Introduction
Preliminaries
Distance measure and similarity measure of PFSs
Authors | Similarity measure |
---|---|
Li et al. [36] |
\(S_{L}(M,N)=1-\sqrt{\frac{\sum _{i=1}^n((\mu _M(x_i)-\mu _N(x_i))^2+(\nu _M(x_i)-\nu _N(x_i))^2)}{2n}} \)
|
Chen [37] |
\(S_C(M,N)=1-\frac{\sum \nolimits _{i=1}^n|\mu _M(x_i)-\nu _M(x_i)-(\mu _N(x_i)-\nu _N(x_i))|}{2n} \)
|
Chen and Chang [38] |
\(S_{CC}(M,N)=1-\frac{1}{n}\sum \nolimits _{i=1}^n(|\mu _M(x_i)-\mu _N(x_i)|\times (1-\frac{\pi _M(x_i)+\pi _N(x_i)}{2})+ \)
|
\((\int _{0}^1|\mu _{M_{x_i}}(z)-\mu _{N_{x_i}}(z)|d_z)\times (\frac{\pi _M(x_i)+\pi _N(x_i)}{2}))\)
| |
\( \text {where}~~~ \mu _{M_{x_i}}(z)= {\left\{ \begin{array}{ll} 1,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text {if}~~z=\mu _M(x_i)=1-\nu _M(x_i), \\ \frac{1-\nu _M(x_i)-z}{1-\mu _M(x_i)-\nu _M(x_i)},~~~~~~~~~\text {if}~~z\in [\mu _M(x_i),1-\nu _M(x_i)], \\ 0,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text {otherwise}.\\ \end{array}\right. }\)
| |
Hung and Yang [39] |
\(S_{HY1}(M,N)=1-\frac{\sum \nolimits _{i=1}^n\text {max}(|\mu _M(x_i)-\mu _N(x_i)|,|\nu _M(x_i)-\nu _N(x_i)|)}{n},\)
|
\(S_{HY2}(M,N)=\frac{e^{S_{HY1}(M,N)-1}-e^{-1}}{1-e^{-1}},S_{HY3}(M,N)=\frac{S_{HY1}(M,N)}{2-S_{HY1}(M,N)}\)
| |
Hong and Kim [40] |
\(S_{HK}(M,N)=1-\frac{\sum \nolimits _{i=1}^n(|\mu _M(x_i)-\mu _N(x_i)|+|\nu _M(x_i)-\nu _N(x_i)|)}{2n}\)
|
Li and Cheng [41] |
\(S_{LC}(M,N)=1-\root p \of {\frac{\sum _{i=1}^n|\psi _{M}(x_i)-\psi _{N}(x_i)|^p}{n}},\)
|
where \(\psi _{M}(x_i)=\frac{\mu _M(x_i)+1-\nu _M(x_i)}{2},\psi _{N}(x_i)=\frac{\mu _N(x_i)+1-\nu _N(x_i)}{2}, \text {and} ~1\le p<\infty \). | |
Li and Xu [42] |
\(S_{LX}(M,N)=1-\frac{\sum \nolimits _{i=1}^n(|\mu _M(x_i)-\nu _M(x_i)-(\mu _N(x_i)-\nu _N(x_i))|+|\mu _M(x_i)-\mu _N(x_i)|+|\nu _M(x_i)-\nu _N(x_i)|)}{4n}\)
|
Liang and Shi [43] | \( S_{LS1}(M,N)=1-\root p \of {\frac{\sum _{i=1}^n|\phi _{\mu }(x_i)+\phi _{\nu }(x_i)|}{n}},S_{LS2}(M,N)=1-\root p \of {\frac{\sum _{i=1}^n|\varphi _{\mu }(x_i)+\varphi _{\nu }(x_i)|}{n}}\), |
