\chapter*{CERTIFICATE}

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%%   CERTIFICATE
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This is to certify that the thesis entitled, INVESTIGATIONS IN EVOLUTION OF TYPE-1 AND TYPE-2 FUZZY SYSTEMS submitted by Mr. SATVIR SINGH, for the award of the degree of Doctor of Philosophy in Electronics \& Communication Engineering to Maharshi Dayanand University, Rohtak (India) is a record of bonafide research work carried out by him under our guidance and supervision.

The results presented in this thesis have not been submitted to any other University for the award of any other degree or diploma.

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\begin{tabular}{l@{\extracolsep{0.2in}}r}
\textbf{(Supervisor)}                       &   \textbf{(Supervisor)}\\[5pt]
\textbf{Arun Khosla, Ph.D.},                &   \textbf{J. S. Saini, Ph.D.},\\[-4pt]
\textit{Associate Professor},               &   \textit{Professor \& Chairman},\\[-4pt]
Department of Electronics \& Comm. Engg.,   &   Department of Electrical Engineering,\\[-4pt]
Dr. B. R. Ambedkar                          &   Deenbandhu Chhotu Ram\\[-4pt]
National Institute of Technology,           &   University of Sc. \& Tech.,\\[-4pt]
Jalandhar (PB) INDIA                        &   Murthal, Sonipat (HR) INDIA\\


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%\multicolumn{2}{c}{\bfseries Prof.}\\
%\multicolumn{2}{c}{\textit Dean}\\
%\multicolumn{2}{c}{University College}\\
%\multicolumn{2}{c}{Maharishi Dayanand University}\\
%\multicolumn{2}{c}{Rohtak, Haryana, INDIA}\\

\end{tabular}
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