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The fuzzy subset obtained based on N single-factor evaluation indices constitutes fuzzy sets: R = left[ {begin{array}{*{20}c} {r_{11} } & {r_{12} } & {r_{13} } & {r_{14} } bullet & bullet & bullet & bullet bullet & bullet & bullet & bullet {r_{n1} } & {r_{n2} } & {r_{n3} } & {r_{n4} } end{array} } right]_{n times 4}.
We denote by ( langle bullet, bullet rangle ) the distributional pairing using this density.
bullet ; circ to left{ {begin{array}{l} { bullet bullet,quad r_{1} } { circ bullet,quad r_{2} } end{array} } right}, circ bullet to left{ {begin{array}{l} { bullet circ, quad r_{2} } { bullet bullet,quad r_{1} } end{array} } right},; bullet bullet to ; left{ {begin{array}{l} { bullet circ,quad r_{3} } { circ bullet, quad r_{3} } end{array} } right}, (2).
Here dm is the invariant density coming from the contact form and normalized to have ( int _M dm = 1 ) and ( langle bullet, bullet rangle ) denotes distributional pairing.
And circ circ to left{ {begin{array}{l} { bullet bullet, quad r} { circ bullet, quad r_{0} } { bullet circ, quad r_{0} } end{array} } right}.
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The purpose of visualizing R s (v) for the two vertices is to check whether all vertices of the abovementioned sets (mathcal {V}_{bullet }(bullet,bullet)) are already included in the vertex set (mathcal {V}_{s}) at the current tree node s.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com