Fuzzy set and its application
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This document discusses fuzzy systems and their applications. It introduces fuzzy logic as an extension of Boolean logic that allows for partial set memberships and uncertainties. It provides examples of fuzzy systems in washing machines, vacuum cleaners, rice cookers, and cars. Fuzzy logic is used in washing machines to adjust operations based on sensor readings. Vacuum cleaners use fuzzy logic to control motor speed based on distance sensors. Rice cookers employ neuro-fuzzy systems for precise heat adjustment. Cars can use fuzzy logic for automatic transmissions to shift gears like an experienced human driver.
![CLASSICAL CONCEPT
Boolean logic.
No partial memberships.
Sharp boundaries of membership functions.
No uncertainties allowed.
FUZZY CONCEPT
Fuzzy logic.
Partial membership is allowed.
Membership function varies in the range [0,1].
Smooth boundries.](https://image.slidesharecdn.com/fuzzysetanditsapplication-200217163157/85/Fuzzy-set-and-its-application-4-320.jpg)
Fuzzy set and its application
- 1. FUZZY SYSTEMS AND ITS APPLICATIONS By Dr. R. Kalaivanan
- 2. INTRODCUTION Fuzzy logic is an extension of Boolean logic by Lotfi Zadeh in 1965 based on the mathematical theory of fuzzy sets. Fuzzy logic is a generalization of the classical set theory. Fuzzy logic provides a valuable flexibility for uncertainty and reasoning. Fuzzy logic is essential to the development of human-like capabilities.
- 3. HISTORY Cantor (CRISP SETS): Set Theory at the end of 19th century. Sanders Pierce : Uncertainty theory. Jan Lukasiewicz : Many- valued logic. Max Black : Proto – fuzzy sets. Lotfi.A. Zadeh : Fuzzy logic.
- 4. CLASSICAL CONCEPT Boolean logic. No partial memberships. Sharp boundaries of membership functions. No uncertainties allowed. FUZZY CONCEPT Fuzzy logic. Partial membership is allowed. Membership function varies in the range [0,1]. Smooth boundries.
- 5. FUZZY SET
- 6. FUZZY RULES A Fuzzy rule can be defined as a conditional statement in the form: IF 𝑥 is A THEN y is B Where 𝑥 and y are linguistic variables; and A and B are linguistic values determined by fuzzy sets on the universe of discourses X and Y, respectively. FUZZIFICATION Input variables are converted to the fuzzy set. To determine the degree of truth for each rule premise. DEFUZZIFICATION Output variables are converted the fuzzy set to a crisp set.
- 7. POSSIBILITY VS PROBABILITY Possibility is a measure of degree of ease for a variable to take a value, while probability measures likelihood for a variable to take a value. EXAMPLE If we are talking about height of say a person: Probability view The height is between 5 and 6 feet. Possibility view The person is somewhat tall.
- 8. IMPORTANCE OF FUZZY It overcomes the limitations of conventional mathematical tools. Ease of describing human knowledge involving vague concepts. Cost Effective solution to real world problems.
- 9. APPLICATIONS WASHING MACHINE Fuzzy logic is actually a mathematical concept. It is a mathematical system that is capable of analyzing analog input values and converting them into logical variables. Put in simple terms, Fuzzy logic, in the case of a washing machine, employs sensors to judge varying conditions inside the machine and adjusts its operation accordingly.
- 10. WASHING MACHINE(CONTD) The sensors in the washing machine that will control the entire washing process, performing operations according to varying water intake, wash time, rinse performance, and spin speed.
- 11. VACUUM CLEANER Fuzzy logic controlled motor of vacuum cleaner. The vacuum cleaner controller has one input and one output system. The input is a distance which is two set of infrared sensors are used to detect the range of the dust, and the output is the speed of the motor to suck the dust.
- 12. VACUUM CLEANER(CONTD) For the embedded fuzzy logic controller, the behavior must be approximately encoded for the target processor, and then downloaded to the chip for execution. Once start the operation, the vacuum cleaner will start to suck dust and attempts to adjust the speed by comparing the distance. The fuzzy logic algorithm and PIC controller are use to control the operation of the vacuum cleaner.
- 13. RICE COOKER Neuro-Fuzzy Heat Adjuster Fine-tuned heat adjustment Three sensors help the Neuro-Fuzzy make the precise choice. Sensitive to the exact quantity and your tastes, you get tasty, fluffy rice every time, just the way you like it.
- 14. CARS Automatic gear shift (Fuzzy logic) Consider how a conventional auto-shift car can react when you ease off the throttle on a steep downhill. Its likely to misread the cars gathering momentum as a call for a higher gear so it changes up. And you lose engine-braking effect just when you may need it most.
- 15. CARS(CONTD) Mitsubishi galant’s ‘fuzzy logic’ auto shift puts an end to all that. It reacts as would an experienced driver controlling a manual shift not hunting up and down the gears at every variation in terrain and driving tempo, but instead holding on to the most appropriate gear which exhances your control of the car.