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I would like to describe a hypothesis, formally. So I have defined $p = {t_1,t_2,t_3, \cdots, t_n}$

and I would like to say

"A pattern $p_i$ is more important than $p_j$, if $t \in p_i$ is more important than $t \in p_j$", I know that it is a bit vague to describe in this manner, so what will be a better option, the ideas I have in mind.

  • To define an importance function or weight function saying $f(p) \propto f(t) $
  • To describe purely in words.

I kind of want to avoid 2nd option as I want to find a way and learn how to formally define relationship between variables.

Thank you.

Regards, Andy

  • 0
    That makes more sense...2011-12-20

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Let $P$ and $Q$ be unordered $n$-tuples of real numbers. More formally, $P\subset \mathbb{R}$ and $Q\subset \mathbb{R}$ with $|M|=|N|=n$.

Let $f$ be a function which assigns an importance weight to each element in $P$ and $Q$. Formally, $f$ is a function $f:P\cup Q\rightarrow \mathbb{R}^+$.

Definition $P \text{ is more important than } Q :\Leftrightarrow \sum_{t\in P}f(t) \ge \sum_{u \in Q}f(u)$