\chapter*{ABSTRACT}

%% ===================================================================================================================================================
%% ===================================================================================================================================================
%%   ABSTRACT
%% ===================================================================================================================================================
%% ===================================================================================================================================================

\section*{Introduction}
There were times when researchers strived to develop simple machines (systems) to increase production, then to automate them and, now, it's an era where the systems are not only automated but intelligent as well. Such systems are capable of learning from environmental changes, make creative decisions and, generalize them on their own. This could be possible with new paradigms of Artificial Intelligence (AI), viz., Genetic Algorithms (GAs), Particle Swarm Optimization (PSO), Fuzzy Logic (FL), Artificial Neural Networks (ANNs), Ant Colony Optimization (ACO), and many more, which are rooted in the natural systems rather than traditional mathematical models.

\section*{Major Contributions, Developments \& Observations}
This thesis advances the state of the art by contributing some of concepts to AI paradigms. Broadly saying, this thesis results in design implementations of some Type-1 (T1) and Interval Type-2 (IT2) Fuzzy Logic Systems, development of two, easy-to-use, toolboxes in the MATLAB environment and a framework for design automation of FLSs.

\subsection*{FLS Design Applications}
Two rudimentary T1 FLS designs are implemented, in hardware, with the objective of getting insights into design issues, during the initial stage of research. Both FLSs were meant for same application of captive power management, however, based on two different circuit design approaches, i.e., FPGA based digital circuitry and Op-Amp based analog circuitry. Then some more applications, involving advanced FLS design issues, are taken up to conduct deeper investigations. A T1 FLS for autonomous navigational control system for non-holonomic mobile vehicle is implemented, in simulation environment. From any arbitrary location, in the designated navigational area, with an arbitrary orientation the vehicle is allowed to navigate towards a fixed parking/docking location. To contain the uncertainties, originated from the use of linguistic variables of rule-base, the T1 FLS is then upgraded to IT2 FLS. With help of multiple simulation results it is concluded that the IT2 FLS design involves more computations, however, results in less traveled distance and better final vehicle alignment; hence, capable of outperforming the T1 FLS.

Two different FLS designs, i.e., T1 FLS and IT2 FLS, for another application of species classification of iris flowers are evolved using PSO and benchmark training data. However, the data set used for training, in latter design, is corrupted with uniform noise. It is observed from the simulations that IT2 FLS is capable of giving better classification results, even in the presence of noise.

\subsection*{Development of Toolboxes}
The necessity of programming, experienced during investigation of above FLS design application, spurred us to develop following general purpose toolboxes, in the MATLAB environment:
\begin{itemize}
\item[1.] Generalized Fuzzy System (GFS) Toolbox
\item[2.] Nature Inspired (NI) Toolbox
\end{itemize}
The GFS Toolbox facilitates the designing of FLSs based on T1 and/or IT2 FSs. During FLS design implementations, it is observed that to-date available literature addresses representation of IT2 FSs using LMF and UMF only. However, none has addressed the issue of how to obtain these LMF and UMF for every IT2 FS in real-world FLS design applications.

We have explored two more approaches, i.e., Left T1 FS+Right T1 FS and Principal FS+FOU, to represent IT2 FSs and, therefore, embedded into GUI of the GFS Toolbox. FLSs can be evaluated for their performance, in simulation, using GFS Rule Analyzer and GFS Surface Analyzer modules of the toolbox. Designing T1 FLS itself requires considerable knowledge in FL, so as to valuate various FLS parameters and this problem becomes more baffling once IT2 FSs are considered. As designing an FLS can be translated into an NP-hard optimization problem, so can be solved with EAs, available in modern heuristics and optimization science, to produce near optimal FLS design. PSO, relatively new among EAs, is getting increasingly popularity and, therefore, investigated in detail to develop another, easy to use, general purpose toolbox (NI Toolbox). This toolbox is helpful in exploiting most popular PSO models, topologies, neighbourhood sizes, and strategy parameters, etc. to find optimal solution to any general problem. During experimentations, a different swarm topology (named as \emph{hbest} PSO) is investigated and embedded in the toolbox where each particle is made to interact with \emph{pbest}, \emph{lbest} and \emph{gbest} particles, simultaneously. From repeated simulations to optimize benchmark test functions, it is observed that \emph{hbest} PSO is faster and capable of escaping local optima.