\( S_{LS3}(M,N)=1-\root p \of {\frac{\sum _{i=1}^n (\eta _1(x_i)+\eta _2(x_i)+\eta _3(x_i))^p}{3n}},\)
| |
where \(\phi _{\mu }(x_i)=\frac{|\mu _M(x_i)-\mu _N(x_i)|}{2},\phi _{\nu }(x_i)=\frac{|\nu _M(x_i))-\nu _N(x_i)|}{2},\varphi _{\mu }(x_i)=\frac{|m_{M1}(x_i)-m_{N1}(x_i)|}{2},\) | |
\(\varphi _{\nu }(x_i)=\frac{|m_{M2}(x_i)-m_{N2}(x_i)|}{2},m_{M1}(x_i)= \frac{|\mu _{M}(x_i)+m_{M}(x_i)|}{2},m_{N1}(x_i)=\frac{|\mu _{N}(x_i)+m_{N}(x_i)|}{2}, \)
| |
\(m_{M2}(x_i)=\frac{|1-\nu _{M}(x_i)+m_{M}(x_i)|}{2},m_{N2}(x_i)=\frac{|1-\nu _{N}(x_i)+m_{N}(x_i)|}{2},m_{M}(x_i)=\frac{|\mu _{M}(x_i)+1-\nu _{M}(x_i)|}{2}, \)
| |
\(m_{N}(x_i)=\frac{|\mu _{N}(x_i)+1-\nu _{N}(x_i)|}{2} ,\eta _1(x_i)=\frac{|\mu _{M}(x_i)-\mu _{N}(x_i)|+|\nu _{M}(x_i)-\nu _{N}(x_i)|}{2},\)
| |
\( \eta _2(x_i)=\frac{|(\mu _{M}(x_i)-\nu _{M}(x_i))-(\mu _{N}(x_i)-\nu _{N}(x_i))|}{2}, \eta _3(x_i)=\text {max}(\frac{\pi _M(x_i)}{2},\frac{\pi _N(x_i)}{2})-\text {min}(\frac{\pi _M(x_i)}{2},\frac{\pi _N(x_i)}{2}).\)
| |
Mitchell [44] | \(S_M(M,N)=\frac{\rho _{\mu }(M,N)+\rho _{\nu }(M,N)}{2}\), |
where \(\rho _{\mu }(M,N)=1-\root p \of {\frac{\sum _{i=1}^n|\mu _M(x_i)-\mu _N(x_i)|^p}{n}},\rho _{\nu }(M,N)=1-\root p \of {\frac{\sum _{i=1}^n|\nu _M(x_i)-\nu _N(x_i)|^p}{n}}, \text {and} ~1\le p<\infty \). | |
Ye [45] |
\(S_Y(M,N)=\frac{1}{n}\sum \nolimits _{i=1}^n\frac{\mu _M(x_i)\mu _N(x_i)+\nu _M(x_i)\nu _N(x_i)}{\sqrt{\mu _M^2(x_i)+\nu _M^2(x_i)} \sqrt{\mu _N^2(x_i)+\nu _N^2(x_i)}}\)
|
Wei and Wei [32] |
\(S_W(M,N)=\frac{1}{n}\sum \nolimits _{i=1}^n\frac{\mu _M^2(x_i)\mu _N^2(x_i)+\nu _M^2(x_i)\nu _N^2(x_i)}{\sqrt{\mu _M^4(x_i)+\nu _M^4(x_i)} \sqrt{\mu _N^4(x_i)+\nu _N^4(x_i)}}\)
|
Zhang [33] |
\(S_Z(M,N)=\)
|
\(\frac{1}{n}\sum \nolimits _{i=1}^n\frac{|\mu _M^2(x_i)-\nu _N^2(x_i)|+|\nu _M^2(x_i)-\mu _N^2(x_i)|+|\pi _M^2(x_i)-\pi _N^2(x_i)|}{|\mu _M^2(x_i)-\mu _N^2(x_i)|+|\nu _M^2(x_i)-\nu _N^2(x_i)|+|\pi _M^2(x_i)-\pi _N^2(x_i)|+|\mu _M^2(x_i)-\nu _N^2(x_i)| +|\nu _M^2(x_i)-\mu _N^2(x_i)|+|\pi _M^2(x_i)-\pi _N^2(x_i)|}\)
