1. ? ?saf?? ?????? ?a? ?? ?e?????????? ?fa?

1
1. ? ?saf?? ???????a? ?? ?e?????????? ?fa?µ????
t??

• G??f?µa ?saf??? S?st?µat?? ??????? µe ???s? t??
  MATLAB

2
? ?S?F??? ?a? ???????????t?? ???ssa? p?? µ???µe
?a? t?? ?????a? p?a?µat???t?ta?sta ??T???????

• "So far as laws of mathematics refer to reality,
  they are not certain.
• And so far as they are certain, they do not refer
  to reality".
• Albert Einstein (1879-1955)
• Geometrie und Erfahrung,
• ?µ???a st?? ???s??? ??ad?µ?a (1921)

3
???st?t???? ? d?µ??????? t?? ??t?µ?? (0-1)
???????

• M?a ?????? p??tas? µp??e? ?a e??a? a????? (1) ?
  ?e?d?? (0),
• ap???e???ta? t??t? ??s?
• ???? t?? t?? ???t?? ?p???e?se??
• (???st?t????-???a??? ? ??????)
• ? ???st?t???? (St??e??a, 382-322 p.?.) ?ta?
  a??a??? ?????a? f???s?f?? (?e??pat?t??? S????),
  µa??t?? t?? ???t??a ?a? d?s?a??? t?? ?.
  ????a?d???. ?p???e s?f?? µe?a??f???, d?µ???????
  t?? d?t?µ?? (0-1) ???????, µ??a? f?s??d?f?? ?a? ?
  s?µa?t???te??? ap? t??? d?a?e?t????? t??
  a??a??t?ta?.

4
1.1. ? ??as??? d?t?µ? (0-1)???st?t??e?a ??????

• ? ??as??? d?t?µ? (???st?t??e?a) ?????? e??a?
  ???st? ap? t?? ???a??t?ta (500 p.?.), ?eµe??????e
  ap? t??? a??a???? ?????e? f???s?f???
  (???st?t????, ???a???a?, St?????-???s?pp??,
  ?.?p.) ?a? ap?te?e? t? ß?s? t?? ?e??µe???
  d?t???? s????? ?a? t?? d?t???? p???t?sµ??.
• S?µf??a µe t?? ??as??? d?t?µ? ?????? µ?a ??????
  p??tas? µp??e? ?a p??e? µ???? d?? t?µ??, d??.
  µp??e? ?a e??a? a????? ? ?e?d?? (1 ? 0),
  ap???e???ta? t??t? ??s? (???? t?? ?p???e?s?? t??
  ???t??). ?ts? s?µf??a µe t? ??t?µ? ??????, a? µ?a
  ?????? p??tas? de? e??a? a????? (?sp??) t?te ?a
  e??a? a?a??a?a ?e?d?? (µa???), e?? a? de? e??a?
  ?e?d?? t?te ?a e??a? a?a??a?a a?????.

5
1.2. ??a ?St????? ?????? pa??d??? t?? ??t?µ?S
(???st?t??e?a?) ??????S

• ?? pa??d??? t?? ???t???? ?p?µe??d? "???te? ?e?
  ?e?sta? - ?? ???t???? ???e p??ta ??µata ?
  ?p?µe??d?? ??e? ?t? ?? ???t???? ???e p??ta ??µata
  ? ?p?µe??d?? ?µ?? e??a? ???t???? ??a ?
  ?p?µe??d?? ??e? ??µata, ?t? ?? ???t???? ?e?d??ta?
  ??a ?? ???t???? ???e t?? a???e?a ??a ?a? ?
  ?p?µe??d?? ??e? t?? a???e?a ??a ?? ???t????
  e??a? ?e?te?, ?.?.?. (fa???? ??????).
• ???. ? ???t???? ?p?µe??d?? ?e?deta? ?ta? ??e? ?t?
  ???? ?? ???t???? ???e p??ta ??µata ???
  ?e?deta?, ??e? t?? a???e?a. ???? e?? ??e? t??
  a???e?a, t?te ?e?deta?.
• ??t?fas? t?? d?t?µ?? ???????

6
1.3. ??t?µ? ?????? ?a???e??t?µ?-?saf?? ??????