\subsection*{Framework to Design FLSs}
One of our major contributions is the framework for design automation of T1 and/or IT2 FLSs from input-output training data using PSO (NI Toolbox). Using the proposed framework even non-proficient FLS designers can design their systems with ease. Another application of single-stage forecasting of Mackey-Glass time-series is taken up to validate this framework, where four T1 FLS designs are evolved from training data sets that are corrupted with different noise levels. To contain uncertainties, due to noise present in the training data, these T1 FLSs are then upgraded to IT2 FLSs by adding certain amount of FOU in each FS. From forecasting simulation results it is observed, once again, that IT2 FLSs do have the capacity to handle uncertainties (noise) and, therefore, surpass the performance of T1 FLSs by giving better forecasts with the noisy inputs.

\section*{Chapter-wise Brief Outline}
Chapter 1 presents a gentle overview of the thesis as a whole. It gives introduction to the topic of research, motivation, objectives, and contributions, etc. The ending section of this chapter discusses the organization and outline of remaining chapters of the thesis.

Chapter 2 introduces the historical developments in the fields of FL and PSO. Lotfi A. Zadeh in 1965, introduced concepts of Fuzzy Sets (FSs), now termed as Type-1 (T1) FSs, which are capable of modeling systems, i.e., FLSs, based on the human-reasoning. In these FLSs, FSs are used to model words which cannot be appreciated completely as words mean different things to different people. In 1975, Zadeh extended his concept T1 FSs to generalized FSs, now called as T2 FSs, and popularly known as Zadeh's Extension Principle. In such T2 FSs the membership grade for a crisp input is not a crisp value but another T1 FSs and, therefore, computationally more complex due to their three dimensional nature. This domain of research remained in stalemate for nearly 20 years, after the introduction of T2 FSs and FLSs, may be due to its computationally baffling nature.

In mid-nineties, Jerry M. Mendel and his students reported some pioneering works in reopening the issues pertaining to the T2 FSs and FLSs. In this chapter, all these important developments are discussed at a length, systematically. Mendel \emph{et al}. have introduced many new terms for proper communication about T2 FSs and FLSs, simplified the designing of T2 FLSs and introduced a simpler version of T2 FSs, i.e., IT2 FSs, where all secondary membership grades are set to be unity. The FLSs based on such IT2 FSs are computationally less intensive. Various other facets of IT2 FSs and FLSs are also presented in the chapter.

This is followed by developments in the PSO, a relatively new paradigm in the Swarm Intelligence (SI) area, introduced by Kennedy and Eberhart in 1995. The concept of PSO originated from a computer simulation program meant for simulating the behavior of a bird flock. Later, its potential to find optimal location, in the search space, was realized and used as optimization tool in some other problems. Since then, researchers are constantly investigating its various facets such as effects of different swarm topologies, way the particles interact with each other, and PSO strategy parameters, etc. This chapter investigates such facets, including \emph{gbest} (Global Best) and \emph{lbest} (Local Best) PSO models with different topologies, at a length, and highlights the scope of further investigations. However, primary purpose of PSO studies, in this thesis, has been to find out the most suitable algorithm for the evolution of FLSs.

Chapter 3 concerns about Generalized Fuzzy System (GFS) Toolbox, developed in MATLAB environment, to explore the use of concepts regarding T1 and IT2 FLSs introduced in Chapter 2. This toolbox facilitates the process of designing T1 and/or IT2 FLSs through its user-friendly Graphical User Interface (GUI). This toolbox takes the burden of all the computations at the back end and gives an easy-to-use environment to the FLS designer.

Lower Membership Function (LMF) and Upper Membership Function (UMF) together are popularly used in most of research papers to represent IT2 FSs, however, none of these papers explains as to how to obtain LMF and UMF, in real-life applications, from data sets. In another approach to represent IT2 FSs, principal T1 FS and measure of uncertainty, termed as Footprint of Uncertainty (FOU), are used collectively. This approach is suitable in the cases where noise characteristics or effect of uncertainties on the T1 FSs are predictable or known to the designer. A new approach that is much suitable to find IT2 FSs, in real-world application, is proposed where each IT2 FS is represented with two T1 FSs, i.e., extreme left T1 FS and extreme right T1 FS, and the range in between represents the FOU.

