1 Correction to: Granular Computing https://doi.org/10.1007/s41066-017-0068-z

Unfortunately there were several typesetting mistakes in the original article.

In Section 2.6, fourth line, the lower membership function has to read \({\underset{\raise0.5em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu } {_{\tilde {A}}}}.\) This was also incorrect in the following equation. The correct equation is:

$${\bar {\mu }_{\tilde {A}}}\left( x \right)=\left\{ {\begin{array}{*{20}{l}} {\frac{{x - a}}{{b - a}}}&&{\quad {\text{if}}\quad a \leqslant x \leqslant b} \\ 1&&{\quad {\text{if}}\quad b \leqslant x \leqslant c} \\ {\frac{{d - x}}{{d - c}}}&&{\quad {\text{if}}\quad c \leqslant x \leqslant d} \\ 0&&{\quad {\text{otherwise}}} \end{array}} \right.\quad {\text{and}}\quad {\underset{\raise0.5em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu } {_{\tilde {A}}}}\left( x \right)=\left\{ {\begin{array}{*{20}{l}} {\frac{{x - e}}{{f - e}}w}&&{\quad {\text{if}}\quad e \leqslant x \leqslant f} \\ w&&{\quad {\text{if}}\quad f \leqslant x \leqslant g} \\ {\frac{{h - x}}{{h - g}}w}&&{\quad {\text{if}}\quad g \leqslant x \leqslant h} \\ 0&&{\quad {\text{otherwise}}} \end{array}} \right..$$

In Table 2 the ranking values of Qin and Liu (2015) were incorrectly displayed. It is conformable with the previous presentations.

In Section 5.1, equation 5, the symbols “-” and “~” were wrongly placed. The correct equation reads:

$$\begin{aligned} &{\text{Find}}\;X({x_1},\,{x_2}, \ldots ,\,{x_n})\;{\text{so}}\;{\text{as}}\;{\text{to}} \\ &{\text{Maximize}}\;DV\left( {{{\tilde {\tilde {Z}}}_k}} \right)=\mathop \sum \limits_{{j=1}}^{n} DV\left( {{{\tilde {\tilde {c}}}_{kj}}} \right){x_j};\quad k=1,2, \ldots ,K \\ &{\text{Subject}}\;{\text{to}}\;\mathop \sum \limits_{{j=1}}^{n} DV\left( {{{\tilde {\tilde {a}}}_{ij}}} \right){x_j} \leqslant \; \! DV\left( {{{\tilde {\tilde {b}}}_i}} \right);\quad i=1,2, \ldots ,m \\ & {x_j} \geqslant 0;\qquad\qquad\qquad\quad \qquad\quad \qquad\quad j=1,2, \ldots .,n \\ \end{aligned}$$
(5)

In equation 6, the first line is to be replaced by Find X(x_1,x_2,…,x_n ) in place of X(x_1,-x_2,-,…,-x_n ). Also the sign '~' is to be deleted after '≤' sign in fourth line of equation 6.