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Fuzzy sets and applications

Fuzzy sets and applications. t-norm. t –norm 是模糊理論中常見的數學式子表示法，必遵守下列４種定律 t:[0,1] × [0,1] → [0,1] for each a,b,c ∈ [0,1]; t ( a,b ) = t( b,a ) ( commutativity ) t( a,t ( b,c )) = t(t( a,b ),c) ( associativity ) t( a,b ) ≤ t( a,c ),if b ≤ c ( monotonicity )

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Fuzzy sets and applications

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  1. Fuzzy sets and applications

  2. t-norm • t –norm是模糊理論中常見的數學式子表示法，必遵守下列４種定律 • t:[0,1]×[0,1] →[0,1] for each a,b,c∈ [0,1]; • t(a,b) = t(b,a) (commutativity) • t(a,t(b,c)) = t(t(a,b),c) (associativity) • t(a,b) ≤t(a,c),if b ≤c (monotonicity) • t(a,0) = 0 and t(a,1) = a, for any a ∈[0,1] (boundary conditions)

  3. 基本介紹 • Ｘ。Ａ＝Ｂ max{t(x1,a11),t(x2,a21),…,t(xm,am1)}=b1, max{t(x1,a12),t(x2,a22),…,t(xm,am2)}=b2, . . . max{t(x1,a1n),t(x2,a2n),…,t(xm,amn)}=bn

  4. Ａ∨Ｂ＝Ａ，Ｂ中取其大者 • Ａ∧Ｂ＝Ａ，Ｂ中取其小者 • a。b ＝∨(ai∧bi) (i = １～ｎ) • a⊙b ＝∧(ai∨bi) (i = １～ｎ)

  5. Examples • a。b=(0.1∧0.3) ∨(0.5∧0) ∨(0∧0.8) ∨(0.6∧0.2) =0.2; • a⊙b =(0.1∨0.3)∧(0.5∨0)∧(0∨0.8)∧(0.6∨0.2)=0.3;

  6. 生活實例 假設某人屬於高個子的程度為0.9，而屬於胖子的程度為0.4，那麼他屬於高個子或胖子的程度為0.9 ∨0.4=0.9; 他屬於高個子且胖子的程度為0.9 ∧0.4=0.4。

  7. 任何模糊集合的問題都可透過解模糊來轉化為普通集合論解決，而普通集合論則可透過模糊化來轉化為模糊集合。而在任何實際應用中都免不了要經過這２種步驟。任何模糊集合的問題都可透過解模糊來轉化為普通集合論解決，而普通集合論則可透過模糊化來轉化為模糊集合。而在任何實際應用中都免不了要經過這２種步驟。

  8. 應用 • ＡＩ人工智慧 • 洗衣機

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