Fuzzy logic is an appropriate way to map an input space into an output space, with the methodology of solving problems with thousands of applications stored in the controlling and information processing. Fuzzy Logic provides a simple way to describe certain conclusions from the information ambiguous, vague - vague, or inappropriate. In a sense, fuzzy logic resembles human decision making with the ability to work from the interpreted data and finding the right solution.
Fuzzy logic is basically a much valued logic (multivalued logic) that can define the value of conventional circumstances, such as yes or no, right or wrong, black or white, and so forth. Fuzzy reasoning provides a way to understand the performance of the system by assessing the input and output system from the observations.
* History of Fuzzy Logic
In conventional logic truth value must have a condition that is true or false (true or false), with no conditions in between. This principle was put forward by Aristotle some 2000 years ago as a law of excluded Middle and legal logic has dominated the thinking until recently. But, of course thinking about the conventional logic with a definite truth value that is right or wrong in real life is not perfect. Fuzzy logic (fuzzy logic) is a logic that can represent the situation existing in the real world.
On the set of fuzzy logic theory was first proposed by Prof.. Lofti Zadeh around the year 1965 in a paper entitled "Fuzzy Sets'. He argues that the logic of right and wrong from boolean logic / conventional can not resolve problems in the real world. After that, since the mid-1970s, Japanese researchers have succeeded in applying this theory to practical problems. Unlike Boolean logic, fuzzy logic has a continuous value. Samar expressed in degrees of membership and a degree of truth. Therefore, something can be said to partly right and partly wrong at the same time. Set theory an individual can have a degree of membership with continuous values, not just 0 and 1 (Zadeh, 1965 in Asta, D.,: 2002).
With fuzzy logic set theory, we can represent and handle the problems to no certainty that in this case could mean doubt, inappropriate, inadequate information, and the truth which is partly (Altrock: 1997). In the real world, we often face a problem that information is very difficult to translate into a formula or numbers are accurate because the information is qualitative (can not be measured quantitatively).
* Reason Using Fuzzy Logic
A variety of reasons many people using fuzzy logic:
* The concept of fuzzy logic is easily understood. The underlying mathematical concept of fuzzy reasoning is very simple and easily understood.
* Fuzzy Logic is very flexible.
* Fuzzy Logic has a tolerance of data that is not appropriate.
* Fuzzy logic can model nonlinear functions are very complex.
* Fuzzy Logic can build and apply the experiences of experts directly without having to go through the training process.
* To be working with fuzzy logic techniques in the conventional control.
* Fuzzy logic is based on natural language.
* The set of fuzzy
Fuzzy sets: a group representing a condition under certain circumstances in a fuzzy variable
have two possibilities, namely:
* • One (1), which means that an item becomes a member in a set, or
* • Zero (0), which means that an item does not become a member in a set
*
* The set of fuzzy has two attributes:
* Linguistics, which is naming a group representing a particular state or condition by using natural language, such as: YOUNG, PAROBAYA, TUA
* Numerical, that is a value (number) that shows the size of a variable such as: 40, 25, 35
* Fuzzy Inference System
Fuzzy Inference System (Fuzzy Inference System / FIS) is also called fuzzy inference engine is a system that can perform reasoning with principles similar to humans do reasoning with her instincts.
There are several types of FIS which is a known Mamdani, Sugeno and Tsukamoto. FIS is the most easily understood, because most suited to the human instinct is the Mamdani FIS. FIS is working based on linguistic rules and has a fuzzy algorithm that provides an approximation to enter mathematical analysis.
Processes in the FIS is shown on the input provided to the FIS is a certain number and the output must also be a certain number. The rules in the language of linguistics can be used as an input that is accurate must be converted first, then perform reasoning based on rules and reasoning to convert these results into output that is accurate.
Our group will discuss the Fuzzy Inference System using Mamdani method.
