Data processing: artificial intelligence – Fuzzy logic hardware – Fuzzy neural network
Reexamination Certificate
1999-08-03
2002-04-30
Grant, William (Department: 2121)
Data processing: artificial intelligence
Fuzzy logic hardware
Fuzzy neural network
C706S005000, C706S900000, C700S048000, C700S050000
Reexamination Certificate
active
06381591
ABSTRACT:
FIELD OF AND BACKGROUND OF THE INVENTION
The invention relates to new and useful improvements to the transformation of fuzzy logic, which is used to simulate a technical process, into a neural network.
In neuro-fuzzy systems, the input/output response of fuzzy systems can be optimized using neural networks. This makes it possible to compensate for the disadvantages of fuzzy systems and those of neural networks. One option for using a neural network to optimize a fuzzy system is to transform a fuzzy system into a neural network, which is then trained using input/output measured values. While the system response of the technical process that is to be simulated can be reflected in the fuzzy system, the transformation into a neural network allows additional optimization using input/output measured values from the technical process to be simulated. In this case, the optimization process can be automated using optimization algorithms, which can be executed by the neuro-fuzzy system using a computer.
Various methods are known for transforming the components of a fuzzy system into the structures of a neural network. In particular, a fuzzy system has fuzzy logic which, as a rule, is composed of the three components “fuzzification”, “control” and “defuzzification”. The three components can each be modeled using specific types of neurons. The fundamental design of a neuro-fuzzy system, i.e., the individual components of the fuzzy logic within a neuro-fuzzy network, is shown in FIG.
1
. When the fuzzy logic FS is being transformed into the neural network NN, the fuzzification F, control base R and defuzzification D components in the neural network NN are represented as a neural fuzzification network NF, a neural control base network NR and a neural defuzzification network ND.
As a result of linguistic rules in the fuzzy logic FS, the control base R component, in particular, results in a number of linguistic values being emitted to the defuzzification D component. The result of a linguistic rule is always a linguistic value. The linguistic values, which are preferably single-element functions, are then united in the defuzzification D component, by defuzzification, to form a single, “sharp” value.
By way of example,
FIG. 2
shows single-element functions F
1
, F
2
. . . Fm of the type which, as a rule, are first normalized with respect to a first maximum value MW
1
of magnitude 1. A singleton position A
1
, A
2
. . . Am and at least one singleton weighting factor R
1
, R
2
, R
3
. . . Rn−1 are respectively assigned to the single-element functions F
1
. . . Fm, which are also called “singletons”.
The singleton positions A
1
. . . Am represent, in particular, the result of rules contained in the control base R component of the fuzzy logic FS. This corresponds in particular to the “THEN” part of so-called linguistic “IF—THEN” rules, such as “IF pressure high, THEN explosion hazard high”. The singleton positions A
1
. . . Am may lie in any desired value range.
The singleton weighting factors R
1
. . . Rn correspond in particular to the weighting of the “THEN” part of a linguistic rule in the control base R component of the fuzzy logic FS. The singleton weighting factors R
1
. . . Rn are in this case used to weight the single-element functions F
1
. . . Fm, and one single-element function F
1
. . . Fm can also be assigned a number of singleton weighting factors R
1
. . . Rn. For example, the weighting factors of the rules “IF pressure high, THEN explosion hazard high” and “IF temperature high, THEN explosion hazard high” both relate to the same single-element function “explosion hazard” with the singleton position “high”. In the example in
FIG. 2
, the two singleton weighting factors R
1
and R
2
are assigned to the single-element function F
1
having the singleton position A
1
.
The singleton positions A
1
. . . Am (weighted with the singleton weighting factors R
1
. . . Rn) of the single-element functions F
1
. . . Fm are unified, to form a single value y, in the defuzzification D component of the fuzzy logic FS, by defuzzification. This is done, for example, using the so-called height method:
y
=
∑
υ
=
1
n
R
υ
·
A
(
υ
)
∑
υ
=
1
n
R
υ
=
y1
∑
υ
=
1
n
R
υ
By way of example,
FIG. 4
a
shows conventional modeling of the fuzzy logic FS in the neural network NN. An output signal y
1
is formed by addition, via a summing neuron S
1
, from the singleton positions A
1
. . . Am weighted with the singleton weighting factors R
1
. . . Rn. In this case, each weighting factor R
1
. . . Rn is assigned:
y
1
=(
R
1
·
A
1
)+(
R
2
·
A
1
)+(
R
3
·
A
2
)+ . . . +(
Rn·Am
)
for weighting the corresponding singleton position A
1
. . . Am. A disadvantage of this transformation method is that one singleton position A
1
. . . Am is in each case assigned to each singleton weighting factor R
1
. . . Rn for summing by the summing neuron S
1
. While there is one degree of freedom of m singleton positions A
1
. . . Am in the fuzzy logic FS, the neural network NN generally has many degrees of freedom n for the singleton weighting factors R
1
. . . Rn.
FIG. 4
b
shows how the singleton positions A
1
. . . Am of the weighting factors R
1
. . . Rn are optimized during the training of the neural network NN that is carried out following the transformation. In this case, the values of the individual singleton positions A
1
. . . Am are varied. In comparison with a number m of singleton positions A
1
. . . Am before optimization, this results in the number n>=m of optimized singleton positions B
1
. . . Bn after the optimization process. The optimized neural network NN thus generally has more degrees of freedom n than before the optimization in order to form the output signal y
1
′.
FIG. 5
shows the single-element functions F′
1
. . . F′n transformed back by reverse transformation of the neural network NN into an optimized fuzzy system FS. While the number of single-element functions F
1
. . . Fm was m before the transformation, the fuzzy system FS after reverse transformation disadvantageously now has n single-element functions F′
1
. . . F′n. As a rule, n>=m, which means that there are usually more single-element functions after reverse transformation than there were before the transformation.
It is disadvantageous that, for example, this may lead to such a neuro-fuzzy system no longer being feasible on standardized, conventionally available fuzzy system software after the optimization process, since such software allows only a specific maximum number of degrees of freedom, that is to say such software can process only a maximum number of singleton positions or single-element functions.
OBJECT OF THE INVENTION
It is therefore a first object of the invention to provide an improved method for transformation of fuzzy logic into a neural network. It is a further, specific object to provide such a method, in which the singleton positions (A
1
. . . Am) in the neural network (NN) can be adjusted, in order to optimize this network, such that their number before and after the optimization process remains constant and thus, in any case, subsequent reverse transformation of the neural network (NN) can be carried out to optimize fuzzy logic (FS). This advantageously allows the use of, in particular, standardized fuzzy system software to describe the optimized fuzzy logic (FS).
SUMMARY OF THE INVENTION
According to one formulation of the invention, these and other objects are achieved by a method for transforming fuzzy-logic, which is used to simulate a technical process, into a neural network in order to form a defuzzified output value from normalized single-element functions. This method includes:
assigning a singleton position and at least one singleton weighting factor to each of the normalized single-element functions, wherein each of the normalized single-element functi
Hoffmann Wolfgang
Schwulera Erik
Frank Elliot
Grant William
Siemens Aktiengesellschaft
Sughrue & Mion, PLLC
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