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■+└&ëG&ëë╛n Ä┌9&9ptHÄ▄9&9vt=╕PPÄ▐9& 6û& 6öÜ`┘â─╕æ% PÄ▐9& 6û& 6öÜZ┘â─ÜT┘δ╕╡% PÜ|α â─╗TÄ :ë₧■îå■&╟╕╨PÜ╒ â─ëF∞ëVε╕pPÜ╒ â─ëF≡ëV≥+└ëF÷ëF⌠èå{ ■å{ <vΘvâ~uZ 6`# 6^#╕└% P ╢~ VÜαα â─ ╕P ╢~ VÜ" α â─P ╢~ VÜJ] ship function for the fuzzy value. In the MAXIMUM method, one
of the variable values at which the fuzzy subset has its maximum truth
value is chosen as the crisp value for the output variable.
Extended Example:
Assume that the variables x, y, and z all take on values in the interval
[0,10], and that the following membership functions and rules are defined:
low(t) = 1 - ( t / 10 )
high(t) = t / 10
rule 1: if x is low and y is low then z is high
rule 2: if x is low and y is high then z is low
rule 3: if x is high and y is low then z is low
rule 4: if x is high and y is high then z is high
Notice that instead of assigning a single value to the output variable z, each
rule assigns an entire fuzzy subset (low or high).
Notes:
1. In this example, low(t)+high(t)=1.0 for all t. This is not required, but
it is fairly common.
2. The value of t at which low(t) is maximum is the same as the value of t at
which high(t) is minimum, and vice-versa. This is also not required, but
fairly common.
3. The same membership functions are used for all variables. This isn't
required, and is also *not* common.
In the fuzzification subprocess, the membership functions defined on the
input variables are applied to their actual values, to determine the
degree of truth for each rule premise. The degree of truth for a rule's
premise is sometimes referred to as its ALPHA. If a rule's premise has a
nonzero degree of truth (if the rule applies at all...) then the rule is
said to FIRE. For example,
x y low(x) high(x) low(y) high(y) alpha1 alpha2 alpha3 alpha4
This is a *partial* list of some of the researchers and research
organizations in the field of fuzzy logic and fuzzy expert systems.
A list of "Who's Who in Fuzzy Logic" may be obtained by sending a
message to listserver@vexpert.dbai.tuwien.ac.at with
GET LISTSERVER WHOISWHOINFUZZY
in the message body. New entries and corrections should be sent to
Robert Fuller <rfuller@finabo.abo.fi>.
Center for Fuzzy Logic and Intelligent Systems Research (Texas A&M):
This group publishes a Technical Report Series, in addition to the
proceedings and video tapes of the first and second International Workshop
on Industrial Fuzzy Control and Intelligent Systems (IFIS 91/92).
Dr. John Yen
Center for Fuzzy Logic and Intelligent Systems Research
Texas A&M University
MS 3112
Harvey R. Bright Building
Texas A&M University
College Station, TX 77843 USA
Phone: 409-845-5466
Fax: 409-847-8578
Email: cfl@cs.tamu.edu
German National Research Center for Computer Science (GMD):
The GMD supports a fuzzy logic group which does research in
- adaptive control
- VLSI design
- image processing
Liliane E. Peters
GMD-SET
P. O. Box 1316
D-5205 St. Augustin 1, Germany
Phone: 49-2241-14-2332
Fax: 49-2241-14-2342
Email: peters@borneo.gmd.de
Swiss Federal Institute of Technology (SFIT):
Email: stegmaier@ifr.ethz.ch, vestli@ifr.ethz.ch
Tokyo Institute of TechUï∞ü∞ WVìF≡PÜ(α â─ìF≡PÜ0α â─Ä┬ï╪ï√îF÷&èO ╕╙αëF°&ïGï╚&ïG║ï≥Ö≈■╛<ï┴ï╩ï╨ï┴ëå⌠■ï┬Ö≈■ï╞ï╩≈«⌠■ï≡±╗Ä$6ë₧·■îåⁿ■&╟ ╗~Ä&6ë₧÷■îå°■&ïÄF÷&9EtLÉΦ2╕pP3└P ╢°■ ╢÷■Ü α â─ÄF÷&ïE─₧÷■&ëÄ(6&â>ptÄ*6&â>vt
