qualifiers, cases, and operators
of the fuzzy rules. The fuzzy logic system may be utilized in applications
requiring constantly-updated fuzzy rules and also in applications where
fuzzy rules are difficult to pre-define due to a large quantity of input
data, such as, for example, stock market forecasting.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram illustrating various components of the fuzzy
logic system of the present invention;
FIG. 2 is a flow chart illustrating the various steps involved in the
implementation of the present invention;
FIG. 3 is a graph showing the points of intersection of specific values for
an exemplary feature D.sub.1 ;
FIG. 4 is a graph showing the points of intersection of specific values for
an exemplary feature D.sub.2 ;
FIG. 5 is a graph showing the results of the application of two exemplary
rules on the exemplary features of FIGS. 4 and 5; and
FIG. 6 is a block diagram of an exemplary prior art fuzzy logic system.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
FIG. 1 is a block diagram illustrating various components of an exemplary
embodiment of the fuzzy logic system of the present invention.
A fuzzy logic system 100 constructed in accordance with the present
invention comprises a fuzzy processor 115, a fuzzifier 130, a fuzzy
inference engine 140 connected to the fuzzifier 130, a defuzzier 150
connected to the fuzzy inference engine 140, and a fuzzy memory 120
connected to the fuzzy inference engine 140. Connected to fuzzy processor
115 is a genetic algorithm processor 160. The genetic algorithm processor
160 stores and executes genetic algorithms 165 and has a direct link to
the fuzzy memory 120 which stores the fuzzy rules. The fuzzy inference
engine 140 is directly connected to the processor 160.
The fuzzifier 130 receives crisp inputs from a database and generates a
fuzzy input set to the fuzzy inference engine 140. For example, the
database might contain historical daily stock data for the entire market
or certain market segments, and might span a period of months or years.
The fuzzy inference engine 140 receives the fuzzy input set from the
fuzzifier 130 and retrieves the fuzzy rule(s) stored in the fuzzy memory
120. The first time the system is operated the fuzzy memory 120 only
contains one default set of rules. The fuzzy inference engine 140 then
generates a fuzzy output set by using the default rules and conventional
inference procedures. The fuzzy inference engine 140 then provides the
fuzzy input set, the fuzzy output set and the default rule(s) to the
genetic algorithm processor 160.
The genetic algorithm processor 160 utilizes GAs to create a first new
fuzzy rule set and provides this first new fuzzy rule set to the fuzzy
memory 120 for storage. As GAs evolve the rule to create a near-optimal
fitness in a given environment, the fuzzy rules generated by the genetic
algorithm processor 160 improve with each iteration.
The fuzzy inference engine 140 receives the first new fuzzy rule set
generated by the genetic algorithm processor 160 and applies this first
new fuzzy rule set to the internal logic of the fuzzy inference engine
140. The fuzzy inference engine then generates a new output to the
defuzzifier 150 by applying the database information to the fuzzy input
set. It then compares the output to the expected output (based on the
database information) of the fuzzy output set and determines a fitness
function.
The fitness function is a pre-defined parameter measuring an error
component between a desired output stored in the database and the actual
output (of the fuzzy output set). In an exemplary case, it might be
related to a Euclidian Distance. The fuzzy inference engine 140 then
forwards the fitness function value to the genetic algorithm processor
160. The genetic algorithm processor 160 uses the fitness function and
then creates another set of fuzzy rules which is based on the fitness
function value and the previously supplied rules. It then provides another
new fuzzy rule set (termed a "better rule") to the fuzzy inference engine
140.
The fuzzy inference engine 140 takes the better rules and applies them to
its internal logic engine to create another output. It then compares this
output to the expected output as calculated from the data in the database
and computes a new fitness function. It also compares the new fitness
function value to the old fitness function value from the previous
computations. If there is an improvement from the old fitness function
value to the new fitness function value, the new fitness function value is
forwarded back to the processors running GAs to develop an even better
fuzzy rule.
