Decisive set method [32] A fuzzy approach

Modified subgradient method [32]

A fuzzy approach

Zimmermann’s extended approach [15]

An IF approach

Our proposed approach

An IF approach

$x_1=1.690331$

$x_1=1.45804$

$x_1=1.333333$

$x_1=1.99453$

$x_2=0.0$

$x_2=7.8\times {10}^{-8}$

$x_2=0.0$

$x_2=0.0$

$\alpha \mathrm{<mi>\; </mi>}=\mathrm{<mi>\; </mi>0.5556}$

$\alpha \mathrm{<mi>\; </mi>}=\mathrm{<mi>\; </mi>0.90}$

$\beta \mathrm{<mi>\; </mi>}=\mathrm{<mi>\; </mi>0.142}$

$\beta \mathrm{<mi>\; </mi>}=\mathrm{<mi>\; </mi>0.09}$

$Z^{*}=1.690331$

$Z^{*}=1.45804$

$Z^{*}=1.333333$

$Z^{*}=1.99453$