• ? d?t?µ? ???st?t??e?a ?????? ep????t?se p?????
  ap? t?? 10? a???a st?? d?t??? p???t?sµ?, ??a d??
  ?????? ??????
• 1?) ??at? ap???ste?e? ?at? p??? t? s??????st???
  t?? p??ß??µ?t??, ?a?
• 2?) ??at? ap?d?de? ap???t? ßeßa??t?ta st??
  ap?de??? ?a? ap?d??? t?? a???e?a?.
• ?µ?? a?t? ? ap???t? ßeßa??t?ta t?? d?t?µ??
  ??????? ?a??? ?a? ?? f?s???? at??e?e? t??
  asp??µa???? s??????st???? t??, ap?de?????a?
  a????p?-?????? a?epa??e?? ??a t?? e?µ??e?a t?s?
  t?? f?s???? ???ssa? ?a? t?? a????p????
  s?µpe??f????, ?s? ?a? t?? s?????? asaf???
  p?a?µat???t?ta? p?? µa? pe??ß???e?.

7
? ?saf?? ?????? e??a? ep??tas? t?? ??t?µ??
???????, ap? t? d?t?µ? s????? 0,1 st?
ape???t?µ? 0,1

• ? ?saf?? ?????? e??a? ? p??sp??e?a t??
  ep?st?µ???? ?a? ?????? a?t?? p?? as??????ta? µe
  t?? te???t? ???µ?s??? ?a µe?et?s??? ?a? ?a
  µa??µat???p???s??? t? d?µ? t?? f?s???? ???ssa?
  t?? a????p??.
• ?e t?? asaf? ?????? ?a ???aµe ?e?????ta? ap? t?
  d?t?µ? ??as??? ?????? (0 ? 1) ?a t?? epe?te????µe
  e?s????ta?, as?fe?a, a???st?a, aßeßa??t?ta ?t?,
  ?ts? ?ste afe??? ?a p??se????e? t?? e?f?ast???
  d??aµ? ?a? ap??t?ta t?? f?s???? ???ssa?, a??? ?a?
  afet???? ?a pe??s??e? ?s?? t? d??at?? pe??ss?te??
  t? ???st? µa??µat??? d?µ? t?? ??as???? ???????.

8

• ?ts?, ta a?t?a p?? ??a?a? a?ap?fe??t? t??
  ep??tas? t?? d?t?µ?? ??????? ?a? ?d???sa? st?
  d?µ??????a p?e??-t?µ?? ??????? ?p?? ? ?saf??
  ?????? (d??. se ??????? µe p??? ap? d?? t?µ??),
  ?ta? ?????? ? a????? µa??µat???p???s?? t??
  f?s????-?a??µ????µ???? ???ssa? t?? a????p?? ?a?
  t?? f?s???? as?fe?a? p?? d??pe? t?? a????p???
  ???µ?s???-s?µpe??f???, ?a??? ?a? ?
  a?a??a??t?ta ??a µ?a p?? ?ea??st??? ?e???s? t??
  ?????a? t?? aßeßa??t?ta? st?? p????.
• St?? ?saf? ?????? ???p?? e?t?? t?? d?? t?µ??
  a???e?a? 0 ?a? 1, ????µe ?? t?µ? a???e?a?
  (a????t?µ?) ?a? ???e a???µ? st? ??e?st?
  ape???-d??st?µa 0,1.

9

• 1.4. ?st????? d?ad??µ? t?? ?saf??? ???????
• ?p? t?? a??a??t?ta a??µ? ?ta? ???st?? ?? at??e?e?
  t?? ??t?µ?? ??????? ?p?? p.?. ta ?st????? ??????
  pa??d??a t?? S?f?st?? (?????- ?p?µe??d??, ??p),
  a??? ?a? ?? s??????e? ep?st?µ?????? ?e???se??
  ?p?? ? ???? t?? ?ßeßa??t?ta? t?? Werner
  Heisenberg e?te ? Te???a S?et???t?ta? t?? Albert
  Einstein, ?d???sa? st?? a??pt??? t?? ??e??t?µ??
  (????t?µ?? d??. µe p????? t?µ??) ??????? st??
  de?aet?e? t?? 1920-1930 ?a? te???? st? d?µ??????a
  t?? s???????? ?saf??? ???????.
• ??? s???e???µ??a, ap? t?? a???? t?? 20?? a???a ?
  ?????? f???s?f?? ?a? µa??µat???? Bertrand Russel
  p??ßa??e t?? a?t?f?se?? t?? ??t?µ?? ??????? (p??
  ap? t?? 19? a???a e??e ?d? ?eµe????e? ?? ?
  ap???t? ??as??? S??????e???a ap? t?? Ge?µa??
  µa??µat??? Georg Cantor).
• ???? µet? t? 1920, p??t?? ? ??????? µa??µat????
  Jan Lukasiewiscz a??pt??e ??a µ?-d?t?µ? a???
  t??-t?µ? ?????? s?st?µa µe ped?? t?µ?? 3
  a????t?µ??, d??. p?? µp??e? ?a e?f???e? 3 ???????
  ?atast?se??-t?µ?? ?p?? p.?. ??a p?t??? ?de?? (0),
  µ?s??eµ?t? ? µ?s??de?? (1/2), ?a? ?eµ?t? (1).
• ???? a???te?a (1937) ? ?µe???a??? f???s?f?? ?a?
  ?ßa?t???? f?s???? Max Black s?µp????se a?t? t?
  ?e???a ?a? ??ese t?? f???s?f???? ß?se?? ??a ta
  asaf? s????a.