The above iterations continue until the accumulated fitness function value
of the population has approached a constant (no improvement is seen or the
fitness function value is highest, e.g. error=0). This implies that the
processor running the GAs cannot provide better rules for that population,
indicating that either a good fuzzy rule having a low error value has been
created or that the actual error has been reduced to zero. This process is
repeated by evolving new generations, using the previously selected rules
of the bin and the newly generated random rules.
The fuzzy inference engine 140 receives the good fuzzy rule from the
genetic algorithm processor 160 and utilizes it to create an actual fuzzy
output set which is then forwarded to the defuzzifier 150. The defuzzifier
150 receives the actual fuzzy output set and generates a crisp output
which is available for use by a plurality of applications.
FIG. 2 is a flow chart illustrating the various steps involved in the
implementation of the present invention.
The fuzzy inference engine 140 defines a random default rule set at step
201. The default rule set is stored in the fuzzy memory 120 and is a
generic rule set comprising some of the possible combinations and
sub-combinations of features, operators, cases, etc.
In step 203, the fuzzifier 130 receives the crisp inputs and in step 205 it
generates a fuzzy input set. In step 207, the fuzzifier 130 forwards the
fuzzy input set to the fuzzy inference engine 140.
In step 209, the fuzzy inference engine 140 generates a fuzzy output set
based on the random default rule set (defined in step 201) if it is the
first iteration, and based on the accumulation of random and previously
binned rules for subsequent iterations.
Next, in step 211, the fuzzy inference engine 140 compares the fuzzy output
set to the "predicted" output of the fuzzy output set. The predicted
output is calculated in a known manner based on historical data stored in
the database. Based on this comparison, the fuzzy inference engine 140
computes a fitness function for use by the GA in step 213. The fitness
function is a pre-determined parameter and may be a well known error
computation variable. In an exemplary case, this fitness function may be
the inverse of a Euclidean Distance.
Once the fitness function has been computed, at step 215 the GA of the
genetic algorithm processor 160 creates a new fuzzy rule (better rule)
based on the new fitness function new fuzzy input set, and new output set.
This new fuzzy rule has a lower error (i.e., better/higher fitness
function) component than the prior rules. The fuzzy inference engine 140
receives this new fuzzy rule in step 217 and then, at step 219, the new
fuzzy rule was analyzed to determined if the new rule can be improved. If
it is determined that the new rule can be improved for that population,
then the process returns to set 209 wherein the newly created rule is
utilized with the default rule set and the steps 209 through 225 are
repeated.
If it is determined that the fitness function cannot be further improved,
implying that fitness function has either reached a plateau (e.g., becomes
substantially constant) or is highest (i.e., the error is zero), then the
best performing rule (the new rule) is selected and stored at step 221.
This fuzzy rule may not be the optimal rule, as the GAs only can compute
the best rule available in a given fuzzy input set and in a given fuzzy
output set and the optimal rule may be difficult to determine.
Once the best rule has been evolved from the default rule set this best
performing rule is stored (e.g., in a bin) at step 221, and then, in step
223 a determination is made as to whether or not a threshold number of
rules stored in the bin has been reached. For example, if there needed to
be at least 15 rules stored in the bin before a presumption can be made
that the best rules are available for use, and it is determined that 15
rules have been stored, then the process can proceed directly to step 227,
at which point the process is stopped.
If, on the other hand, a determination is made that less than 15 rules
havebeend stored, then at step 225 a check is made to if the overall
fitness function of the rules stored in the bin has plateued. If it has
plateued, then the process can proceed to step 227 at which point it is
stopped.
If on the other hand, a determination is made that the overall fitness
function of the rules in the bin has not plateaued (and that the threshold
number of rules in the bin has not been reached), the process returns to
step 207 and the rules for the optimal rule set stored in the bin are
combined with the newly generated random rules, to make a new population
for a new evolutionary process.
When fuzzifier 130 receives a new set of crisp inputs, it creates a new
fuzzy input set and a new fuzzy output set which are forwarded to the
fuzzy inference engine 140.
