Data processing: artificial intelligence – Fuzzy logic hardware – Defuzzification processing
Reexamination Certificate
2001-02-23
2004-01-06
Davis, George B. (Department: 2121)
Data processing: artificial intelligence
Fuzzy logic hardware
Defuzzification processing
C706S004000
Reexamination Certificate
active
06675154
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to the areas of quantum mechanics, quantum computation and fuzzy logic. In particular, the present invention provides a method and system for fuzzy representation of information using quantum mechanics, allowing fuzzy logic operations and fuzzy control operations to be performed via quantum mechanics.
BACKGROUND INFORMATION
Fuzzy logic is a way of representing and processing information that generalizes ordinary Boolean logic to include a continuous range of propositional values. Applications of classical-mechanically implemented fuzzy logic have ranged from fuzzy logical models of chemical systems to fuzzy control of very large mechanical devices, such as power stations, and distributed systems, such as subways.
Fuzzy information is distinct from digital, binary information in that it is generally represented using the entire range [0,1] of the real numbers, rather than using a binary set of integers such as the set of its endpoints {0,1}.
Fuzziness is usually associated with uncertainty about the nature or state of an object or event. However, fuzziness is distinct from probabilistic uncertainty, though the two are not dissimilar in some respects; for example, they both represent information using the entire numerical range [0,1]. Probability is generally defined as a measure of the frequency with which a random variable takes values inside a specified region in the relevant parameter space, the region representing a “crisp set.” A crisp set is one in which a single event is attributed either of the Boolean values, 0 or 1. For example, in an ideal coin toss, there is a probability associated with the result of the coin landing heads-up. The outcome of a coin toss is either one in which the coin is located in a region of parameter space where the upper side of the coin is “heads,” 1 for heads, or not, in which case it must be “tails,” 0 for heads. By contrast, with fuzziness the uncertainty of a single event is described by its “degree of membership” in a region of parameter space, this region representing a “fuzzy set.”
For example, the characteristic of age lends itself to fuzzy representation. An evaluation of a person in middle age with regard to “oldness” reveals that a middle-age person is to some extent old, and to some extent young. A person is of increasing “oldness” with increasing age. For example, a 40-year-old man might have an “old” value of 0.4 and “young” value of 0.6 while a 60-year old might have an “old” value of 0.6 and a “young” value of 0.4. Thus, in the first example, the 40-year old man has a fuzzy membership degree of 0.4 in the fuzzy set “old” and a fuzzy membership degree of 0.6 in the fuzzy set “young.” Similarly, in the second example, the 60-year old man has a fuzzy membership degree of 0.6 in the fuzzy set “old” and a fuzzy membership degree of 0.4 in the fuzzy set “young.” In general, a fuzzy set associates with each object or event a value from the entire interval [0,1], instead of only the set {0,1} as in the case of a crisp set. This value is not taken to represent a frequency, as in the case of a probability. Rather, it is a description of the degree to which the object or event is attributed the property in question.
Fuzzy control is the use of fuzzy information to exert control over an object. A fuzzy rule-set or knowledge base, rather than a traditional modeling algorithm, is used to exert fuzzy control. The “knowledge base” is a set of prescribed (or learned) fuzzy rules that first quantifies input data (the “fuzzification” stage), carries out inferences (the fuzzy matching stage), and produces a control output (the “defuzzification” stage), which is used by an actuator to perform a resulting control action. Devices for carrying out fuzzy control are referred to as “fuzzy logic controllers.”
In certain contexts, fuzzy control operates more efficiently than standard control because it does not require: i) the exact solution of the mathematical problem arising from a crisp characterization of the system under control, or ii) highly precise sensing of the system's state.
The processing of fuzzy information and control operations are traditionally implemented using a computing device such as a general purpose digital computer. Typically, the computing device is equipped with a central processing unit, memory storage, an input/output mechanism and appropriate software to carry out the fuzzy representation and/or control.
FIG. 1
a
, which is prior art, illustrates a process effected by a fuzzy control system. As shown in
FIG. 1
a
,
102
input received from control object
105
is fuzzified in block
110
. Processing block
120
processes fuzzified information, which is then defuzzified at block
130
to generate control output
140
. Control output
140
is then used to control control object
105
. Note that fuzzify block
110
, process block
120
and defuzzify block
130
are typically combined in a single device such as a general purpose digital computer system.
FIG. 1
b
, which is prior art, illustrates a block diagram of a fuzzy logic control system. Fuzzy logic controller
150
includes processor
160
, crisp control actuator
165
and crisp input sensor
170
. Fuzzy logic controller
150
is coupled to control object
105
via crisp control actuator
165
and crisp input sensor
170
. Crisp input sensor
170
receives input data from control object
105
and transmits this input data to processor
160
, which may be, for example, a general-purpose digital computer. Processor
160
performs fuzzy logic processing using input provided by crisp input sensor
170
. In particular, processor
160
performs fuzzification, fuzzy logic processing and defuzzification (i.e., blocks
110
,
120
and
130
in
FIG. 1
a
) as a function of input provided by crisp input sensor
170
. Output generated by processor
160
is used to control actuator
165
, which in turn controls control object
105
.
FIG. 1
c
, which is prior art, illustrates a fuzzy control pair. In fuzzy control operations, membership functions corresponding to fuzzy logic propositions form fuzzy control pairs, i.e. fuzzy logic patches or fuzzy rules, known as the “fuzzy rule set.” The first proposition of the fuzzy pair (
114
a
-
114
d
) is applied to an input, while the second of the fuzzy pair (
117
a
-
117
d
) is applied to generate an output, which is then utilized for control of a system.
Known methods and systems for performing fuzzy logic operations and fuzzy control such as those depicted in
FIG. 1
c
rely upon conventional/classical computing devices and present inherent limitations for efficient realization of fuzzy logic and control at defuzzification. In particular, typically classical computing architectures are non-parallel, which limits the speed and efficiency in performing fuzzy logic operations. Although significant research has been directed at parallel computing devices, implementing classical fuzzy logic on them still involves a non-negligible number of traditional logical operations.
In recent years, significant research has been directed toward realization of quantum computing devices, which promise significantly greater computational efficiency than conventional classical mechanical digital devices using serial or parallel architectures. Quantum computing is the use of quantum mechanical systems to represent and process information, suggested by Feynman in 1982. Since then, it has been a subject of increasingly active research. The central technology of quantum computing is the quantum computer, a qualitatively novel information processing device.
Aside from the dramatic potential increases in computational efficiency promised by quantum computing devices, the consideration of quantum effects in computation is also necessitated by Moore's Law. Moore's Law describes the rate of miniaturization of information processing systems, such as microchips and predicts an inevitable reduction of the size of a digital computer's functional element
Davis George B.
MagiQ Technologies, Inc.
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