On m-Polar Interval-valued Fuzzy Graph and its Application

Figures & data

Figure 1. 3-PFG.

Table 1. $m$-PFS on $V$.

	$a$	$b$	$c$	$d$	$e$
$p_1\circ V$	$0.5$	0.4	0.3	0.5	0.4
$p_2\circ V$	$0.4$	0.2	0.5	0.8	0.3
$p_3\circ V$	$0.7$	0.6	0.9	0.9	0.7

Table 2. $m$-PFS on $E$_.

	$ab$	$bc$	$cd$	$de$	$ae$
$p_1\circ E$	$0.3$	0.1	0.2	0.4	0.3
$p_2\circ E$	$0.2$	0.2	0.5	0.2	0.1
$p_3\circ E$	$0.5$	0.6	0.7	0.5	0.5

Figure 2. An IVFG.

Table 3. IVFS on $V$_.

	$a$	$b$	$d$	$e$
${\mu }_A^l$	$0.2$	0.2	0.5	0.3
${\mu }_A^u$	$0.4$	0.3	0.7	0.5

Table 4. IVFS on $E$.

	$ab$	$de$	$ae$
${\mu }_B^l$	$0.2$	0.3	0.2
${\mu }_B^u$	$0.3$	0.4	0.4

Figure 3. A $3$-PIVFG.

Figure 4. A $3$-PIVFG $G$ which is not complete.

Figure 5. A 3-PIVFG.

Figure 6. The complement of the 3-PIVFG of Figure 5.

Figure 7. A 3-PIVFG.

Figure 8. Complement of the 3-PIVFG of Figure 7.

Figure 9. Modified $\overline{G}$.

Figure 10. A $3$-PIVFG $G_1\left(V_1,A_1,B_1\right)$.

Figure 11. A $3$-PIVFG $G_2\left(V_2,A_2,B_2\right)$.

Figure 12. A $3$-PIVFG $G_1$

Figure 13. A $3$-PIVFG $G_2$.

Figure 14. A $3$-PIVFG $G$

Figure 15. Complement $\overline{G}$_.

Figure 16. A $3$-PIVFG $G_1=\left(V_1,A_1,B_1\right)$.

Figure 17. A $3$-PIVFG $G_2=\left(V_2,A_2,B_2\right)$.

Figure 18. A $3$-PIVFG $G_1=\left(V_1,A_1,B_1\right)$.

Figure 19. A $3$-PIVFG $G_2=\left(V_2,A_2,B_2\right).$

Figure 20. For the graph $G_1.$

Table 5. Marks given to each candidate.

	$Aman\left(v_1\right)$	$Survi\left(v_2\right)$	$Karan\left(v_3\right)$	$Piu\left(v_4\right)$	$Bibhu\left(v_5\right)$
$a$	$\left[0.3,0.6\right]$	$\left[0.4,0.6\right]$	$\left[0.2,0.5\right]$	$\left[0.1,0.7\right]$	$\left[0.1,0.5\right]$
$b$	$\left[0.2,0.3\right]$	$\left[0.3,0.5\right]$	$\left[0.4,0.6\right]$	$\left[0.2,0.6\right]$	$\left[0.4,0.9\right]$
$c$	$\left[0.1,0.4\right]$	$\left[0.2,0.6\right]$	$\left[0.4,0.9\right]$	$\left[0.2,0.8\right]$	$\left[0.3,0.7\right]$
$d$	$\left[0.1,0.2\right]$	$\left[0.2,0.6\right]$	$\left[0.3,0.7\right]$	$\left[0.2,0.6\right]$	$\left[0.4,0.6\right]$

Table 6. Marks given to each candidate.

	$v_1$	$v_2$	$v_3$	$v_4$	$v_5$
$ab$	$25$	$40$	$30$	$35$	$30$
$bc$	$20$	$30$	$45$	$40$	$50$
$ad$	$15$	$40$	$35$	$35$	$30$
$cd$	$15$	$35$	$40$	$40$	$45$
$bd$	$15$	$35$	$45$	$40$	$50$

Table 7. Rank given to each candidate.

	$R_1$	$R_2$	$R_3$	$R_4$	$R_5$
$ab$	$v_2$	$v_4$	$v_3$ and $v_5$	$v_1$
$bc$		$v_3$	$v_4$	$v_2$	$v_1$
$ad$	$v_2$	$v_3$ and $v_4$	$v_5$	$v_1$
$cd$	$v_5$	$v_3$ and $v_4$	$v_2$	$v_1$	$v_5$
$bd$	$v_5$	$v_3$	$v_4$	$v_1$	$v_1$

Table 8. Score of each candidate.

Candidate	Score
Aman	8
Survi	17
Karan	19
Piu	18
Bibhu	21