Alem desses, Gershenson introduz outros tres: equivalencia, grau de
contradiςao e projeςao. Equivalencia e definida como (o autor utilizou um
espa9o bi-dimensional para as explicates):
‰y) = (l-y,W) ɑ)
Conforme a Figura 1, equivalentes sao os pontos simetricos em rela9ao
a linha fuzzy, por exemplo (1, 1) e (0, 0) ou (0.25, 1) e (0, 0.75). Pontos sem
contradi9ao (ao longo da linha fuzzy) nao tem equivalentes alem deles
mesmos.
Figura 1. Pontos equivalentes.
Ja a Contradiςao e definida atraves de um coeficiente que permite
determinar quao Contraditoria e uma proposi9ao. Esse coeficiente e definido
atraves da seguinte equa9ao 3:
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