Table 1 Fuzzy mean divergence measures

$A\left(A,B\right)={\displaystyle \sum _{i=1}^n\left(\frac{{\mu }_A\left(x_i\right)+{\mu }_B\left(x_i\right)}{2}+\frac{2-{\mu }_A\left(x_i\right)-{\mu }_B\left(x_i\right)}{2}\right)}$

$G\left(A,B\right)={\displaystyle \sum _{i=1}^n\left(\sqrt{{\mu }_A\left(x_i\right){\mu }_B\left(x_i\right)}+\sqrt{\left(1-{\mu }_A\left(x_i\right)\left)\right(1-{\mu }_B\left(x_i\right)\right)}\right)}$

$H\left(A,B\right)={\displaystyle \sum _{i=1}^n\left(\frac{2{\mu }_A\left(x_i\right){\mu }_B\left(x_i\right)}{{\mu }_A\left(x_i\right)+{\mu }_B\left(x_i\right)}+\frac{2\left(1-{\mu }_A\left(x_i\right)\right)\left(1-{\mu }_B\left(x_i\right)\right)}{2-{\mu }_A\left(x_i\right)-{\mu }_B\left(x_i\right)}\right)}$

$N\left(A,B\right)={\displaystyle \sum _{i=1}^n\left(\frac{{\mu }_A\left(x_i\right)+\sqrt{{\mu }_A\left(x_i\right){\mu }_B\left(x_i\right)}+{\mu }_B\left(x_i\right)}{3}+\frac{\left(1-{\mu }_A\left(x_i\right))+\sqrt{\left(1-{\mu }_A\left(x_i\right)\left)\right(1-{\mu }_B\left(x_i\right)\right)}+(1-{\mu }_B\left(x_i\right)\right)}{3}\right)}$

$C\left(A,B\right)={\displaystyle \sum _{i=1}^n\left(\frac{{\mu }_A^2\left(x_i\right)+{\mu }_B^2\left(x_i\right)}{{\mu }_A\left(x_i\right)+{\mu }_B\left(x_i\right)}+\frac{{\left(1-{\mu }_A\left(x_i\right)\right)}^2+{\left(1-{\mu }_B\left(x_i\right)\right)}^2}{2-{\mu }_A\left(x_i\right)-{\mu }_B\left(x_i\right)}\right)}$

$S\left(A,B\right)={\displaystyle \sum _{i=1}^n\left(\sqrt{\frac{{\mu }_A^2\left(x_i\right)+{\mu }_B^2\left(x_i\right)}{2}}+\sqrt{\frac{{\left(1-{\mu }_A\left(x_i\right)\right)}^2+{\left(1-{\mu }_B\left(x_i\right)\right)}^2}{2}}\right)}$

$R\left(A,B\right)={\displaystyle \sum _{i=1}^n\left(\frac{2\left({\mu }_A^2\left(x_i\right)+{\mu }_A\left(x_i\right){\mu }_B\left(x_i\right)+{\mu }_B^2\left(x_i\right)\right)}{3\left({\mu }_A\left(x_i\right)+{\mu }_B\left(x_i\right)\right)}+\frac{2\left({\left(1-{\mu }_A\left(x_i\right)\right)}^2+\left(1-{\mu }_A\left(x_i\right)\right)\left(1-{\mu }_B\left(x_i\right)\right)+{\left(1-{\mu }_B\left(x_i\right)\right)}^2\right)}{3\left(2-{\mu }_A\left(x_i\right)-{\mu }_B\left(x_i\right)\right)}\right)}$