| |
Peng et al. [34] |
\(S_{P1}(M,N)=1-\frac{\sum \nolimits _{i=1}^n|\mu _M^2(x_i)-\nu _M^2(x_i)-(\mu _N^2(x_i)-\nu _N^2(x_i))|}{2n} \)
|
\(S_{P2}(M,N)=\frac{1}{n}\sum \nolimits _{i=1}^n\frac{(\mu _M^2(x_i)\bigwedge \mu _N^2(x_i))+(\nu _M^2(x_i)\bigwedge \nu _N^2(x_i))}{(\mu _M^2(x_i)\bigvee \mu _N^2(x_i))+(\nu _M^2(x_i)\bigvee \nu _N^2(x_i))}\)
| |
\(S_{P3}(M,N)=\frac{1}{n}\sum \nolimits _{i=1}^n\frac{(\mu _M^2(x_i)\bigwedge \mu _N^2(x_i))+(1-\nu _M^2(x_i))\bigwedge (1-\nu _N^2(x_i))}{(\mu _M^2(x_i)\bigvee \mu _N^2(x_i))+(1-\nu _M^2(x_i))\bigvee (1-\nu _N^2(x_i))}\)
| |
Boran and Akay [46] |
\(S_{BA}(M,N)=1-\root p \of {\frac{\sum \nolimits _{i=1}^n \{ |t(\mu _M(x_i)-\mu _N(x_i))-(\nu _M(x_i)-\nu _N(x_i))|^p+|t(\nu _M(x_i)-\nu _N(x_i))-(\mu _M(x_i)-\mu _N(x_i))|^p \}}{2n(t+1)^p}}\)
|
Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | Case 6 | |
---|---|---|---|---|---|---|
M
|
\(\{\langle x,0.3,0.3\rangle \} \)
|
\( \{\langle x,0.3,0.4\rangle \}\)
|
\(\{\langle x,1,0\rangle \} \)
|
\(\{\langle x,0.5,0.5\rangle \} \)
|
\(\{\langle x,0.4,0.2\rangle \} \)
|
\(\{\langle x,0.4,0.2\rangle \} \)
|
N
|
\(\{\langle x,0.4,0.4\rangle \} \)
|
\( \{\langle x,0.4,0.3\rangle \}\)
|
\( \{\langle x,0,0\rangle \} \)
|
\(\{\langle x,0,0\rangle \} \)
|
\( \{\langle x,0.5,0.3\rangle \} \)
|
\(\{\langle x,0.5,0.2\rangle \} \)
|
\(S_{L} \) [36] |
\(\mathbf{0.9}\)
|
\(\mathbf{0.9}\)
| 0.2929 | 0.5 |
\(\mathbf{0.9} \)
| 0.9293 |
\(S_{C}\) [37] |
\(\mathbf{1}\)
| 0.9 | 0.5 |
\( \mathbf{1}\)
|
\( \mathbf{1}\)
| 0.95 |
\(S_{CC}\) [38] | 0.9225 | 0.88 | 0.25 | 0.5 | 0.9225 | 0.8913 |
\(S_{HY1}\) [39] |
\(\mathbf{0.9} \)
|
\( \mathbf{0.9}\)
|
\( \mathbf{0}\)
| 0.5 |
\(\mathbf{0.9} \)
|
\( \mathbf{0}.\mathbf{9}\)
|
\(S_{HY2}\) [39] |
\(\mathbf{0.8495} \)
|
\( \mathbf{0.8495}\)
|
\( \mathbf{0}\)
| 0.3775 |
\(\mathbf{0.8495} \)
|
\(\mathbf{0}.\mathbf{8495} \)
|
\(S_{HY3}\) [39] |
\( \mathbf{0.8182}\)
|
\(\mathbf{0.8182} \)
|
\(\mathbf{0} \)
| 0.3333 |
\( \mathbf{0.8182}\)
|
