Table 2.

I/O variables membership functions used in the proposed FL-OLMPSO.

S. no.	Input variables	Mathematical representation of membership functions (MFs)	Graphical representation of MFs
1	LocalInt ((μlocalint(l))	${\mu }_{\text{localint},\text{small}}\left(l\right)=\left\{\begin{array}{cc}\left(0.35-l\right)/0.35,& 0\le l\le 0.35\\ 0,& \text{else}\end{array}\right\}$ ${\mu }_{\text{localint},\text{medium}}\left(l\right)=\left\{\begin{array}{cc}\left(l/0.35\right),& 0\le l\le 0.35\\ \left(0.65-l\right)/0.3,& 0.35\le l\le 0.65\end{array}\right\}$ ${\mu }_{\text{localint},\text{large}}\left(l\right)=\left\{\begin{array}{cc}\left(l-0.35\right)/0.35,& 0.35\le l\le 0.65\\ \left(1-l\right)/0.35,& 0.65\le l\le 1\end{array}\right\}$ ${\mu }_{\text{localint},\text{v}.\text{large}}\left(l\right)=\left\{\begin{array}{cc}\left(l-0.65\right)/0.35,& 0.65\le l\le 1\\ 0,& \text{else}\end{array}\right\}$
2	GlobalInt (μglobalInt(G))	${\mu }_{\text{globalint},\text{small}}\left(G\right)=\left\{\begin{array}{cc}\left(0.35-g\right)/0.35,& 0\le g\le 0.35\\ 0,& \text{else}\end{array}\right\}$ ${\mu }_{\text{globalint},\text{medium}}\left(G\right)=\left\{\begin{array}{cc}g/0.35,& 0\le g\le 0.35\\ \left(0.65-g\right)/0.3,& 0.35\le g\le 0.65\end{array}\right\}$ ${\mu }_{\text{globalint},\text{large}}\left(G\right)=\left\{\begin{array}{cc}\left(0.35-g\right)/0.35,& 0\le g\le 0.35\\ 0,& \text{else}\end{array}\right\}$ ${\mu }_{\text{globalint},\text{v}.\text{large}}\left(G\right)=\left\{\begin{array}{cc}g/0.35,& 0\le g\le 0.35\\ \left(0.65-g\right)/0.3,& 0.35\le g\le 0.65\end{array}\right\}$
3	Prevelocity (μprevelocity(PV))	${\mu }_{\text{prevelocity},\text{v}.\text{slow}}\left(PV\right)=\left\{\begin{array}{cc}\left(0.5-pv\right)/0.5,& 0\le pv\le 0.5\\ 0,& \text{else}\end{array}\right\}$ ${\mu }_{\text{prevelocity},\text{slow}}\left(PV\right)=\left\{\begin{array}{cc}pv/0.25,& 0\le pv\le 0.25\\ \left(1-pv\right)/0.75,& 0.25\le pv\le 1\end{array}\right\}$ ${\mu }_{\text{prevelocity},\text{medium}}\left(PV\right)=\left\{\begin{array}{cc}\left(pv-1\right)/0.75,& 0.25\le pv\le 1\\ \left(1.5-pv\right)/0.5,& 1\le pv\le 1.5\end{array}\right\}$ ${\mu }_{\text{prevelocity},\text{fast}}\left(PV\right)=\left\{\begin{array}{cc}\left(pv-1.5\right)/0.5,& 1\le pv\le 1.5\\ \left(2-pv\right)/0.5,& 1.5\le pv\le 2\end{array}\right\}$ ${\mu }_{\text{prevelocity},\text{v}.\text{fast}}\left(PV\right)=\left\{\begin{array}{cc}\left(pv-2\right)/0.5,& 1.5\le pv\le 2\\ 0.& \text{else}\end{array}\right\}$
4	Output, UV (μoutput,UV(UV))	${\mu }_{UV,\text{v}.\text{slow}}\left(UV\right)=\left\{\begin{array}{cc}uv/0.2,& 0\le uv\le 0.1\\ \left(0.4-uv\right)/0.2,& 0.1\le uv\le 0.2\end{array}\right\}$ ${\mu }_{UV,\text{slow}}\left(UV\right)=\left\{\begin{array}{cc}\left(uv-0.3\right)/0.2,& 0.1\le uv\le 0.25\\ \left(0.5-uv\right)/0.2,& 0.25\le uv\le 0.4\end{array}\right\}$ ${\mu }_{UV,\text{medium}}\left(UV\right)=\left\{\begin{array}{cc}\left(uv-0.8\right)/0.2,& 0.3\le uv\le 0.45\\ \left(1-uv\right)/0.2,& 0.45\le uv\le 0.6\end{array}\right\}$ ${\mu }_{UV,\text{fast}}\left(UV\right)=\left\{\begin{array}{cc}\left(uv-0.8\right)/0.2,& 0.5\le uv\le 0.65\\ \left(1-uv\right)/0.2,& 0.65\le uv\le 0.8\end{array}\right\}$ ${\mu }_{UV,\text{v}.\text{fast}}\left(UV\right)=\left\{\begin{array}{cc}\left(uv-0.8\right)/0.2,& 0.7\le uv\le 0.85\\ \left(1-uv\right)/0.2,& 0.85\le uv\le 1\end{array}\right\}$