ABSTRACT
In 1965, Zadeh introduced the concept of fuzzy set which transformed and stimulated most branches of science and engineering including mathematics. The concept of fuzziness found its place in probabilistic metric spaces due to Menger. The main reason was that uncertainty in the distance between two points was due to fuzziness rather than randomness. With this idea Kramosil and Michalek extended the concept of probabilistic metric spaces to the fuzzy situation. Since the definition of fuzzy metric space due to Kramozil and Michalek is closely related to the definition of Menger spaces; therefore we recall some definitions from probabilistic metric space theory. In 1988, M. Grabiec initiated the study of fixed point theory in fuzzy metric space and established the fuzzy Banach contraction and fuzzy Edelstein contraction theorem. Shukla and Abbas considered the fuzzy metric-like, which is a combination of fuzzy metric and metric-like and proved some basic versions of fixed point theorems in spaces endowed with fuzzy metric-like.