\(\mathbf{0}.\mathbf{8182} \)
|
\(S_{HK}\) [40] |
\(\mathbf{0.9} \)
|
\(\mathbf{0.9} \)
|
\(\mathbf{0.5} \)
|
\(\mathbf{0.5} \)
|
\(\mathbf{0.9} \)
| 0.95 |
\(S_{LC} \) [41] |
\(\mathbf{1} \)
| 0.9 | 0.5 |
\( \mathbf{1}\)
|
\(\mathbf{1} \)
| 0.95 |
\(S_{LX} \) [42] | 0.95 | 0.9 | 0.5 | 0.75 |
\( \mathbf{0.95}\)
|
\(\mathbf{0}.\mathbf{95} \)
|
\(S_{LS1} \) [43] |
\(\mathbf{0.9} \)
|
\(\mathbf{0.9} \)
|
\(\mathbf{0.5} \)
|
\(\mathbf{0.5} \)
|
\(\mathbf{0.9}\)
| 0.95 |
\(S_{LS2} \) [43] | 0.95 | 0.9 | 0.5 | 0.75 |
\(\mathbf{0.95} \)
|
\(\mathbf{0}.\mathbf{95}\)
|
\(S_{LS3} \) [43] |
\(\mathbf{0.9333 }\)
|
\(\mathbf{0.9333}\)
| 0.5 | 0.6667 |
\(\mathbf{0.9333} \)
| 0.95 |
\(S_{M} \) [44] |
\( \mathbf{0.9}\)
|
\(\mathbf{0.9} \)
|
\(\mathbf{0.5} \)
|
\(\mathbf{0.5} \)
|
\( \mathbf{0.9}\)
| 0.95 |
\(S_{Y} \) [45] |
\( \mathbf{1}\)
| 0.96 |
\(\text {N/A} \)
|
\( \text {N/A}\)
| 0.9971 | 0.9965 |
\(S_W \) [32] |
\(\mathbf{1} \)
| 0.8546 | N / A | N / A |
\( \mathbf{0.9949}\)
| 0.9963 |
\(S_Z \) [33] | 0.5 |
\( \mathbf{0}\)
|
\(\mathbf{0.5} \)
|
\( \mathbf{0.5}\)
|
\(\mathbf{0.6 }\)
| 0.7 |
\(S_{P1}\) [34] |
\(\mathbf{1}\)
| 0.93 | 0.5 |
\(\mathbf{1} \)
| 0.98 | 0.955 |
\(S_{P2}\) [34] |
\(\mathbf{0.5625} \)
|
\(\mathbf{0.5625} \)
|
\(\mathbf{0} \)
|
\(\mathbf{0} \)
|
\( \mathbf{0.5882}\)
| 0.6897 |
\(S_{P3}\) [34] |
\( \mathbf{0.8692}\)
|
\(\mathbf{0.8692} \)
| 0.5 | 0.6 |
\( \mathbf{0.8843}\)
| 0.9256 |
\(S_{BA}\) [46] | 0.967 | 0.9 | 0.5 | 0.8333 | 0.9667 | 0.95 |
\(S(\text {proposed}) \)
| 0.9825 | 0.9300 | 0.3750 | 0.9375 | 0.9625 | 0.9438 |
Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | Case 6 | |
---|---|---|---|---|---|---|
M
|
\(\{\langle x,0.5,0.5\rangle \} \)
|
\( \{\langle x,0.6,0.4\rangle \}\)
|
\(\{\langle x,0,0.87\rangle \} \)
|
\(\{\langle x,0.6,0.27\rangle \}\)
|
\(\{\langle x,0.125,0.075\rangle \} \)
|
\(\{\langle x,0.5,0.45\rangle \} \)
|
N
|
\(\{\langle x,0,0\rangle \} \)
|
\( \{\langle x,0,0\rangle \}\)
|
\( \{\langle x,0.28,0.55\rangle \} \)
|
\(\{\langle x,0.28,0.55\rangle \}\)