* Mamdani Method
In this model, fuzzy rules are defined as:
IF x1 is A1 AND ... .. AND xn is An THEN y is B
where: A1, ... .., An, and B are linguistic values (or fuzzy sets) and "x1 is A1" states that the variable x1 is a member of the fuzzy sets A1.
Mamdani method is often known by the name of Max-Min method. This method was introduced by Ebrahim Mamdani in 1975.Untuk get the output required four stages:
* Establishment of fuzzy set
In the Mamdani method, both input and output variables are divided into one or more fuzzy.
* Application of the implication function
In the Mamdani method, the implication function used is the Min.
* Composition rules
Unlike monotonic reasoning, if the system consists of several rules, the inference obtained from the collection and correlation between the rules. There are three methods used in performing fuzzy inference systems, namely:
* Method Max (Maximum)
In this method, the solution fuzzy set is obtained by taking the maximum value of the rule, then use it to modify the fuzzy areas, and applying it to the output by using the OR operator (union). If all propositions have been evaluated, the output will contain a fuzzy set that reflected the contribution of each proposition. Generally it can be written as follows:
msf [xi] = max (msf [xi], mkf [xi]) with:
msf [xi] = membership value of fuzzy solution to the i-th rule
mkf [ix] = value of the consequences of fuzzy membership to the i-th rule
* Additive Method (sum)
In this method, the solution fuzzy set is obtained by means of bounded-sum of all output fuzzy region.
Generally written:
msf [ix] = min (1, msf [xi] + mkf [xi]) with:
msf [xi] = membership value of fuzzy solution to the i-th rule
mkf [ix] = value consequent fuzzy membership to the i-th rule
* Method Probalistik OR (probor)
In this method, the solution fuzzy set is obtained by doing the product of all output fuzzy region. Generally written:
msf [xi] = (msf [xi] + mkf [xi]) - (msf [xi] * mkf [xi]) with:
msf [xi] = membership value of fuzzy solution to the i-th rule
mkf [ix] = value consequent fuzzy membership to the i-th rule
* The assertion (defuzzy)
Input from defuzzy process is a fuzzy set obtained from the composition atuan fuzzy rules, while the output is a fuzzy set of numbers in it. So if given a fuzzy set in a certain range, it must be taken a certain crisp value as output.
Fuzzy
The most popular technique is the centroid technique. This method to find center of gravity (COG) of the aggregate set:
Centre of gravity (COG): finding a solution to the point that divides the area into two equal parts
Defuzzy is a mechanism to convert or change the results of the fuzzy output into a coherent output nonfuzzy. Output in the form of fuzzy results can not be directly used. In theory, fuzzy logic, there are several methods used defuzzy, namely:
* Center of Gravity
In this method, the crisp output is obtained by taking a regional center that covered the fuzzy membership function (z ') or can be written with the equation:
Center of gravity method surplus assertion lies in the results an acceptable reason (intutive plausibility), while the drawbacks lies in the intensive computational requirements.
* Center of Average
In this method, the crisp output is obtained by taking a weighted average of the center w of n fuzzy sets. Crisp output can be mathematically defined by:
Assertion method of average or centroid center is the most widely used method in fuzzy systems and fuzzy control. In computing, this method is easier and more sensible.
* Bisector
In this method, the crisp output is obtained by taking the value on the domain which has a fuzzy membership value of half of the total value of membership in the fuzzy area or can be written:
zp
* MOM (Mean of Maximum)
In this meode, crisp output is obtained by taking the average value of B domain which has a maximum value kenggotaan. Crisp output can be mathematically defined by:
* LOM (Largest of Maximum)
In this meode, crisp output is obtained by taking the largest value of B domain which has a maximum value kenggotaan. Crisp output can be mathematically defined by:
* SOM (Smallest of Maximum)
In this method, the crisp output is obtained by taking the smallest value of B domain which has a maximum value kenggotaan. Crisp output can be mathematically defined by:
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