10

• ?e???? t? 1965, ? Lotfi Zadeh (?µe???a???
  µ??a?????, ??s?-pe?s???? ?ata?????, ?a????t??
  t?? ?a?/µ??? Berkeley t?? ?a??f????a?),
  d?µ?s?e?se t?? eµp?e?sµ??? e??as?a t?? µe t?t??
  Fuzzy Sets-?saf? S????a, ?p?? e?s??a?e ??a
  p??t? f??? t?? ?????a t?? ?saf??? S?????? µe
  ped?? a????t?µ?? t? ape???d??st?µa 0,1 ?a? t??
  ??? fuzzy st? d?e??? ß?ß?????af?a, a??????ta?
  pa??????a t? d??µ? ?a? ??a t?? p?a?t????
  efa?µ???? t?? (a????? st? ????????a,
  ????????????a, f???s?f?a, ?t?).
• ?et? t?? a????? d?sp?st?a ?a? t?? p??te?
  f?s????????? aµf?sß?t?se?? t?? ??a? Te???a?,
  s??t?µa a???????sa? ?a? ?? te?????????? efa?µ????
  t?? ?saf??? ???????, ?????? sta d??aµ???
  µ?-??aµµ??? s?st?µata e?????? (non-linear control
  systems), ?p?? s?????? ta s?µßat??? µa??µat???
  µ??t??a de? ?s????? p?a.
• ??a? ap? t??? p??t??? p?? ???s?µ?p???se t?? ?saf?
  ?????? ??a t?? ?atas?e?? e??? ?saf??? S?st?µat??
  ??????? st? ?e?t?????a µ?a? atµ?µ??a???, ?ta? ?
  ??eta??? µ??a????? Ebrahim Mamdani ?at? t?
  de?aet?a t?? 1970. ????????sa? t? 1978 st? ?a??a
  ?? P. Hoenblad ?a? Jens-Jorgen Ostergaard p??
  ?at?fe?a? ?a? ?ft?a?a? t? p??t? asaf?? s?st?µa
  a?t?µat?? e?????? ??a t? d?ad??as?a pa?a?????
  ts?µ??t??.

11
1.5. ?F????G?S t?? ?S?F??S ??G???S

• S?µe?a e??a? p???????µe? se ??? t?? ??sµ? ??
  ?e?????????? ?a? Te???t???? efa?µ???? t?? ?saf???
  ???????.
• ??a s?µa?t??? efa?µ??? e??a? t? s?st?µa a?t?µ?t??
  e?????? t?? µet?? t?? ?ap?????? p???? Sendai t??
  Miyamoto Yasonubu. ?? µet?? a?t? ?e?t?????se
  ???? st? 1987, ?a? e??a? t? p?? apa?? ?a? ?p??
  st?? ????s? µet?? t?? ??sµ??! e?? e???????µe?
  e????e?a ?a? µe???e? t? ??st?? ?at? 10 ??? 25.
• S?µe?a ??e? ??????e?t??? p??µµ???se? ? a???? µe
  s?s?e??? p?? e?s?µat????? asafe?? e?e??t??
  (p???t???a, ???e?a, ???µat?st???, ??ß?t?a
  ta??t?t??, ABS, ??p), ?p?? ?a? asafe?? e?e??t??
  µ?-epa?d??µ???? ???µ?t??-ae??s?af??, ?e?t?????a?
  ts?µe?t?ß??µ??a????, ß??te??aµe???, ??µp?t,
  ?at????? d?????s??, a?a?s??s?a?, ?e??????????,
  ?t?.
• ?????, de? ?p???e? ?s?? ep?st?µ?????? ???d??
  s?µe?a p?? ?a µ?? epe?te??eta? ?a?da?a se ?????e?
  ?a? efa?µ???? t?? ?saf??? ???????, ?p??
  ?a??µat??? (asaf?? ???eß?a ? ??p?????a, asafe??
  ???a??t?te?), ??????µ?a, Stat?st???, F???s?f?a,
  Se?sµ?????a, ?at????, ??µp?t???, ???????a,
  ????????a, ????????a, ??ast?µ???, ????????????a,
  ????????, Ge?et???, ?t?.