|
\( \{\langle x,0.175,0.025\rangle \} \)
|
\(\{\langle x,0.55,0.4\rangle \}\)
|
\(S_{L} \) [36] | 0.5 | 0.4901 |
\(\mathbf{0}.\mathbf{6993} \)
|
\(\mathbf{0}.\mathbf{6993}\)
|
\(\mathbf{0}.\mathbf{95} \)
|
\(\mathbf{0}.\mathbf{95}\)
|
\(S_{C}\) [37] |
\(\mathbf{1}\)
| 0.9 |
\(\mathbf{0}.\mathbf{7} \)
|
\( \mathbf{0}.\mathbf{7} \)
|
\( \mathbf{0}.\mathbf{95}\)
|
\(\mathbf{0}.\mathbf{95}\)
|
\(S_{CC}\) [38] | 0.5 | 0.45 | 0.7395 | 0.7055 | 0.9125 | 0.95 |
\(S_{HY1}\) [39] | 0.5 | 0.4 |
\( \mathbf{0}.\mathbf{68}\)
|
\(\mathbf{0}.\mathbf{68} \)
|
\(\mathbf{0}.\mathbf{95} \)
|
\( \mathbf{0}.\mathbf{95}\)
|
\(S_{HY2}\) [39] | 0.3775 | 0.2862 |
\( \mathbf{0}.\mathbf{5668}\)
|
\( \mathbf{0}.\mathbf{5668}\)
|
\(\mathbf{0}.\mathbf{9229} \)
|
\(\mathbf{0}.\mathbf{9229}\)
|
\(S_{HY3}\) [39] | 0.3333 | 0.25 |
\(\mathbf{0}.\mathbf{5152} \)
|
\(\mathbf{0}.\mathbf{5152} \)
|
\( \mathbf{0}.\mathbf{9048}\)
|
\(\mathbf{0}.\mathbf{9048} \)
|
\(S_{HK}\) [40] |
\(\mathbf{0.5} \)
|
\(\mathbf{0}.\mathbf{5} \)
|
\(\mathbf{0}.\mathbf{7} \)
|
\(\mathbf{0}.\mathbf{7} \)
|
\(\mathbf{0}.\mathbf{95} \)
|
\(\mathbf{0}.\mathbf{95}\)
|
\(S_{LC} \) [41] |
\(\mathbf{1} \)
| 0.9 |
\(\mathbf{0}.\mathbf{7} \)
|
\( \mathbf{0}.\mathbf{7}\)
|
\(\mathbf{0}.\mathbf{95} \)
|
\( \mathbf{0}.\mathbf{95}\)
|
\(S_{LX} \) [42] | 0.75 | 0.7 |
\(\mathbf{0}.\mathbf{7} \)
|
\(\mathbf{0}.\mathbf{7} \)
|
\( \mathbf{0}.\mathbf{95}\)
|
\(\mathbf{0}.\mathbf{95} \)
|
\(S_{LS1} \) [43] |
\(\mathbf{0.5} \)
|
\(\mathbf{0}.\mathbf{5} \)
|
\(\mathbf{0}.\mathbf{7} \)
|
\(\mathbf{0}.\mathbf{7} \)
|
\(\mathbf{0}.\mathbf{95} \)
|
\(\mathbf{0}.\mathbf{95}\)
|
\(S_{LS2} \) [43] |
\(\mathbf{0.75} \)
|
\(\mathbf{0}.\mathbf{75} \)
|
\(\mathbf{0}.\mathbf{7} \)
|
\(\mathbf{0}.\mathbf{7} \)
|
\(\mathbf{0}.\mathbf{95} \)
|
\(\mathbf{0}.\mathbf{95}\)
|
\(S_{LS3} \) [43] | 0.6667 | 0.6333 |
\(\mathbf{0}.\mathbf{7933} \)
|
\(\mathbf{0}.\mathbf{7933} \)
|
\(\mathbf{0}.\mathbf{9667} \)
|
\(\mathbf{0}.\mathbf{9667}\)
|
\(S_{M} \) [44] |
