A New Distance Measure and Ranking Method for Generalized Trapezoidal Fuzzy Numbers

Table 3

Comparison of other methods for the examples in Figure 1.

Chang	𝐺1≻𝐺2	𝐻1≻𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽1≺𝐽2≺𝐽3	𝐾3≺𝐾2≺𝐾1	𝐿1≻𝐿2
Kerre	𝐺1≺𝐺2	𝐻1≺𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽3≺𝐽2≺𝐽1	𝐾3≺𝐾2≺𝐾1	𝐿1≈𝐿2
Lee-Lee
𝑂	𝐺1≺𝐺2	𝐻1≺𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽3≺𝐽2≺𝐽1	𝐾3≺𝐾2≺𝐾1	𝐿1≈𝐿2
𝐺	𝐺1≺𝐺2	𝐻1≺𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽3≺𝐽2≺𝐽1	𝐾3≺𝐾2≺𝐾1	𝐿1≈𝐿2
Liou-Wang
𝛾=1	𝐺1≺𝐺2	𝐻1≈𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽1≈𝐽2≈𝐽3	𝐾3≺𝐾2≺𝐾1	𝐿1≺𝐿2
𝛾=.5	𝐺1≺𝐺2	𝐻1≺𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽3≺𝐽2≺𝐽1	𝐾3≺𝐾2≺𝐾1	𝐿1≈𝐿2
𝛾=0	𝐺1≺𝐺2	𝐻1≺𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽3≺𝐽2≺𝐽1	𝐾3≈𝐾2≈𝐾1	𝐿1≺𝐿2
Jain
𝑘=1	𝐺1≻𝐺2	𝐻1≺𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽1≈𝐽2≈𝐽3	𝐾3≺𝐾2≺𝐾1	𝐿1≻𝐿2
𝑘=2	𝐺1≻𝐺2	𝐻1≺𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽1≈𝐽2≈𝐽3	𝐾3≺𝐾2≺𝐾1	𝐿1≻𝐿2
𝑘=.5	𝐺1≈𝐺2	𝐻1≺𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽1≈𝐽2≈𝐽3	𝐾3≺𝐾2≺𝐾1	𝐿1≻𝐿2
Proposed
𝜆=1	𝐺1≺𝐺2	𝐻1≺𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽3≺𝐽2≺𝐽1	𝐾3≺𝐾2≺𝐾1	𝐿1≈𝐿2
𝜆=.5	𝐺1≻𝐺2	𝐻1≻𝐻2	𝐼3≺𝐼2≺𝐼1	𝐽1≺𝐽2≺𝐽3	𝐾3≺𝐾2≺𝐾1	𝐿1≻𝐿2
𝜆=0	𝐺1≻𝐺2	𝐻1≻𝐻2	𝐼1≈𝐼2≈𝐼3	𝐽1≺𝐽2≺𝐽3	𝐾3≺𝐾2≺𝐾1	𝐿1≻𝐿2