12
? e?sa???? t?? ?saf??? ??????? ?a? ?
s?????? t?? s?et??? ap??? ?d?a? t?? ?saf???
S?????? ????e ap? t?? ?e?s???? ?ata?????,
?µe???a?? ?a????t? Lotfi Zadeh. ??a ß??d? t??
????? t?? 1964 st?? ??a ????? ?a? d?µ?s?e????e
st? d??s?µ? p?a e??as?a t?? t? 1965, (??. Fuzzy
Sets, Information and Control, 8 (1965) 338353).
.? Zadeh ?e??????e t? 1921 st? Baku t?? t?te
S?ß?et???? ??e?µpa?t???. ?? 1931 ? ???????e?? t??
µeta??µ?se st?? ?e?e???? ?a? t? 1943 pt????????
µ??a????? ?d? st?? ???. ???e t? Masters degree
ap? t? ??? t? 1944 ?a? t? d?da?t????? t?? ap? t?
Columbia t? 1949.
Lotfi A. Zadeh
?e?s?-?µe???a??? ???a?????

Teµe???t?? t?? ?saf??? ???????
13
1.6. ? ?saf?? ?????? ßas??eta? st?? ep??tas? t??
?????a? t?? ??as???? s?????? p?? ????eta? st?
d?t?µ? s????? 0,1 , st? ?e???e?µ??? ?????a t??
asaf??? s?????? p?? ????eta? st? ??e?st?
ape???d??st?µa 0,1.

• O? ???st??, s??p?? t?? d?t?µ?? ??as???? s??????
  e??a? ?a pa?ast?se? µa??µat???, d??. ?a e?f??se?
  s?µß????? ??p??a d?t?µ? ?????? ?????a, p.?.
• ? ?????a ?? a???a??? a???µ?? p?? e??a? µeta?? 2
  ?a? 6, µp??e? ?a pa?asta?e? µe t? s?????
  ,
• ?p?? ? s?µß????e? t? s????? t?? a?e?a???.
• ?ts? p??ta ??e?a??µaste ??a s????? a?af???? ?
  s?µpa? p?? pe????e? ??a ta st???e?a ta s?et??? µe
  t?? ?????a p?? ?????µe ?a e?p??s?p?s??µe µ?s? t??
  s?????? ?, (?p?? ed? ?p?? t? s????? a?af????
  e??a? t? ?).
• ???a? ???st? ep?s??, ?t? ?e???? ??a d?t?µ? s?????
  ? ?? p??? s????? a?af???? ? , µp??e? ?a
  pa?asta?e? ?s?d??aµa µ?s? t?? ?a?a?t???st???? (?
  de??t??a?) s????t?s?? t?? ??, d??ad?
• 
  
• 
  d??.

14

• S??ep?? sta ???st? ??as??? s????a, t? a? a???e? ?
  de? a???e? ??p??? st???e?? x t?? s?µpa?t?? X st?
  s????? A, e??a? ap???t?? saf?? ?a? ?ts? ???e
  ??as??? s????? A d?a?????e? ta st???e?a t??
  s?µpa?t?? X se d?? d?a?e???µ??e? ?at?????e?
•  
• st?? ?at?????a µe ta st???e?a t?? X p?? a??????
  st? A, ?a?
• st?? ?at?????a µe ta st???e?a t?? X p?? de?
  a?????? st? A.
• ?µ??, a? ep??e????saµe ?a e?f??s??µe µa??µat???
  µ?s? t?? pa?ap??? ??as???? d?t?µ?? s??????, µ?a
  ap?? ?a??µe???? ?e?t??? f??s? t?? µ??f?? ?ta?
  ?aµ?? de?a??? f??t?t??, ?a ?ta? ad??at??, af??
  µ?a t?t??a ?a??µe???? µe? a??? a???st?-asaf??
  ?????a de? µp??e? ?a d?a????se? saf?? t? s?????
  a?af???? t?? a?e?a??? ? se d?? ?a?a??? ?at?????e?
  st???e??? (se a?t? p?? a??????, ?a? se a?t? p??
  de? a?????? st? ?), ded?µ???? ?t? ? ?????a
  ?aµ?? de?a??? d??. pe??p?? d??a de? ??e?
  ?e???a?a-saf? ???a, ?p?? apa?t??? ta ??as???
  d?t?µa µa??µat???.

