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362 Biofuels for a More Sustainable Future
(1986) (1986) (2000) (2000)
References Atanassov (2007a) Xu Atanassov (2007a) Xu al. et De al. et De
(13.4)
(13.3) j¼1 υ α j (13.5) (13.6)
Q n numbers numbers
, 1 υ α j
1 μ α j fuzzy Q n j¼1 fuzzy numbers numbers
numbers 1 Q n j¼1 intuitionistic j¼1 μ α j , intuitionistic real real
fuzzy ¼ are 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 ¼ are (13.7) positive (13.8) positive
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
