WELCOME TO THE WORLD OF FUZZY SYSTEMS DEFINITION

WELCOME TO THE WORLD OF FUZZY SYSTEMS

DEFINITION • Fuzzy logic is a superset of conventional (Boolean) logic that has been extended to handle the concept of partial truth -- truth values between "completely true" and "completely false".

History 1965 The Foundation of the “Fuzzy Set Theory” 1970 First Application of Fuzzy Logic in Control Engineering (Europe) 2000 Fuzzy Logic Becomes a Standard Technology Application of Fuzzy Logic in Business and Finance.

DETERMINISTIC BEHAVIOUR OF FUZZY § Fuzzy system is totally deterministic. fuzzy logic is a logic OF fuzziness, not a logic which is ITSELF fuzzy …!

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

IMPORTANCE TO ENGINEERS • Engineers consists largely of recommending decisions based on insufficient information and even ignorance on the basis of subjective acceptance criteria. So fuzzy provides them ways for treating those uncertainties

CONCEPTUAL STUDY • CLASSICAL CONCEPT This concept is constraintful and has a limited applications in real world as it uses the basis of idealism. • FUZZY CONCEPT This is a more general typed concept and can deal nonlinear and ill-understood problems.

CLASSICAL CONCEPT • Boolean logic. • No partial memberships. • Sharp boundries of membership functions. • No uncertainties allowed.

FUZZY CONCEPT • Fuzzy logic. • Partial membership is allowed. • Membership function varies in the range [0, 1]. • Smooth boundries.

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.

PROBABILITY • POSSIBILITY

• HOW TO SOLVE A PROBLEM USING FUZZY LOGIC ? We need to follow a 4 step process to solve a problem using fuzzy logic. Before that let us discuss important terms associated.

TERMS REGARDING FUZZY CONCEPT • Membership functions • Linguistic variables • Fuzzy rules

MEMBERSHIP FUNCTIONS These are the functions that maps objects in a domain of concern to their membership value in the set.

A membership function usually takes shape as shown below : TRIANGULAR TRAPEZOIDAL

LINGUISTIC VARIABLES A Linguistic variable is like a composition of symbolic variable and a numeric variable. EXAMPLE: Temprature is High. In the above sentence TEMPRATURE is linguistic variable.

FUZZY RULES These are the rules which are the core of the logic and so are made by the experts of the respective areas. These have the form: • IF<antecedent> THEN<consequent> EXAMPLE: IF the annual income is high THEN the person is rich

STEPS OF FUZZY LOGIC • • Fuzzification Inferences Composition Defuzzification

FUZZIFICATION • Under FUZZIFICATION, the membership functions defined on the input variables are applied to their actual values, to determine the degree of truth for each rule premise.

INFERENCES • Under INFERENCE, the truth value for the premise of each rule is computed, and applied to the conclusion part of each rule.

COMPOSITION • Under COMPOSITION, all of the fuzzy subsets assigned to each output variable are combined together to form a single fuzzy subset for each output variable.

DEFUZZIFICATION • Finally is the (optional) DEFUZZIFICATION, which is used when it is useful to convert the fuzzy output set to a crisp number.

APPLICATIONS • Applied in different fields of computer science by different names. • e. g. Fuzzy control , Fuzzy arithmetic artificial intelligence expert systems etc. • Fuzzy neural networks theory • Fuzzy pattern recognizer. • About 1100 Successful Fuzzy Logic Applications

CONCLUSION !

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