Fuzzy mathematics is considered to be an important aspect in the field of mathematics that interprets the uncertainties and deals with the unreliable information and vagueness of data. In this chapter we shall discuss the concept of fuzzy mathematics as fuzzy set and fuzzy logics and the beginning of fuzzy set theory and the fuzzy logics with their applications in the real life. As fuzzy mathematics and fuzzy logics are becoming increasingly significant as it is applied in almost every field of developments, engineering design and models and in new technologies also. We also discuss some recent models of fuzzy logics given by T. Patro[8] and C.K. Muthumaniraj [2] Fuzzy logics are playing very important role in many areas. I tried to make this chapter as a strong base for researchers and students so that it can prove strong base for further researches for comparative study of fuzzy set theory and fuzzy logics.