Introduce Fuzziness Fuzzy logic extends Boolean logic to handle the expression of vague concepts. To express imprecision quantitatively,a set membership function maps elements to real values between zero and one (inclusive).The value indicates the degree to which an element belongs to a set. A fuzzy logic representation for the "hotness"of a room,would assign100 F a membership value of one and25°F a membership value of zero.75°F would have a membership value between zero and one
Introduce Fuzziness ⚫ Fuzzy logic extends Boolean logic to handle the expression of vague concepts. ⚫ To express imprecision quantitatively, a set membership function maps elements to real values between zero and one (inclusive). The value indicates the “degree” to which an element belongs to a set. ⚫ A fuzzy logic representation for the “hotness” of a room, would assign100°F a membership value of one and 25°F a membership value of zero. 75°F would have a membership value between zero and one
Bivalence and Fuzz 10
Bivalence and Fuzz
Being Fuzzy For fuzzy systems,truth values (fuzzy logic)or membership values (fuzzy sets)are in the range [0.0,1.0],with 0.0 representing absolute falseness and 1.0 representing absolute truth. For example, "Dan is balding. If Dan's hair count is 0.3 times the average hair count,we might assign the statement the truth value of 0.8.The statement could be translated into set terminology as: "Dan is a member of the set of balding people." This statement would be rendered symbolically with fuzzy sets as: mBALDING(Dan)=0.8 where m is the membership function,operating on the fuzzy set of balding people and returns a value between 0.0 and 1.0
Being Fuzzy ⚫ For fuzzy systems, truth values (fuzzy logic) or membership values (fuzzy sets) are in the range [0.0, 1.0], with 0.0 representing absolute falseness and 1.0 representing absolute truth. ⚫ For example, "Dan is balding." If Dan's hair count is 0.3 times the average hair count, we might assign the statement the truth value of 0.8. The statement could be translated into set terminology as: "Dan is a member of the set of balding people." This statement would be rendered symbolically with fuzzy sets as: mBALDING(Dan) = 0.8 where m is the membership function, operating on the fuzzy set of balding people and returns a value between 0.0 and 1.0
Fuzzy Is Not Probability Fuzzy systems and probability operate over the same numeric range. The probabilistic approach yields the natural- language statement,"There is an 80%chance that Dan is balding.The fuzzy terminology corresponds to Dan's degree of membership within the set of balding people is 0.80
Fuzzy Is Not Probability ⚫ Fuzzy systems and probability operate over the same numeric range. ⚫ The probabilistic approach yields the naturallanguage statement, “There is an 80% chance that Dan is balding.” The fuzzy terminology corresponds to “Dan's degree of membership within the set of balding people is 0.80
Fuzzy Is Not Probability The probability view assumes that Dan is or is not balding (the Law of the Excluded Middle) and that we only have an 80%chance of knowing which set he is in. Fuzzy supposes that Dan is“more or lessi” balding,corresponding to the value of 0.80. Confidence factors also assume that Dan is or is not balding.The confidence factor simply indicates how confident,how sure,one is that he is in one or the other group
Fuzzy Is Not Probability ⚫ The probability view assumes that Dan is or is not balding (the Law of the Excluded Middle) and that we only have an 80% chance of knowing which set he is in. ⚫ Fuzzy supposes that Dan is “more or less” balding, corresponding to the value of 0.80. ⚫ Confidence factors also assume that Dan is or is not balding. The confidence factor simply indicates how confident, how sure, one is that he is in one or the other group