CHAPTER ONE

INTRODUCTION

1.1 Background to the Study

The fundamental concept of fuzzy sets was introduced by Zadeh in 1965 to represents

information possessing non-statistical uncertainties. The fuzzy algebraic structures play a

prominent role in mathematics with wide applications in many other branches such as

theoretical physics, computer science, control engineering, information science, coding

theory, group theory, real analysis, measure theory etc.

The first publication in fuzzy set theory by Zadeh (1965) and then by Klaua (1965) showed

the intention of the authors to generalize the classical set. In classical set theory, a subset

of a set     can be defined by its characteristic function                             which is defined by

The mapping may be represented as a set of ordered pairs                       with exactly one