# How to implement fuzzy minimum function via fuzzy maximum

I know that I can represent fuzzy max via power function(i need it in neural network) i.e.

def max(p:Double)(a:Double,b:Double) = pow(pow(a,p) + pow(b,p) , 1/p) // assumption a >=0 and b >=0

It is become maximum when p -> infinity and sum when p = 1

Not sure how correctly implement fuzzy minimum.

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$$\lim_{p \rightarrow \infty} \left( x^p + y^p \right) ^ { 1 \over p } = \max \left( x, y \right)$$ $$\lim_{p \rightarrow -\infty} \left( x^p + y^p \right) ^ { 1 \over p } = \min \left( x, y \right)$$ $$\left( x^2 + y^2 \right) ^ {1 \over 2} = \text{eucledian}(x, y)$$