??? Fuzzy??

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??? Fuzzy??

• ??(relation)????????????,????????????????
• ??????????????????????,??????????????????
• ?????
• ?? ??????????????
• ?? ?????????????
• ?????Fuzzy??
• ????????????????????????,????????,????????????????
  (Cartesiam product)?????
• Fuzzy??????????????

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• ?????(Cartesian product)(?????)
• note ???(u, v)??????(order pair),????U ?
  V??UV?VU?????????
• ?????????U?V???????
• ??????????????????
• Ex.

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• UV??????????,?????????????,????U?V???????(relatio
  n)????,???????U?V???????????UV???????
• Ex. ????????100,?????????
• ?????????,?

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• ????(Binary relation)
• ??U?V???UV??????R??U?V????????????????(u, v) ?
  UV??,???????????????????
• ??????(Binary relational matrix)
• ??????????????????????
• U?V?????,R??U?V?????,???R?????????MR

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• Ex. ?????????

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Fuzzy ??

• ????????????????????,???????????????????????????
  
• ????????????,????????????????,???????????
  ?????,Fuzzy??????????????????
• Fuzzy????????????Fuzzy????
• Fuzzy????(Fuzzy binary relation)
• ?????UV???Fuzzy???R???U?V???Fuzzy????,???????(u,
  v)??????????????R????

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• Fuzzy????(Fuzzy relational matrix)
• Ex.

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• Ex. ????
• note ????????????,??????????100?????????
  ???,???????????????????,????????????,????????????
  ?????????
• ?Fuzzy?????????,??(????)?????100????????????,?
  ?????????????????

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• ???Fuzzy????
• Ex.

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Fuzzy?????

• ???????????,?????????????????????????Fuzzy??????
• ???????????
• R?S?????A?B???????,?R?AB? S?AB,?????????????
• ????(Union)
• ????(Intersection)
• ????(Complement)

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• Ex. ? ?
  ????? ?????????????????R??? ??S???
  

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• Fuzzy???????
• R?S?????A?B???????,?R?AB? S?AB,?????????????
• ????(Union)
• ????(Intersection)
• ????(Complement)
• ?????(Algebraic Product)
• ?????(Algebraic Sum)

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• Ex. ?
  ????? ??R?S????x?y??x???y? Fuzzy??

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(No Transcript)
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• Fuzzy???????

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(No Transcript)
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Fuzzy???????(Composition)

• ????????(product space)?????????,????????(Composit
  ion)????????,????Fuzzy???
• ??????????-????????-???????,?????????????-??
  ??????
• max-min ????
• max-product????

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• Ex.
• ?max-min??

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Fuzzy???????(Projection)

• Fuzzy????
• ?
• R?????(the first projection)???
• R?X????
• R?????(the second projection)???
• R?Y????

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• Ex.

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????(cylindrical extension)

• ???????????Fuzzy???????????????,??????????????????
  ??????????Fuzzy????????
• Ex.

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• note
• Ex.

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• ????R?????,??????????????,????????????????????????
  ????,???????????Fuzzy??

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?????(Fuzzy relation equation)

• Ex.