Fuzzy Logic. This amounts to the use of a characteristic function f for a set A, where f(a)=1 if the element belongs to A, otherwise it is 0;

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1 Fuzzy Logic Introduction: In Artificial Intelligence (AI) the ultimate goal is to create machines that think like humans. Human beings make decisions based on rules. Although, we may not be aware of it, all the decisions we make are all based on computer like if-then statements. If the weather is fine, then we may decide to go out. If the forecast stays the weather will be bad today, but fine tomorrow, then we make a decision not to go today, and postpone it till tomorrow. By abandoning the rigid idea of true or false, Lofti Zadeh, redefined how we think about logic. Constant researches lead to the invention of Fuzzy Logic. For instance, consider the given three statements Dinosaurs have ruled on this planet for a long time (for a million of years) It hasn t rained since a long time (for a couple of months) He waited for his turn for a long time (for a couple of hours) In these statements we cannot infer the true value of for a long time. There is no way to represent this concept in standard binary set theory. In a standard set theory an object is either a member of a set or it is not. Either the value for that object is true or false. There is no in-between. This amounts to the use of a characteristic function f for a set A, where f(a)=1 if the element belongs to A, otherwise it is 0; Definition: Fuzzy logic is a form of many valued logic, superset of Boolean logic that has been extended to handle the concept of partial truth- truth values between "completely true" and "completely false" to deal with reasoning. Consider a Universal set U of which a subset called fuzzy subset A(bar) is defined by function f. If f(x)=1 signify that x is completely contained in A(bar). If f(x)=0 signify that x is not a member of A(bar). Values of 0<f(x)<1 signify that x is a partial member of A(bar). To illustrate this let's talk about people and "youthness". In this case the set U (the universe of discourse) is the set of people. A fuzzy subset YOUNG is also defined, which answers the question "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 } A graph of this looks like: Given this definition, here are some example values: Person Age degree of youth

2 young(x) = { 1, if age(x) <= 20, (30-age(x))/10, if 20 < age(x) <= 30, 0, if age(x) > 30 } A graph of this looks like: Given this definition, here are some example values: Person Age degree of youth Johan Edwin Parthiban Arosha Chin Wei Rajkumar Operations: Union The membership function of the Union of two fuzzy sets A and B with membership functions and respectively is defined as the maximum of the two individual membership functions. This is called the maximum criterion.

3 The Union operation in Fuzzy set theory is the equivalent of the OR operation in Boolean algebra. Intersection The membership function of the Intersection of two fuzzy sets A and B with membership functions and respectively is defined as the minimum of the two individual membership functions. This is called the minimum criterion. The Intersection operation in Fuzzy set theory is the equivalent of the AND operation in Boolean algebra.

Complement The membership function of the Complement of a Fuzzy set A with membership function is defined as the negation of the specified membership function. This is caleed the negation criterion.

4 Complement The membership function of the Complement of a Fuzzy set A with membership function is defined as the negation of the specified membership function. This is caleed the negation criterion. The Complement operation in Fuzzy set theory is the equivalent of the NOT operation in Boolean algebra. The following rules which are common in classical set theory also apply to Fuzzy set theory. De Morgans law Associativity, Commutativity

5 Distributivity Dilation,Concentration & Normalization: Ref pg no 99 of Artificial Intelligence and Expert System by Dan W.Patterson Characteristics: In fuzzy logic, exact reasoning is viewed as a limiting case of approximate reasoning. In fuzzy logic everything is a matter of degree. Any logical system can be fuzzified In fuzzy logic, knowledge is interpreted as a collection of elastic or, equivalently, fuzzy constraint on a collection of variables Inference is viewed as a process of propagation of elastic constraints. Fuzzy Matching Algorithm: Ref pg no 204 of Artificial Intelligence and Expert System by Dan W.Patterson

Fuzzy Logic - A powerful new technology

Fuzzy Logic - A powerful new technology Proceedings of the 4 th National Conference; INDIACom-2010 Computing For Nation Development, February 25 26, 2010 Bharati Vidyapeeth s Institute of Computer Applications and Management, New Delhi Fuzzy