Fuzzy systems can represent complex knowledge and

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ent 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 (1-x)%. 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 (1-x)% 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 24 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" 25 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 10-50%. The sum of the membership values of the overlap are recommended to be less than one. 3. convert problem-specific knowledge into the fuzzy if-then 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 de-fuzzification 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 de-fuzzification approaches. T he speed and success of this fine-tuning 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 26 Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatron...
View Full Document

This document was uploaded on 03/12/2014 for the course MECHANICAL 214 at University of Manchester.

Ask a homework question - tutors are online