Question.3257 - Is fuzzy logic probability? Explain (Please state the references)
Answer Below:
Fuzzy Logic is a mathematical logic that helps in solving problem with the help of given data and input to arrive at the most accurate conclusion by assigning values to an imprecise spectrum of data. They are mainly used by advanced trading systems to easy handle the changing market policies. In other words we can say that Fuzzy logic is a problem solving control system which can work from simple, small, micro controller to large network and data base information and is suitable with all type of hardware, software , or a combination of both. It also helps in fast decisions making and derivate the definite conclusion with the help of given information. It nearly work as same as human do and reach the reasoning the human mind. It also does not need precise inputs to derivate its results. It can also work in the situation of incomplete data and missing inputs. It requires numerical parameters in order to operate. It can be a better method for sorting and handling data but is excellent choice for many control system as it works on the principle of human logic. It required some numerical data on the basis of which it helps in deriving the approximate value. It can be used by defining what is need to be controlled its criteria, relationship between input and output and variables. It works on membership functions which are graphical representation of each input involved in the case. Fuzzy Logic is based on Fuzzy set and generally uses IF- Then rule. For example: Inputs can be ? Condition of car’s engine is Good ? Condition of car’s engine is Average ? Condition of car’s engine is Bad Outputs can be: ? Fast ? Medium ? Slow Define the rule-base: 1. If the engine of car is good, then car will run fast. 2. If the engine of car is average, then car will run with medium speed. 3. If the engine of car is bad, then car will run slow. Fuzzy Logic is some about different from probability. Fuzzy logic use membership functions and how much variable is there in a fuzzy set while probability use how probable be variable in a set. But both are used to express uncertainty. References: 1. http://www.investopedia.com/terms/f/fuzzy-logic.asp 2. http://www.ieeesmc.org/announcements/Newsletter/JAN2003/Probability%20Theory%2 0and%20Fuzzy%20Logic.pdf 3. http://www.mathfuzzlog.org/index.php/Mathematical_Fuzzy_Logic 4. http://www.intelligent-systems.info/classes/ee509/8.pdf 5. http://arri.uta.edu/acs/ee5322/lectures/Ballal%20fuzzy%20logic%20notes.pdf Define and describes with example one of the fuzzy membership functions and one of the fuzzy characteristics? Fuzzy membership functions are one of the important issues to be taken into consideration while resolving any fuzzy set. Membership functions have only one restriction that it had to be in the range of 0 and 1. Therefore any fuzzy set can have infinite membership function. It provides measure of the degree of similarity of an element to a fuzzy set. Membership function can be according to the user’s choice and experience or it can be designed using machine or artificial method. It is a key issue to determine the right membership function because it fully describes the fuzzy set. (Where is the reference of this definition?) References: 1. http://dspace.library.cornell.edu/bitstream/1813/2804/16/05_chapter05.pdf 2. https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDMQFj AA&url=http%3A%2F%2Fwww.tech.dmu.ac.uk%2F~hseker%2FCSCI3406%25202008 09%2FWeek%2520- %25203%2520%2520CSCI%25203006%2520Lecture%25203and4.ppt&ei=edATUbHk O5HOrQeQh4DwBA&usg=AFQjCNFbwZ5Hkef2txviP9Ms_lyMN1eoJQ&sig2=uC_swye Yp_xbgfpOSQNXog Membership functions are of different shape: (Please state the reference) ? Triangular ? Trapezoidal ? Piecewise – linear ? Gaussian ? Bell shaped Triangular Membership function: µ A (x) 1 0 X A b c µ A (x) is a Fuzzy set in which a, b, c are representing three vertices of µ A (x) On X coordinate a and c shows membership degree to be zero and b the centre shows membership degree as 1. The value of µ A (x) is derived as 0 if x <= a x – a if a <=x<=b b – a c - x c – b if b <=x<=c 0 if x >= c Characteristics of Fuzzy logic: (Please give example for one of the following) (And please state also the reference) ? Knowledge is interpreted as collection of variable, elastic or equivalent. ? Fuzzification of any logical system. ? Everything is matter of degree ? Allows decision making with uncertain estimate or incomplete values. ? Suitable for uncertain or approximate reasoning. Explaining one of the characteristic: Everything is matter of degree When to find the degree of youthness for a person in a given universe of people, we have to answer a question that “to what degree is person x young?" To each person in the universe of discourse, we have to assign a degree of membership in the fuzzy subset YOUNG. The easiest way to do this is with a membership function based on the person's age. Young(x) = { 1, if age(x) <= 20, (30-age(x))/10, if 20 < age(x) <= 30, 0, if age(x) > 30 } Given this definition, here are some example values: Person Age degree of youth --------------------------------------------------------- A 10 1.00 B 21 0.90 C 25 0.50 D 26 0.40 E 28 0.20 F 83 0.00 So given this definition, we'd say that the degree of truth of the statement "C” is YOUNG" is 0.50. Reference: 1. http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/sbaa/report.fuzzysets.html Find any example of fuzzy logic as function approximator and the used in decision system?(Please state the references) Function approximator- Function Approximator is needed to solve the numerical as well as econometric problems. It becomes very convenient for any numerical problem to solve with the use of approximate functions. It helps in deriving the relationship between the input and output data and consider the applications like pattern, predictions, data mining, classification and recognition of attributes and variables. Fuzzy Logic as Function approximator – By using the fuzzy logic as function approximator we would be deriving the approximate value instead of certain value which we can get by using other functions. The result will not be 100% correct but would stand between completely accurate and completely in accurate. Example of fuzzy logic as function approximator – If bank has to grant loan he will look into the semantic variables along with mathematical variables. Bank will check the credit worthiness of the applicant by assessing his assets, buildings, property, land, income, etc. All these factors will be considered as input variables while designing the function using fuzzy logic. Some of the above mentioned variables are semantic while rests are numeric, so it would be difficult to assess the exact amount of loan which bank can grant to the applicant. But based on these factors, bank can calculate a range for the credit worthiness of the applicant and provide the loan according to that. Hence, fuzzy logic can help the bank in making these kinds of decisions. Fuzzy logic used in Decision making – (Please state the reference and please add one more paragraph) Decision making of grant of loan by bank: Fuzzy logic is used for calculation. The application consists of input variables, attributes, output variables and rule boxes. Input variable consist of asset, Income, property, building and land. Output variable is credit and rule box consist of credit, applicant and construction. Model is to be constructed. When the model is made, it is necessary to tuned it (to set up the inputs on known values, evaluate the results and to change the rules or weights, if necessary). If the system is tuned, it is possible to use it in practice. Decision could be easily made by the bank managers regarding the amount of the money whether it should be none, low, medium, high or full. Decisions can be taken by evaluating the input variables like if building, land is small then credit provided will be less. If the area of building and land is medium, then medium amount of loan will be granted. If area of building and land is large then high amount of loan will be granted. Reference: 1. http://econ.lse.ac.uk/staff/wdenhaan/numerical/functionapproximation.pdf 2. http://www.petrdostal.eu/papers/cla20.pdf 3. http://atc.ugr.es/I+D+i/revistas/2004/LNCS_2004_2972_0508.pdf 4. http://reference.wolfram.com/mathematica/tutorial/ApproximateFunctionsAndInterpolatio n.htmlMore Articles From Statistics
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