Assume for a specific example involving stock market prediction the
following set of variables: M=Market Capital; P=Price to Earning Ratio
(P/E); V=(Yesterday's Volume)/(Average of the Last 20 Days Volume);
D.sub.1 =Normalized Stock Price Change of Today -1 (Yesterday); D.sub.2
=Normalized Stock Price Change of Today -2 (day before yesterday);
D3=Normalized Stock Price Change of Today -3; D4=Normalized Stock Price
Change of Today -4, D5=Normalized Stock Price Change of Today -5;
D7=Normalized Change in the Average Stock Price of the Current Week
Compared to the Average Stock Price of Last Week; D30=Normalized Change in
the Average Stock Price of the Current Month Compared to the Average Stock
Price of the Previous Month; T=Today's Predicted Change.
Assume that the features M, P, and V use fuzzy membership functions with
the following possible qualifiers: NA=Not Applicable; S=Small, M=Medium
and L=Large. Assume further that the features D.sub.1, D.sub.2, D.sub.3,
D.sub.4, D.sub.5, D.sub.7, D.sub.30, and output features T can have the
following possible membership functions (combination of cases and
qualifiers): PL=Positive Large (representing a predicted large rise in
today's price); PM=Positive Medium (representing a predicted medium rise
in today's price); PS=Positive Small (representing a predicted small rise
in today's price); ZE=Zero (representing no change in day's price);
NS=negative small (representing a predicted small fall in today's price);
NM=negative medium (representing a predicted medium fall on today's
price); NL=negative large (presenting a predicted large fall in today's
price); and NA=not applicable. One way to arrange the above parameters
into a genetic algorithm chromosome is to code them into "binary genes".
Assume for the variables M, P, and V that the fuzzy membership functions
are described as follows: NA=00; S=01; M=10; and L=11. Assume further that
for variables D.sub.1, D.sub.2, D.sub.3, D.sub.4, D.sub.5, D.sub.7,
D.sub.30 and T the fuzzy membership functions are described as follows:
PL=111; PM=110; PS=101; ZE=100; NS=001; NM=010; NL=001; and NA=000.
All of the above variables can be organized into a chromosome as follows
(read top to bottom then left to right):
M P V D.sub.1 D.sub.2 D.sub.3 D.sub.4 D.sub.5 D.sub.7
D.sub.30 T
01 11 01 011 100 100 100 100 100 100 100
For example, if the following is assumed: Market M is small; Price to
Earning Ratio P is large; Normalized Volume V is small; Yesterday's
Normalized Stock Price Change D1 had a small drop (e.g., a negative small)
and that the stock values had not changed on the day before yesterday or
any of the prior 30 days. Finally, assume that, based on historical data,
it can be predicted that today's price T will fall by a small amount. The
chromosome for this scenario using the above described binary genes would
appear as follows:
MSB: M (upper bit) D4 (upper bit)
M (lower bit) D4 (middle bit)
P (upper bit) D4 (lower bit)
P (lower bit) D5 (upper bit)
V (upper bit) D5 (middle bit)
V (lower bit) D5 (lower bit)
D1 (upper bit) D7 (upper bit)
D1 (middle bit) D7 (middle bit)
D1 (lower bit) D7 (lower bit)
D2 (upper bit) D30 (upper bit)
D2 (middle bit) D30 (middle bit)
D2 (lower bit) D30 (lower bit)
D3 (upper bit) T (upper bit)
D3 (middle bit) T (middle bit)
D3 (lower bit) LSB:T (lower bit)
M P V D.sub.1 D.sub.2 D.sub.5 D.sub.4 D.sub.5 D.sub.7
D.sub.30 T
00 00 00 111 100 001 001 001 001 001 111
The above chromosome is interpreted as follows: regardless of the value of
market capital M, price/earning ratio P, and normalized volume V (e.g.,
each of these values has a binary gene "00" identifying it as "not
applicable") if yesterday's stock value D.sub.1 shows a positive change,
while the stocks had no change the day before yesterday (D.sub.2), and the
stock has been monotonically decreasing for the past four days, past week,
and past month, then today's value T of the stock will rise by a large
amount. Other random chromosomes are created for other possible outcomes
and their accuracy for prediction can be checked against historical data
as well.