15

• ?ts? ??a t?? a?t?µet?p?s? t?t???? ???ss????
  asaf?? e?f??se??, t? ?saf?? S????? epe?te??e? t??
  ?????a e??? d?t?µ?? s?????? µ?s? t?? s????t?s??
  s?µµet????, d??.
• St?? ?S?F? ??G??? ? t?µ? a???e?a? µ?a? p??tas??
  de? pa???e? µ???? µ?a ap? t?? d?? t?µ?? 0 ? 1,
  a??? µp??e? ?a pa???e? ?a? ?p??ad?p?te t?µ?
  µeta?? 0 ?a? 1, ?p?te µ?a p??tas? p?? de? e??a?
  a????? de? s?µa??e? a?a??a?a ?t? e??a? ?e?d??,
  a??? µp??e? ?a e??a? µe???? a????? ?a? µe????
  ?e?d??-?p?? ??a µ?s??eµ?t? p?t???.
• St?? ?S?F? ??G??? de? ?s??e? ? ???? t??
  ?p???e?se?? t?? ???t?? p?? ?s??e? st?? ??as???
  ??t?µ? ??????.

16
2. ?S?F?S ??G??? 2.1. ?as???? ?????e?-???sµ??

• ? ?saf?? ?????? ßas??eta? st?? ep??tas? t??
  ?????a? t?? ??t?µ?? S?????? (1), st? ?e???e?µ???
  ?????a t?? ?saf??? S?????? (2)

17
2.2. S?????s? ??as???? ?a? asaf??? s??????
18
2.3. S?G???S? S???TO? S??? ????? ?S?FO?
S????O??-??????????, ?-??ape??e?d??? ?a?
G-?aµpa??e?d???,p?? e?f?????? t?? ?d?a asaf?
?????a, x pe??p?? 55,p.?. ???? ta??t?ta? 55
km/h
19
2.4. ??µ??e?a t?? ?saf?? S???????
??t??e?µe???? ?p??e?µe????t?ta t?? ?saf??
S??????

• ? s????t?s? s?µµet???? e??? a.s. µp??e? ?a
  e?f??se? ?p??e?µe????? ap??e?? ??a t?? ?d?a
  ?????a, se a?t??es? µe t? ?a?a?t???st???
  s????t?s? e??? ??as???? s?????? p?? e?f???e? µ?a
  ap???t?, ???st??? ?????a, a?e???t?t? ap?
  pa?at???t?? (µe t?? ?????a ?t? ???? ??
  pa?at???t?? ?a e??f?a?a? µe t?? ?d?? t??p? µ?a
  ap???t? ?????a).
• p.?. ??a t? a.s. ?x e??a? pe??p?? 2, ?
  µ??f? t?? e?a?t?ta? ap? t? µ?t? t?? pa?at???t?,
  ?p?te µp??e? ?a ????µe d?af??et???? s??a?t?se??
  s?µµet???? p?? ?a e?f?????? t?? ?d?a asaf? ?????a
  ?.
• ??t??eta, t? ??as??? s?????, p.?.
• e?f???e? µ?a ap???t? ?????a ?a? ? s?µas?a t??
  e??a? a?e???t?t? ap? ?p??e?µe????? e?µ??e?e?.