\( \mathbf{0.5}\)
|
\(\mathbf{0}.\mathbf{5} \)
|
\(\mathbf{0}.\mathbf{7} \)
|
\(\mathbf{0}.\mathbf{7} \)
|
\( \mathbf{0}.\mathbf{95}\)
|
\(\mathbf{0}.\mathbf{95} \)
|
\(S_{Y} \) [45] |
\( \text {N/A}\)
|
\(\text {N/A}\)
| 0.8912 | 0.7794 | 0.9216 | 0.9946 |
\(S_W \) [32] | N / A | N / A | 0.968 | 0.438 | 0.9476 | 0.9812 |
\(S_Z \) [33] |
\( \mathbf{0.5}\)
|
\( \mathbf{0.5 }\)
| 0.5989 | 0.1696 | 0.625 | 0.6557 |
\(S_{P1}\) [34] |
\( \mathbf{1}\)
| 0.9 | 0.7336 | 0.7444 | 0.99 | 0.9525 |
\(S_{P2}\) [34] |
\(\mathbf{0} \)
|
\(\mathbf{0} \)
| 0.3621 | 0.2284 | 0.4483 | 0.8119 |
\(S_{P3}\) [34] | 0.6 | 0.6176 | 0.3133 | 0.6028 | 0.9806 | 0.9168 |
\(S_{BA}\) [46] |
\(\mathbf{0.8333} \)
|
\(\mathbf{0}.\mathbf{8333} \)
|
\(\mathbf{0}.\mathbf{7} \)
|
\(\mathbf{0}.\mathbf{7} \)
|
\(\mathbf{0}.\mathbf{95} \)
|
\(\mathbf{0}.\mathbf{95}\)
|
\(S(\text {proposed}) \)
| 0.9375 | 0.8350 | 0.7806 | 0.7379 | 0.9887 | 0.9513 |
Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | Case 6 | |
---|---|---|---|---|---|---|
M
|
\(\{\langle x,0.3,0.7\rangle \} \)
|
\( \{\langle x,0.3,0.7\rangle \}\)
|
\(\{\langle x,0.5,0.5\rangle \} \)
|
\(\{\langle x,0.4,0.6\rangle \} \)
|
\(\{\langle x,0.1,0.5\rangle \} \)
|
\(\{\langle x,0.4,0.2\rangle \} \)
|
N
|
\(\{\langle x,0.4,0.6\rangle \} \)
|
\( \{\langle x,0.2,0.8\rangle \}\)
|
\( \{\langle x,0,0\rangle \} \)
|
\(\{\langle x,0,0\rangle \} \)
|
\( \{\langle x,0.2,0.3\rangle \} \)
|
\(\{\langle x,0.2,0.3\rangle \} \)
|
\(S_{L} \) [36] |
\(\mathbf{0.6863} \)
|
\(\mathbf{0.6863}\)
| 0.5 | 0.4901 |
\(\mathbf{0}.\mathbf{8419} \)
|
\(\mathbf{0}.\mathbf{8419}\)
|
\(S_{C}\) [37] |
\(\mathbf{0.9}\)
|
\(\mathbf{0.9} \)
|
\(\mathbf{1} \)
| 0.9 |
\( \mathbf{0}.\mathbf{85}\)
|
\(\mathbf{0}.\mathbf{85}\)
|
\(S_{CC}\) [38] |
\(\mathbf{0.9}\)
|
\(\mathbf{0.9} \)
| 0.5 | 0.55 | 0.8438 | 0.7685 |
\(S_{HY1}\) [39] |
\(\mathbf{0.9}\)
|
\(\mathbf{0.9}\)
| 0.5 | 0.4 |
\(\mathbf{0}.\mathbf{8} \)
|
\( \mathbf{0}.\mathbf{8}\)
|
\(S_{HY2}\) [39] |
\(\mathbf{0.8494} \)
|
