Table 7 Evaluation grades and corresponding criteria.

From: Pythagorean fuzzy N-bipolar soft sets-based multi-criteria decision-making framework for sustainability evaluation and risk assessment in manufacturing industries

Grade

Criterion

\(r_\varepsilon = 0\)

\(\begin{array}{l} 0.0 \le (\zeta ^{+}(\ell , r_\varepsilon ))^2 + (\zeta ^{-}(\ell , r_\varepsilon ))^2< 0.2 \\ 0.0 \le (\xi ^{+}(\ell , r_{\lnot \varepsilon }))^2 + (\xi ^{-}(\ell , r_{\lnot \varepsilon }))^2 < 0.2 \end{array}\)

\(r_\varepsilon = 1\)

\(\begin{array}{l} 0.2 \le (\zeta ^{+}(\ell , r_\varepsilon ))^2 + (\zeta ^{-}(\ell , r_\varepsilon ))^2< 0.4 \\ 0.2 \le (\xi ^{+}(\ell , r_{\lnot \varepsilon }))^2 + (\xi ^{-}(\ell , r_{\lnot \varepsilon }))^2 < 0.4 \end{array}\)

\(r_\varepsilon = 2\)

\(\begin{array}{l} 0.4 \le (\zeta ^{+}(\ell , r_\varepsilon ))^2 + (\zeta ^{-}(\ell , r_\varepsilon ))^2< 0.6 \\ 0.4 \le (\xi ^{+}(\ell , r_{\lnot \varepsilon }))^2 + (\xi ^{-}(\ell , r_{\lnot \varepsilon }))^2 < 0.6 \end{array}\)

\(r_\varepsilon = 3\)

\(\begin{array}{l} 0.6 \le (\zeta ^{+}(\ell , r_\varepsilon ))^2 + (\zeta ^{-}(\ell , r_\varepsilon ))^2< 0.8 \\ 0.6 \le (\xi ^{+}(\ell , r_{\lnot \varepsilon }))^2 + (\xi ^{-}(\ell , r_{\lnot \varepsilon }))^2 < 0.8 \end{array}\)

\(r_\varepsilon = 4\)

\(\begin{array}{l} 0.8 \le (\zeta ^{+}(\ell , r_\varepsilon ))^2 + (\zeta ^{-}(\ell , r_\varepsilon ))^2 \le 1.0 \\ 0.8 \le (\xi ^{+}(\ell , r_{\lnot \varepsilon }))^2 + (\xi ^{-}(\ell , r_{\lnot \varepsilon }))^2 \le 1.0 \end{array}\)