Characterizations of fuzzy intra-regular Abel- Grassmann's groupoids

The real world has a lot of different aspects which are not usually been specified. In different fields of knowledge like engineering, medical science, mathematics, physics, computer science and artificial intelligence, many problems are simplified by constructing their "models". These models are very complicated and it is impossible to find the exact solutions in many occasions. Therefore, the classical set theory, which is precise and exact, may not be suitable for such problems of uncertainty. In today's world, many theories have been developed to deal with such uncertainties like fuzzy set theory, theory of vague sets, theory of soft ideals, theory of intuitionistic fuzzy sets and theory of rough sets. The theory of soft sets has many applications in different fields such as the smoothness of functions, game theory, operations research, Riemann integration etc. The basic concept of fuzzy set theory was first given by Zadeh