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Biofuels for a More Sustainable Future
fuzzy numbers References (1986) Atanassov (13.3) Q n (2007a) Xu (13.4) , 1 μ α j 1 Q n ¼ j¼1 υ α j j¼1 numbers fuzzy intuitionistic are (1986) Atanassov (13.5) α
β¼(μ α ,υ α ,π α )
(μ β ,υ β ,π β )¼(μ α μ β ,υ α +υ β υ α υ β ) Q n Q n (2007a) Xu (13.6) 1 υ α j ¼ j¼1 j¼1 μ
intuitionistic α β¼(μ α ,υ α ,π α ) (μ β ,υ β ,π β )¼(μ α +μ β μ α μ β ,υ α υ β ) π α j υ α j , …,n) π α j υ α j , …,n) any any
two μ α j , j¼1 α j (j¼1,2, μ α j , j¼1 α j (j¼1,2, λα¼(1 (1 μ α ) λ ,(υ α ) λ ) represents α n ¼((μ α ) n ,1 (1 υ α ) n ) represents
between Formulas ¼ n j¼1 α j where ¼
n j¼1 α j where λ where n where
operations n
n
Arithmetic
13.1 Multiplication Exponentiation
Table Operations Addition