20
T?sse?a d?af??et??? asaf? s????a, p?? e?f??????
t?? ?d?a asaf? ?????a ?x e??a? pe??p??
2.H ?d?a asaf?? ?????a µp??e? ?a e?f???eta? ap?
p???? ?a? d?af??et??? asaf? s????a-(a.s.), se
a?t??es? µe ta ??as??? s????a.? ep????? t??
?at??????? a.s. e??a? ?e???? ?p??e?µe????. ???.
ta a.s. µp????? ?a e?f?????? ?p??e?µe?????
ap??e?? µe a?t??e?µe????-µa??µat??? t??p?, af??
ta ???a e??? a.s. e??a? asaf? ?a? e?a?t??ta?
te???? ap? t?? ???s? t?? pa?at???t?.
21
???f???? ?e????? t?p?? ?saf?? S??????
22
2.5. ?as??? ?a?a?t???st??? t?? asaf??
s??????

• 1) a-d?at?µ? (a-cut) e??? asaf??? s?????? A (??
  p??? s?µpa? X), ???µ??eta? t? d?t?µ? s?????, p??
  ????eta? ?? e???

2) Te???µa A?apa??stas??
?p??
23
3.1. ?safe?? ????µ?? ?saf??
????µ?t???

• ??a? asaf?? a???µ?? ?, ????eta? ?e???? ?? ??a
  e?d??? asaf?? s????? ?? p??? ,

?ts? ?ste
?a e??a?
(i) ?a??????, (d??.
(ii) ???t?, (d??. ??e? ?? a-d?at?µ?? a?t??,
e??a? s????? ??e?st? d?ast?µata), ?a?
(iii) s??e??? ?at? tµ?µata s????t?s?.
24
?a pa?a??t? asaf? s????a A ?a? B de? e??a?
?safe?? ????µ??, e?? t? C e??a?.
25
S?????s? e??? ??as???? p?a?µat???? a???µ?? 3 ,
(ß?. (a)) ?a? t?? asaf??? a???µ?? pe??p??
3 , ((c) -??????????),
?a??? ?a? e??? ??as???? d?ast?µat?? 2,4,
(ß?. (b)) ??a?t? t?? asaf??? d?ast?µat??
pe??p?? 2,4 , (ß?. (d), ??ape??e?d??).
26

?a?ade??µata 6 asaf?? a???µ?? A,B,C,D,E,F,
p?? e?f?????? t?? ?d?a asaf? ?????a x e??a?
pe??p?? ??a
27
??
?a?
e??a? d?? asafe?? a???µ??
µe a?t?st???e? a-d?at?µ??
t?te ?e????
?a?
,
?p??
e??a? µ?a ap? t?? 4 ßas???? ?safe?? ????µ?t????
????e?? (asaf?? p??s?es?-afa??es?-p???ap??s?asµ??-
d?a??es?).
???. ? ???eß?a t?? asaf?? a???µ?? ???eta? µ?s?
t?? a-d?at?µ?? t??? ?a? t?? Te???µat??
??apa??stas??, ?p?te ? ?saf?? ????µ?t???
µetat??peta? te???? st?? ?a?? ???st? a???µ?t???
t?? ??as???? d?ast?µ?t??.
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3.2. ?????????? ?safe?? ????µ??(Triangular Fuzzy
Numbers-TFN)

• St?? efa?µ???? t?? ?saf??? ???????, s??????
  ???s?µ?p?????ta? p?? ap??? asafe?? a???µ??, ?p??
  ?? LR-asafe?? a???µ??, ?? t????????? ?a? ??
  t?ape??e?de??.
• ?d?a?te?a ?? ap???ste??? ?????????? ?safe??
  ????µ?? (TFN) µp????? ?a e?f?ast??? p????? ap?
  µ?a t???da

?a? ????? ?e???? ??aµµ??? (t????????) ???f?µa,
t?? a???????? µ??f??
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?p??,
?a?
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3.3. ?? ?safe?? ????µ?t???? ????e?? t?? TFN

• ??d???, a? ?a?
• e??a? ?et???? TFN, d??.
• t?te ?? 4 ?safe?? ßas???? ????µ?t????
• ????e??, ap??p?????ta?, ?? e???

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4. ?S?F?S ?????????

• ?a s????? ??as??? d?ast?µata t?? d?t?µ??
  pa?ad?s?a??? ???????, p?? pa??st????ta? µ?s? e???
  a??te??? ?a? e??? ?at?te??? a???µ?t???? ????? -
  ?p?? eµpe????e?eta? ? ?p?t???µe?? a???ß?? t?µ?,
  de? ????? t? d??at?t?ta ?a e?f??s??? s????e???se?
  µetaßat???? aß?ßa?e? ?atast?se??, af?? ta ??as???
  d?ast?µata d?aµe?????ta? p??ta µeta?? t??? µe
  ap???ta-?e???a?a s????a, µe s???pe?a ?a
  a??????ta? ?a? ?a ?????ta? s?µa?t???tate?
  p????f???e? ?a? ?p?????sµ?? ?at? t? µetaßat???
  s???pa??? t?? d?af???? asaf?? ?atast?se??, (ß?.
  ep?µe?? S??µa).