\(\mathbf{0.8494}\)
| 0.3775 | 0.2862 |
\(\mathbf{0}.\mathbf{7132} \)
|
\(\mathbf{0}.\mathbf{7132} \)
|
\(S_{HY3}\) [39] |
\(\mathbf{0.8182}\)
|
\(\mathbf{0.8182} \)
| 0.3333 | 0.25 |
\( \mathbf{0}.\mathbf{6667}\)
|
\(\mathbf{0}.\mathbf{6667} \)
|
\(S_{HK}\) [40] |
\(\mathbf{0.9}\)
|
\(\mathbf{0.9} \)
|
\(\mathbf{0.5} \)
|
\(\mathbf{0.5} \)
|
\(\mathbf{0}.\mathbf{85} \)
|
\(\mathbf{0}.\mathbf{85}\)
|
\(S_{LC} \) [41] |
\(\mathbf{0.9} \)
|
\(\mathbf{0.9}\)
|
\(\mathbf{1} \)
| 0.9 |
\(\mathbf{0}.\mathbf{85} \)
|
\( \mathbf{0}.\mathbf{85}\)
|
\(S_{LX} \) [42] |
\(\mathbf{0.9}\)
|
\(\mathbf{0.9} \)
| 0.75 | 0.7 |
\( \mathbf{0}.\mathbf{85}\)
|
\(\mathbf{0}.\mathbf{85} \)
|
\(S_{LS1} \) [43] |
\(\mathbf{0.9}\)
|
\(\mathbf{0.9} \)
|
\(\mathbf{0.5} \)
|
\(\mathbf{0.5} \)
|
\(\mathbf{0}.\mathbf{85} \)
|
\(\mathbf{0}.\mathbf{85}\)
|
\(S_{LS2} \) [43] |
\(\mathbf{0.9}\)
|
\(\mathbf{0.9} \)
| 0.5 | 0.75 |
\(\mathbf{0}.\mathbf{85} \)
|
\(\mathbf{0}.\mathbf{85}\)
|
\(S_{LS3} \) [43] |
\(\mathbf{0.95}\)
|
\(\mathbf{0.95} \)
| 0.6667 | 0.6333 |
\(\mathbf{0}.\mathbf{8833} \)
|
\(\mathbf{0}.\mathbf{8833}\)
|
\(S_{M} \) [44] |
\( \mathbf{0.9}\)
|
\(\mathbf{0.9} \)
|
\(\mathbf{0.5} \)
|
\(\mathbf{0.5} \)
|
\( \mathbf{0}.\mathbf{85}\)
|
\(\mathbf{0}.\mathbf{85}\)
|
\(S_{Y} \) [45] | 0.9832 | 0.9873 |
\(\text {N/A}\)
|
\(\text {N/A}\)
| 0.9249 | 0.8685 |
\(S_W \) [32] | 0.9721 | 0.9929 | N / A | N / A | 0.9293 | 0.6156 |
\(S_Z \) [33] | 0.7174 | 0.7857 |
\(\mathbf{0.5 } \)
|
\(\mathbf{0.5 } \)
| 0.5676 | 0.3684 |
\(S_{P1}\) [34] |
\(\mathbf{0.9} \)
|
\(\mathbf{0.9} \)
|
\( \mathbf{1} \)
| 0.9 | 0.905 | 0.915 |
\(S_{P2}\) [34] | 0.6923 | 0.726 |
\(\mathbf{0} \)
|
\( \mathbf{0} \)
| 0.3448 | 0.32 |
\(S_{P3}\) [34] | 0.75 | 0.6667 | 0.6 | 0.5517 | 0.8 | 0.8482 |
\(S_{BA}\) [46] |
\(\mathbf{0.9}\)
|
\(\mathbf{0.9} \)
|
\(\mathbf{0.8333} \)
|
\(\mathbf{0.8333} \)
|
\(\mathbf{0}.\mathbf{8667} \)
|
\(\mathbf{0}.\mathbf{8667} \)
|
\(S(\text {proposed}) \)
| 0.9075 | 0.9125 | 0.9375 | 0.9350 | 0.9212 | 0.9063 |