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complex knowledge and even knowledge from contradictory sources.
Fuzzy logic deals with situations when we have just one item which partly belongs to one class
and partly to another.
Fuzzy logic can also deal with situations when we think an item belongs to one class with
confidence x% and to another class with confidence (1x)%.
Probability theory assumes that objects are homogeneous, but if we could have had many
replicas of them, x% of them would be of one type and (1x)% of the other. It assumes therefore
that there is an underlying random process that determines the type of object we get. The slope of a field is considered "gentle" if it is between 0 and 20%, it is considered "average"
if it is between 20% and 40%
and it is considered "steep" if it is more than 40%.
We say that the slope S of a field may belong to one of three classes:
Class "gentle" if it is measured to be : 0 % ≤ S ≤ 20% Class "average" if it is measured to be : 20% < S ≤ 40%
Class "steep" if it is measured to be : 40% < S
So, the term "belongs to" is `hard'. It means either yes or no. If the slope of a field is measured
to be 19%, it is classified as "gentle". However, instinctively we understand that such a slope is
almost "average". The "class system" above does not allow us to express this `almost' we feel
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Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department about a 19% slope!
Fuzzy logic says that there are various degrees of "belonging" to a class, according to the
measurement value. Fuzzy logic uses some functions, called membership functions, that take as
input the measurement and produce as output a number that expresses by how much something
belongs to a class:
membership function of class A (measurement of field F) = how much field F belongs to class A Commonly used membership functions look like this: For the case of slope we can define the following membership functions: where:
mG: membership to class "gentle"
mA: membership to class "average"
mS: membership to class "steep"
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Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department If a field has slope 19%, we can use this figure to conclude that it belongs to class "gentle" with
membership 0.55 and to class "average" with membership 0.45. This agrees with
our instinctive understanding that a slope of 19% is neither only "gentle" nor just "average".
“If a field has slope that belongs to class "gentle" and its rock belongs to class "permeable "
and the depth of its soil belongs to class "shallow", this field belongs to class "low" with
respect to its risk to soil erosion." Fuzzy system design (from Sonka)
1. design functional and operational characteristics of the system determine the system
inputs, basic processing approaches, and system outputs. In object recognition, the inputs
are patterns and the output represents the decision.
2. Define fuzzy sets by decomposing each input and output variable of the fuzzy system into
a set of fuzzy membership functions. The number of fuzzy membership functions
associated with each variable depends on the task at hand. Typically, an odd number of
three to nine fuzzy membership functions is created fro each variable. It is recommended
that the neighboring fuzzy membership functions overlap by 1050%. The sum of the
membership values of the overlap are recommended to be less than one.
3. convert problemspecific knowledge into the fuzzy ifthen rules that represent a fuzzy
associative memory. For N variables each of which is divided into M fuzzy membership
functions, MN rules are required to cover all possible input combinations.
4. perform fuzzy composition and defuzzification
5. using a training set, determine the system’s performance. If the fuzzy system’s behavior
does not meet the requirements, modify the fuzzy set descriptions and/or fuzzy rules
and/or the fuzzy composition and/or defuzzification approaches. T he speed and success
of this finetuning step depend on the problem complexity, the designer’s level of
understanding of the problem, and the level of the designer’s experience. Summary:
Object Recognition, pattern recognition.
Pattern recognition is used for region and object classification and represents an
important building block of complex machine vision processes
No recognition is possible without knowledge. Specific knowledge about both the
objects being processes and hierarchically higher and more general knowledge about
classes is required.
Knowledge representation
• Description and features
• Grammars and languages
• Predicate logic
• Production rules
• Fuzzy logic
• Semantic nets
• Frames, scripts
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Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatron...
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This document was uploaded on 03/12/2014 for the course MECHANICAL 214 at University of Manchester.
 Spring '14
 Mechatronics

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