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?.?. ??a asaf??-???ss??? µetaß??t?
A(x)?????a µe 3 ?e?t???? t?µ??-asaf? s????a
A1????, A2?es????a?, A3??????µ????, p??
d?aµe???e? t?? ?????a t?? a????p??, ?at? µ?a
(?p??e?µe????) ?p???.
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4.1. S?G???S? ?S?F??S ???S???S ?????????S

• ? s?µa?t???t?ta t?? ???ss???? (asaf??) µetaß??t??
  ???e?ta? st? ?t? d?e????????? ßa?µ?a?e?
  µetaß?se?? µeta?? d?af??et???? asaf??
  ?atast?se??, µ?s? t?? ???a??? ep??a???e??-overlaps
  (?saf?? ??aµ???s?) ?a? s??ep?? ????? t? f?s???
  ??a??t?ta ?a e?f?????? ?a? ?a ap?d?d??? ?a??te?a
  t?? aßeßa??t?ta ? t?? ?p??e?µe????t?ta,
  s?????t??? µe t?? ??as???? µetaß??t?? p?? de?
  ????? p??fa??? a?t? t?? ??a??t?ta.
• ??t??eta st?? ??as???? µetaß??t??, ?? d?ad?????
  asafe?? ?a? f?s??? a?????ep??a??pt?µe?e?
  µetaßat???? ?atast?se?? (p??? ?aµ??? ?e?µ???as?a,
  ?aµ???, µ?t??a, ?t?), e??aµß????ta? ap? ta
  ??as??? s????a ?? a?st??? d?a????sµ??e? µeta??
  t??? ?atast?se?? se ??a s???e???µ??? s?µe??, µ?s?
  µ?a? ap???t?? (asp??µa????) d?t?µ?? - ??as????
  d?aµ???s??. ????µa p??fa??? p?? de? e?f???e? t?
  s??e??? a?????µetaßa???µe?? p?a?µat???t?ta.

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S?G???S? ?????????S, p.?. Te?µ???as?a st??
pe????? ?1,?2, p?? e?f???eta? (a) ??
?S?F?S ?????????-asaf?? d?aµ???s?, (µ?s? asaf??
a???µ??) ?a? (b) ?? ???S??? ?????????-??as???
d?aµ???s?, (µ?s? s?????? a???µ??).
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5. ?saf? S?st?µata (Fuzzy Systems)

• ??a ?saf?? S?st?µa e??a? ??a? µ?-??aµµ????
  µetas??µat?sµ?? F, p?? a?t?st?????e? µ?a
  ??s?d?-G??ss??? (?saf?) ?etaß??t? ?, se µ?a
  ???d?-G??ss??? (?saf?) ?etaß??t? ?, d??.  
  , e?te,
• ?saf?? S?st?µa e??a? ??a s????? ap? If-Then
  asafe?? ?a???e?, p?? a?t?st???????? asaf?
  s????a-e?s?d???, se asaf? s????a-e??d???.
• ??? s???e???µ??a
• ??a fuzzy s?st?µa F a?t?st?????e? µ?a asaf?
  µetaß??t? e?s?d? ? (µe t?µ?? ???e??-asaf? s????a)
  se µ?a asaf? µetaß??t? ???d? ? (µe t?µ??
  ???e??-asaf? s????a).

