Optimization of Urban Highway Bypass Horizontal Alignment: A Methodological Overview of Intelligent Spatial MCDA Approach Using Fuzzy AHP and GIS

Table 1

Common fuzzy arithmetical operations using two TFNs.

Operators	^a,bFormulae	Results
Summation	𝐴+𝐵	(𝑎1+𝑏1,𝑎2+𝑏2,𝑎3+𝑏3)
Subtraction	𝐴−𝐵	(𝑎1−𝑏3,𝑎2−𝑏2,𝑎3−𝑏1)
Multiplication	𝐴×𝐵	(𝑎1×𝑏1,𝑎2×𝑏2,𝑎3×𝑏3)
Division	𝐴/𝐵	(𝑎1/𝑏3,𝑎2/𝑏2,𝑎3/𝑏1)
Scalar product	𝑄⋅𝐵	(𝑄×𝑏1,𝑄×𝑏2,𝑄×𝑏3)

^a𝐴=(𝑎₁,𝑎₂,𝑎₃); 𝐵=(𝑏₁,𝑏₂,𝑏₃).
bThe values of 𝐴 and 𝐵 are positive; if negative numbers are used, the corresponding min and max values have to be selected.
𝑎₁<𝑎₂<𝑎₃; 𝑏₁<𝑏₂<𝑏₃; 𝑎_𝑖 and 𝑏_𝑖(𝑖=1to3)>0; 𝑛>0; 𝑄>0.