\chapter*{NOTATIONS}

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%%   NOTATIONS
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\begin{tabbing}
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\hspace{1cm}\= \textbf{Symbols}\qquad\qquad\= \textbf{Description}\\
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\>\textbf{$p_g$}\>Best particle in overall swarm\\
\>\textbf{$p_l$}\>Best particle in the local swarm\\
\>\textbf{$p_i$}\>Best position of $i$th particle visited in past\\
\>\textbf{$\varphi_1$}\>Cognitive acceleration parameter\\
\>\textbf{$\overline{A}$}\>Complement of T1 FS ($A$)\\
\>\textbf{$\chi$}\>Constriction factor\\
\>\textbf{$A_e$}\>Embedded T1 FS of $\tilde{A}$\\
\>\textbf{$\tilde{A}_e$}\>Embedded T2 or IT2 FS of $\tilde{A}$\\
\>\textbf{$\vee$}\>Fuzzy $t$-conorm (union) operator\\
\>\textbf{$\bigstar$}\>Fuzzy $t$-norm (general) operator\\
\>\textbf{$\wedge$}\>Fuzzy $t$-norm (minimum) operator\\
\>\textbf{$\int$}\>Fuzzy union over continuous universe of discourse\\
\>\textbf{$\sum$}\>Fuzzy union over discrete universe of discourse\\
\>\textbf{$w$}\>Inertia weight\\
\>\textbf{$\underline{\mu}_{\tilde{A}}(x)$}\>LMF of T2 or IT2 FS ($\tilde{A}$)\\
\>\textbf{$V_{max}$}\>Maximum particle velocity\\
\>\textbf{$\mu_A(x)$}\>MF for T1 FS ($A$)\\

\rule{35em}{0.5pt}\\[6pt]
\hspace{1cm}\= \textbf{Symbols}\qquad\qquad\= \textbf{Description}\\
\rule{35em}{0.5pt}\\[5pt]

\>\textbf{$\mu_{\tilde{A}}(x)$}\>MF of T2 or IT2 FS ($\tilde{A}$)\\
\>\textbf{$x_i$}\>Present position of $i$th particle in PSO or $i$th input to an FLS\\
\>\textbf{$v_i$}\>Present velocity of $i$th particle\\
\>\textbf{$J_x$}\>Primary membership grade over $x \in X$\\
\>\textbf{$\varphi_2$}\>Social acceleration parameter\\
\>\textbf{$\cup$}\>T1 fuzzy $t$-conorm (union) operator\\
\>\textbf{$\cap$}\>T1 fuzzy $t$-norm (intersection) operator\\
\>\textbf{$\tilde{A}$}\>T2 FS ($A$)\\
\>\textbf{$\sqcup$}\>T2 fuzzy $t$-conorm (join) operator\\
\>\textbf{$\sqcap$}\>T2 fuzzy $t$-norm (meet) operator\\
\>\textbf{$\neg{\tilde{A}}$}\>T2 fuzzy negation operation of $\tilde{A}$\\
\>\textbf{$/$}\>Tuple\\
\>\textbf{$\overline{\mu}_{\tilde{A}}(x)$}\>UMF of T2 or IT2 FS ($\tilde{A}$)\\
\>\textbf{$X$}\>Universe of discourse of $x$\\


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