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Let us understand to fuzzy Family

Let us understand to fuzzy Family. Developed by Joseph Goguen. What is fuzzy sets. Definition . Operations . A={(x1,0.5),(x2,0.7),(x3,0)} B={(x1,0.8),(x2,0.2),(x3,1)} Union Intersection Complement Product of two fuzzy sets Equality Product of a fuzzy set with a crisp no.

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Let us understand to fuzzy Family

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  1. Let us understand to fuzzy Family Developed by Joseph Goguen

  2. What is fuzzy sets • Definition

  3. Operations • A={(x1,0.5),(x2,0.7),(x3,0)} • B={(x1,0.8),(x2,0.2),(x3,1)} Union Intersection Complement Product of two fuzzy sets Equality Product of a fuzzy set with a crisp no. Power of a fuzzy set Difference Disjunctive sum

  4. Properties • Commutativity • Associativity • Distributivity • Idempotence • Identity • Transitivity

  5. Fuzzy Reasoning • Many decision-making task are too complex to be understood quantitatively, however, humans succeed by using knowledge that is imprecise rather than precise. • Fuzzy logic resembles human reasoning in its use of imprecise information to generate decisions. • fuzzy logic incorporates an alternative way of thinking, which allows modeling complex systems using a higher level of abstraction originating from our knowledge and experience. • Fuzzy logic allows expressing this knowledge with subjective concepts such as very big and a long time which are mapped into exact numeric ranges. • Fuzzy logic provides an inference morphology that enables approximate human reasoning capabilities to be applied to knowledge-based systems

  6. Example of Inference rules • Every soldier is strong-willed . • All who are strong-willed and sincere will succeed in their career. • Indira is a soldier . • Indira is Sincere . • Solution: • For all x (soldier(x) -> strong-willed(x)) • For all x ((strong-willed(x) ^sincere(x)) -> succeed_career(x)) • Soldier(indira) • Sincere(indira)

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