Table 5 Notation Set I Set of experts ∀... | Emerald Publishing

Table 5

Notation

Set
$I$	Set of experts $\forall i \in I$
$J$	Set of criteria $\forall j \in J$
$K$	Set of sub-criteria $\forall k \in K$
$R$	Set of rank $\forall r \in R$
Index
$i$	Index of experts (⁠ $i = 1, 2, 3 . . p$ ⁠)
$j$	Index of criteria (⁠ $j = 1, 2, 3 . . n$ ⁠)
$k$	Index of sub-criteria (⁠ $k = 1, 2, 3 . . s$ ⁠)
$r$	Rank of the linguistic variables (⁠ $r = 1, 2 \dots . h)$
Parameters
$\tilde{L_{i j}^{r}}$	Fuzzy linguistic variables positioned at rank $r$ rated to criteria $j$ by expert $i$
$\tilde{L_{i j k}^{r}}$	Fuzzy linguistic variables positioned at rank $r$ rated to sub-criteria $k$ of criteria $j$ by expert $i$
Variables
$\tilde{Z}$	Fuzzy objective function
$\tilde{W_{i j}^{r}}$	Fuzzy weight for criteria $j$ positioned at rank $r$ by expert $i$ ⁠. $\tilde{W_{i j}^{r}} = [l_{i j}, m_{i j}, u_{i j}]$
$\tilde{W_{i j k}^{r}}$	Fuzzy weight for sub-criteria $k$ of criteria $j$ positioned at rank $r$ by expert $i .$ $\tilde{W_{i j k}^{r}} = [l_{i j k}, m_{i j k}, u_{i j k}]$
${D F}_{j}$	Crisp weight of criteria $j$ after defuzzification
${D F}_{j k}$	Crisp weight of sub-criteria $k$ of criteria $j$ after defuzzification
${G W}_{j k}$	Global crisp weight of sub-criteria $k$ of criteria $j$

Set
$I$	Set of experts $\forall i \in I$
$J$	Set of criteria $\forall j \in J$
$K$	Set of sub-criteria $\forall k \in K$
$R$	Set of rank $\forall r \in R$
Index
$i$	Index of experts ( $i = 1, 2, 3 . . p$ )
$j$	Index of criteria ( $j = 1, 2, 3 . . n$ )
$k$	Index of sub-criteria ( $k = 1, 2, 3 . . s$ )
$r$	Rank of the linguistic variables ( $r = 1, 2 \dots . h)$
Parameters
$\tilde{L_{i j}^{r}}$	Fuzzy linguistic variables positioned at rank $r$ rated to criteria $j$ by expert $i$
$\tilde{L_{i j k}^{r}}$	Fuzzy linguistic variables positioned at rank $r$ rated to sub-criteria $k$ of criteria $j$ by expert $i$
Variables
$\tilde{Z}$	Fuzzy objective function
$\tilde{W_{i j}^{r}}$	Fuzzy weight for criteria $j$ positioned at rank $r$ by expert $i$ . $\tilde{W_{i j}^{r}} = [l_{i j}, m_{i j}, u_{i j}]$
$\tilde{W_{i j k}^{r}}$	Fuzzy weight for sub-criteria $k$ of criteria $j$ positioned at rank $r$ by expert $i .$ $\tilde{W_{i j k}^{r}} = [l_{i j k}, m_{i j k}, u_{i j k}]$
${D F}_{j}$	Crisp weight of criteria $j$ after defuzzification
${D F}_{j k}$	Crisp weight of sub-criteria $k$ of criteria $j$ after defuzzification
${G W}_{j k}$	Global crisp weight of sub-criteria $k$ of criteria $j$

Source(s): Created by authors