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• ?a asaf? s?st?µata ßas????ta? se asafe?? ?a???e?
  p?? e??a? ???ss???? e?f??se??,
• ?p?? p.?. st? fuzzy p???t????
• If (t? ap??e?? t?? p???t????? e??a?
  a???a?t?)-
• Then (p??s?ese pe??ss?te?? ap????pa?t???), ?
• If (t? ap??e?? t?? p???t????? e??a? p???
  a???a?t?)-
• Then (p??s?ese p??? pe??ss?te?? ap????pa?t???).
• ?ts?, ?? s????e?? ???e?? a?t?st?????? se
  asaf? s????a, ?? e??? ? ???? ap??e??
  p???t????? µp??e? ?a ?e????e? ?? ?p?s????? t??
  ????? ?e??. ?? ap??e?? µp??e? ?a ?e????e? ??
  asaf?? s????? µe a???sta ???a (?p??
  ?a?a??-a???a?t?-p??? a???a?t?, ?t?) ? ?? ??as???
  s????? µe ?a????sµ??a ???a. St?? p??t? pe??pt?s?
  ta ep??eta, ?a?a??-a???a?t?-p??? a???a?t?, ?t?,
  e??a? fuzzy ?p?s????a t?? ap??e???, ?p??
  a?t?st???a e??a? ep?s?? fuzzy ?p?s????a t??
  p?s?t?ta? t?? ap????pa?t???? t? ????te?? ?
  pe??ss?te?? ap????pa?t???.

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?? d????aµµa ?e?t?????a? e??? ?saf??? S?st?µat??
µe m asafe?? ?a???e?
38
?? d????aµµa ?e?t?????a? e??? ?saf??? S?st?µat??
µe m asafe?? ?a???e?

• ?at? t? ?e?t?????a e??? s??????? ?saf???
  S?st?µat??, µe m asafe?? ?a???e? t?? µ??f??
  IF - THEN , a?t?st???????ta? asaf? s????a t??
  e?s?d?? se asaf? s????a t?? e??d??, ?p?te
  d?µ????????ta? pa??????a asafe??
  ?????-µpa??µata .
• G?a ???e e?s?d?, e?e???p?????ta? ???sµ???? ap?
  t??? asafe?? ?a???e?, s??µat????ta? µ?a asaf?
  ???d?, ?p?te µe ap?asaf?p???s? (defuzzification)
  t?? asaf??? s??????-e??d??, pa?????µe s??????
  st?? efa?µ???? ?? te???? ???d? t?? ?saf???
  S?st?µat?? ??p???? p?a?µat??? a???µ? .

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?? d????aµµa ?e?t?????a? e??? ?saf??? S?st?µat??
µe m3 asafe?? ?a???e?
40
?? d????aµµa ?e?t?????a? e??? ?saf??? S?st?µat??
µe m asafe?? ?a???e?
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??a ?saf?? S?st?µa e??a?
??s?ast??? ??a s????? ap? s????e?? ???ss?????
?a???e? t?? µ??f?? ?? s?µßa??e? t? ? ap? t? ?,
??te ?a s?µßa??e? t? ? ap? t? ?, p??
a?t?st???????? ???ss????-asafe?? ?????e? ? ?a? ?,
s?µf??a µe t? f?s??? ???ssa ?a? t?? ????? ??????,
p.?. ?? ???e? ????, ??te air condition st?
?est?, ? ?? ???e? p??? ????, ??te air condition
st? p??? ?est?, e?te ?? ß???e? p??? ?a?
??at?t?ta µ????, ??te ?aµ???te?? ta??t?ta st?
a?t?????t? , ?t?. ???. st?? ??s?a ta ?saf?
S?st?µata ?p?? ?a? ? ?saf?? ?????? ?e????,
st??e???? ?ste ?a e?s?µat?s??? ?? µ??a??? ?a?
ta µa??µat???, t?? t??p? ??f?as?? t?? ?a??µe?????
f?s???? ???ssa? ?a? t? ???t??p?a t?? ??????
??????? t?? a????p??. S?µe??t??? ?t? ta
µa??µat??? ?a? ?at? s???pe?a ?a? ?? µ??a???
?e?t??????? ?at? ß?s? µ???? s?µe?a, µe t? d?t?µ?
(asp??µa???, 0-1) ?????? t?? ???eß?a? Boole.
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6.1. ? ???ß??? ?saf??? ??f???-?saf??? S??????
(?e????)
?st? ??a asaf?? s????? ? asaf?? s??s? (?????
ap???ste?s?? t??µe???),
(?e????
1) ??te ? p??ß??? t?? ?,
p.?. st?? ????a
e??a?
2) ?µ??a ? p??ß??? t?? ? st?? ??as???
?p?????-ep?ped?,
(d??. e??a? ??a d?d??stat? asaf?? s?????,
p?? ??e?
?? p??? s????? a?af????
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a-d?at?µ??,
?? p??ß???? C ?a? B t?? asaf??? s?????? ?, se
???e ????a
a?t?st???a, e??a? µ???d??stata asaf? s????a
?a? µ???sta t??????e?d??? µ??f??.