Definition

For any a,b ≥ 0 we introduce the bounded division

\left[ \frac{x}{y} \right] = \begin{cases} 1, & \mbox{if } y \leq x\\ x/y, & \mbox{if }x < y \end{cases}

Note that the bounded division for y=0 always gives 1.

Active Minimum Oriented FPD:


\mu_{amin}(a,b) = \prod_i \left[ \frac{b_i}{a_i} \right]

Passive Minimum Oriented FPD:


\mu_{pmin}(a,b) = \prod_i \left[ \frac{a_i}{b_i} \right]

Active Maximum Oriented FPD


\mu_{amax}(a,b) = \mu_{pmin}(a,b)

Passive Maximum Oriented FPS


\mu_{pmax}(a,b) = \mu_{amin}(a,b)

Features

  • a-min is 1 if a ≤ b, i.e. if a dominates b, otherwise a-min < 1
  • p-min is 1 if b ≤ a, i.e. if a is dominated by b, otherwise p-min < 1


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