Table 3 Comparison between N-LDFS and CN-LDFS.

From: Framework development of continuous non-linear Diophantine fuzzy sets and its application to renewable energy source selection

Non-LDFS

Continuous N-LDFS

\(\mathcal{A}+\mathcal{B}\le 1\) or \((\mathcal{A}{f}_{1}+\mathcal{B}{f}_{2})\ge 1\)

\((\mathcal{A}{f}_{1}+\mathcal{B}{f}_{2})\le 1\) or \((\mathcal{A}{f}_{1}+\mathcal{B}{f}_{2})\ge 1\)

0 ≤ \({(\mathcal{A})}^{q}\)+\({\mathcal{B}}^{q}\) ≤1

0 ≤ \({(\mathcal{A}{f}_{1})}^{q}\)+\({\left(\mathcal{B}{f}_{2}\right)}^{q}\) ≤1

\(0\le \mathfrak{M}\left({\mathcal{A}}^{q}\right)+\mathfrak{N}\left({\mathcal{B}}^{q}\right)\le 1\)

\(0\le \left({f}_{1}\mathfrak{M}\right){\left({f}_{1}\mathcal{A}\right)}^{q}+{\left({f}_{2}\mathcal{B}\right)}^{q}\left({f}_{2}\mathfrak{N}\right)\le 1\)

\(0\le \mathfrak{M},\mathfrak{N},\mathcal{A},\mathcal{B}\le 1\)

\(0\le \left({f}_{1}\mathfrak{M}\right),\left({f}_{2}\mathfrak{N}\right),\left(\mathcal{A}{f}_{1}\right),\left(\mathcal{B}{f}_{2}\right)\le 0\)

\(\Gamma \Phi = \sqrt[q]{{1 - {\mathfrak{M}}\left( {{\mathcal{A}}^{q} } \right) + {\mathfrak{N}}\left( {{\mathcal{B}}^{q} } \right)}}\)

\({\Gamma }_{c}\Phi =\sqrt[q]{1-\left(\left({f}_{1}\mathfrak{M}\right){\left({f}_{1}\mathcal{A}\right)}^{q}+{\left({f}_{2}\mathcal{B}\right)}^{q}\left({f}_{2}\mathfrak{N}\right)\right)}\)

\(\mathfrak{M}\left({\mathcal{A}}^{q}\right)+\mathfrak{N}\left({\mathcal{B}}^{q}\right)\le 1\)

\(\left({f}_{1}\mathfrak{M}\right){\left({f}_{1}\mathcal{A}\right)}^{q}+{\left({f}_{2}\mathcal{B}\right)}^{q}\left({f}_{2}\mathfrak{N}\right)\le 1\) or \(\left({f}_{1}\mathfrak{M}\right){\left({f}_{1}\mathcal{A}\right)}^{q}+{\left({f}_{2}\mathcal{B}\right)}^{q}\left({f}_{2}\mathfrak{N}\right)\le 1\)

Back to article page