All these approaches are embedded into this toolbox and user is free to explore any one as per convenience and application under consideration. The other features/modules of the toolbox, viz. GFS Set Editor, GFS Rule Editor, GFS Rule Analyzer, GFS Surface Analyzer, etc. are illustrated with figures and snap-shots, in later sections.

Chapter 4 is devoted to PSO algorithms and development of a second toolbox, named as Nature Inspired (NI) Toolbox, which is useful in evolution of a near optimal solution for any problem, especially FLS designs. Most popular PSO models, viz., \emph{gbest} and \emph{lbest}, are embedded into the toolbox along with various options for swarm size, topologies, PSO strategy parameters, fitness functions, string encoding, and termination criteria, etc. Functioning of the NI Toolbox is tested and validated with a testbed of benchmark optimization functions.

This toolbox also interfaces with popularly used software, MS Excel, to receive particle string element details and training data sets, and to deliver output, i.e., evolved best solution. The toolbox is capable of resuming the process of evolution from the point where it is stopped due to any reason.
The \emph{gbest} PSO model is fast but suffers from a critical problem of premature convergence as particles are prone to be trapped in local optima. On the other hand, \emph{lbest} is capable of avoiding premature convergence at the cost of more computations and, therefore, comparatively slower. A new PSO model, named as \emph{hbest} (Hybrid Best), is proposed where each particle is made to experience attractions towards both \emph{lbest} and \emph{gbest} particles in the swarm instead of only one. This model is then tested with benchmark optimization functions and found better than the former ones.

Chapter 5 focuses on the collective use of GFS Toolbox and NI Toolbox in presenting a framework for designing FLSs from input-output training data. Various techniques to encode all the features of singleton/non-singleton and T1/IT2 FLSs as particle strings are discussed at length. Identification of a suitable fitness function can help in easy evolution of proper solution in the end. Various error-based fitness functions are explained, mathematically, which are suitable for the problems where input-output training data is provided with the problem.

Many a times, elements in the particle strings may attain invalid values, due to analog nature of PSO, during the process of evolution. Before these strings are evaluated with the fitness function, they must be validated using  a separately written string validation subroutine whose name is to be specified in the toolbox GUI. This NI Toolbox is enabled to evolve a near optimal solution for any NP-complete problem whose fitness function is either single-objective or multi-objective. The chapter, in the end, presents a PSO strategic planning, useful to evolve FLSs, derived from literature survey and experimentations.

Chapter 6 illustrates designing of T1 and IT2 FLSs for single-stage forecasting of Mackey-Glass time-series using framework presented in the previous chapter. For a fair presentation, four T1 FLSs have been evolved, using \emph{hbest} PSO, from same input-output data set, however, corrupted with four different levels of noise, i.e., Signal-to-Noise Ratio (SNR) = 15dB, 20dB, 25dB, and 30dB. Then the extent of uncertainty (FOU) in each FLS is studied and embedded in each case to upgrade them to IT2 FLSs. To conclude, with the help of simulation results, it is demonstrated that IT2 FLSs give better forecasts, with similar noisy inputs, than those of T1 FLSs.

Chapter 7 presents an assortment of FLS applications, starting off with rudimentary hardware design implementations of T1 FLSs with an objective of gaining insights into the design issues and other facets of FLSs. This involves designing of two FLSs for same application of captive power management using analog circuitry based on Op-Amp (Operational Amplifiers) and digital circuitry based on FPGA (Field Programmable Gate Array) and VHDL (Very high speed integrated circuit Hardware Description Language) programming. These applications spurred us to investigate and design FLSs by taking up advanced design issues.

Later part of the chapter discusses the advanced design implementations of FLSs for two more distinct applications, viz., autonomous navigational control of non-holonomic mobile robot based on experiential knowledge and IRIS data classifier based on noise-free and noisy training data sets. In each application, both T1 and IT2 FLSs are designed and studied for their comparative performances, where IT2 FLSs, once again, outperformed T1 FLSs.

Chapter 8 is devoted to conclusions, and all the offshoots, beyond initially set targets in the Chapter 1, as scope for future research. This leaves a continuum not only for us but also for other researchers in the area.

\vspace*{0.4in}
\begin{center}
\begin{tabular}{p{4.6in}l p{1in}r }
Place: SBSCET Firozpur  &      \\
Date: \today            &   Satvir Singh
\end{tabular}
\end{center} 