lpetrich's latest activity
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lpetrich replied to the thread I Axioms of Fuzzy Logic.This piecewise linear version is equivalent to x ⊕ y = min( max(x,y), max(1-x,1-y) ) = max( min(x,1-y), min(y,1-x) ) and all three...
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lpetrich replied to the thread I Axioms of Fuzzy Logic.Exclusive or again. The previous versions: Quadratic (simple negation): x ⊕ y = x + y - 2*x*y Biquadratic (bilinear negation): x ⊕ y =...
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lpetrich replied to the thread I Axioms of Fuzzy Logic.As I'd mentioned earlier, (distributiveness) > (absorption) > (idempotence) > (Gödel-Zadeh minmax and-or) > (Idempotence), (absorption)...
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lpetrich replied to the thread I Axioms of Fuzzy Logic.These functions can be used to set up an exclusive-or function that satisfies the xor-inversion axioms: fxor(x) = - fneg(x), fixor(x) =...
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lpetrich replied to the thread I Axioms of Fuzzy Logic.Let's look at negation more closely. Most fuzzy-logic work assumes simple reflection: ¬ x = 1 - x It is easy to show involution...
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lpetrich replied to the thread I Axioms of Fuzzy Logic.Having found exactly one conjunction-disjunction set that is distributive, let us see what one can find of complementation. Here...
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lpetrich replied to the thread I Axioms of Fuzzy Logic.Continuing further, let us consider the consequences of fuzzy logic having the distributive property. x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z)...
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Boolean algebra, or crisp logic, involves functions of two truth values: true (T) and false (F). These functions satisfy various...
