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

$x_1=1.1474$

$x_1=1.1475$

$x_1=1.470526$

$x_1=1.598683$

$x_2=0.7508$

$x_2=0.7514$

$x_2=0.9410526$

$x_2=1.173458$

$\alpha \mathrm{<mi>\; </mi>}=\mathrm{<mi>\; </mi>0.5491}$

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

$\beta \mathrm{<mi>\; </mi>}=\mathrm{<mi>\; </mi>0.08421}$

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

$Z^{*}=4.5474$

$Z^{*}=4.5492$

$Z^{*}=5.7642098$

$Z^{*}=6.735325$