A primary reason for utilizing the present invention in the stock market is
that stock market prediction may require many different rules to properly,
thoroughly and accurately make a prediction. Since an accordance with the
present invention the rules are generated "on the fly" instead of being
pre-selected, there is no practical limit on the number of rules that can
be used. Thus, for example, while the above discussion gives examples of
features based on days or weeks (e.g., D.sub.1 and D.sub.7), the features
can be based on any time frame, e.g., minutes, seconds, years, etc.
FIGS. 3 through 5 illustrate a simplified example of the present invention
used in connection with stock market forecasting. For the purpose of this
example, it is presumed that the following rules have been evolved:
Rule 1: If D.sub.1 is PL and D.sub.2 is NL, then T is PL
Rule 2: If D.sub.1 is PS and D.sub.2 is NL, then T is PS
As shown in FIG. 3 in this example a "positive small" PS is deemed to be
any value between 0 and 0.75 and a "positive large" PL value is deemed to
be any value from 0.5 to 1. It is understood that the ranges from 0 to 1
and 0 to -1 along the X axis are normalized values representing the values
that D.sub.1 can take. Further, a "negative small" NS is deemed to be any
value between 0 and -0.75, and a "negative large" NL is deemed to be any
value from -0.5 to -1.
It is further assumed for this example that the input value for D.sub.1
(correspondence to the actual rise or fall value for yesterday's market)
is 0.65, and the input value D.sub.2 (corresponding to the actual rise or
fall of the market two days prior to the current date) is -0.85.
As shown in FIG. 3, when D1 is 0.65 this value intersects both the PS curve
at 0.3 and the PL curve at 0.8 along the Y axis. The ranges from 0 to 1
along the Y axis represent normalized values that the membership function
of D.sub.1 can take. This indicates that the value for D1 is a fuzzy value
which can be considered either a positive small or a positive large. As
shown in FIG. 4, when D.sub.2 is -0.85, it intersects only the NL curve.
This indicates, among other things, that the value for D.sub.2 is a crisp
value. Thus, for the input values of D1=0.65 and D.sub.2 =-0.85, the
following "sets" exist:
Set 1: D.sub.1 is PL and D.sub.2 is NL;
Set 2: D.sub.1 is PS and D.sub.2 is NL.
Since, as noted above, we know that the rules include Rules 1 and 2 which
correspond to these values (e.g., Rule 1 gives us a solution "T is PL"
when D.sub.1 is PL and D.sub.2 is NL; Rule 2 give us the result "T is PS"
when D.sub.1 is PS and D.sub.2 is NL) then we can apply each of these two
rules to Sets 1 and 2.
When a rule contains an AND operation, one method of applying the rule is
by calculating the MIN for the two variables D.sub.1 and D.sub.2 in the
equation. Thus, for Rule 1 the following equation applies:
T=PL.vertline..sub.MIN(0.8, 1) ; thus, T=PL.vertline..sub.0.8
Thus the result for Rule 1 is that T is 0.8 on the positive large curve.
The same operation is applied to Rule 2 using the following equation:
T=PS.vertline..sub.MIN(0.3, 1) ; thus, T=PS.vertline..sub.0.3
The result is that T is 0.3 along the PS curve.
FIG. 5 shows the result of the application of the two rules. As shown in
FIG. 5, the PL and PS curves of FIG. 3 have been reduced to reflect the
application of Rules 1 and 2 to the input values, so that the PL curve is
"cut off" at 0.8, defining a trapezoidal area 1, and the PS curve is cut
off at 0.3, defining a second trapezoid defined by area 2. By taking the
centroid of these two trapezoids, the projection for today's market can be
achieved taking into consideration the fuzzy values associated with the
input D.sub.1. The centroid can be calculated by adding the area of
trapezoids 1 and 2 and dividing them by the length L corresponding to the
total span of the bases of the two trapezoids. For example, if we assume
that area 1 equals 0.402 and area 2 equals 0.235, and that length L equals
1, then the projection for today's market T equals 0.637.
While there has been described herein the principles of the invention, it
is to be understood by those skilled in the art that this description is
made only by way of example and not as a limitation to the scope of the
invention. Accordingly, it is intended by the appended claims, to cover
all modifications of the invention which fall within the true spirit and
scope of the invention.
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