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Table 4 For modification of relations

From: Similarity in fuzzy systems

Scheme Modified relations μ R (u,v) Type
mr1 min ( μ R ( u , v ) / s , 1 ) , if s > 0 1 , otherwise Expansion
mr2 min((1 – s)+s.μ R (u, v),1) Reduction
mr3 min(1 – s+μ R (u, v),1) Expansion
mr4 max(1 – s.μ A (u), μ B (v)) Reduction
mr5 max(1 – s.μ A (u), min(μ A (u), μ B (v)))  
mr6 max(1 – s, min(s, max(1 – μ A (u), min(μ A (u), μ B (v)))))  
mr7 min(1 – μ A (u).s+s.μ A (u).μ B (v),1)