Fuzzy sets are an extension of the classical set theory used in fuzzy logic. A fuzzy set is characterized by a ''membership function (mathematics)'', which maps the members of the universe (mathematics) into the unit interval [0,1]. The value 0 means that the member is not included in the given set, 1 describes a fully included member (this behaviour corresponds to the indicator function of classical sets). The values between 0 and 1 characterize fuzzy members. For the universe ''X'' and given the membership-degree function ''f'' : ''X''→[0,1], the fuzzy set ''A'' is defined as ''A'' = {(''x'', ''f''(''x'')) | x ∈ ''X''}. The fuzzy set ''B'', where ''B'' = {(3,0.3), (4,0.7), (5,1), (6,0.4)} would be enumerated as ''B'' = {0.3/3, 0.7/4, 1/5, 0.4/6} using standard fuzzy notation. Note that any value with a membership grade of zero does not appear in the expression of the set. The standard notation for finding the membership grade of the fuzzy set ''B'' at 6 is μ''B''(6) = 0.4. == See also == * Defuzzification * Fuzzy logic * fuzzy set operations * Rough set ==External links== [http://pami.uwaterloo.ca/tizhoosh/set.htm Fuzzy Image Processing] Fuzzy logic Set theory
''Fuzzy sets are an extension of the classical set theory used in fuzzy logic.'' They are intended to be, but they are not! Membership functions are just that - functions. Functions are defined in terms of sets. So the definition of a fuzzy set depends on (and therefore is not an extension of) the definition of a set. User:BlaiseFEgan 21:53, 28 Apr 2005 (UTC)
See other meanings of words starting from letter:
Words begining with Fuzzy_set:
Fuzzy_set
Fuzzy_set
Fuzzy_sets
Fuzzy_set_Operations
Fuzzy_set_operations
Fuzzy set
Fuzzy sets are an extension of the classical set theory used in fuzzy logic. A fuzzy set is characterized by a ''membership function (mathematics)'', which maps the members of the universe (mathematics) into the unit interval [0,1]. The value 0 means that the member is not included in the given set, 1 describes a fully included member (this behaviour corresponds to the indicator function of classical sets). The values between 0 and 1 characterize fuzzy members. For the universe ''X'' and given the membership-degree function ''f'' : ''X''→[0,1], the fuzzy set ''A'' is defined as ''A'' = {(''x'', ''f''(''x'')) | x ∈ ''X''}. The fuzzy set ''B'', where ''B'' = {(3,0.3), (4,0.7), (5,1), (6,0.4)} would be enumerated as ''B'' = {0.3/3, 0.7/4, 1/5, 0.4/6} using standard fuzzy notation. Note that any value with a membership grade of zero does not appear in the expression of the set. The standard notation for finding the membership grade of the fuzzy set ''B'' at 6 is μ''B''(6) = 0.4. == See also == * Defuzzification * Fuzzy logic * fuzzy set operations * Rough set ==External links== [http://pami.uwaterloo.ca/tizhoosh/set.htm Fuzzy Image Processing] Fuzzy logic Set theory
Fuzzy set
''Fuzzy sets are an extension of the classical set theory used in fuzzy logic.'' They are intended to be, but they are not! Membership functions are just that - functions. Functions are defined in terms of sets. So the definition of a fuzzy set depends on (and therefore is not an extension of) the definition of a set. User:BlaiseFEgan 21:53, 28 Apr 2005 (UTC)
See other meanings of words starting from letter:
F
FA | FB | FC | FD | FE | FG | FH | FI | FJ | FK | FL | FM | FN | FO | FP | FR | FS | FT | FU | FW | FX | FY | FZ |Words begining with Fuzzy_set:
Fuzzy_set
Fuzzy_set
Fuzzy_sets
Fuzzy_set_Operations
Fuzzy_set_operations
Sponsored links: praca, nurkowanie.
These materials are based on Wikipedia and licensed under the GNU FDL
YouTube.com videos better site than Turbo Tax 2007
