Skip to main content

Table 3 For translation of relations

From: Similarity in fuzzy systems

R Conditional relations Translation (μ R (u, v))
R 1 Reichenbach s-implication 1 - μ A (u)+μ A (u)*μ B (v)
R 2 Kleen-Dienes s-implication max(1 - μ A (u), μ B (v))
R 3 Lukasiewicz r- and s-implications min(1 - μ A (u)+μ B (v),1)
R 4 Rescher-Gaines r-implication 1 , if μ A ( u ) μ B ( v ) ) 0 , otherwise
R 5 Godel r-implication 1 , if μ A ( u ) μ B ( v ) ) μ B ( v ) , otherwise
R 6 Goguen r-implication min ( μ B ( v ) / μ A ( u ) , 1 ) , if μ A ( u ) > 0 1 , otherwise
R 7 Standard t-norm min(μ A (u), μ B (v))
R 8 Bounded sum t-norm max(μ A (u)+μ B (v) - 1,0)
R 9 Product t-norm μ A (u)*μ B (v)