On the fuzzy metric spaces

Abstract EN

Zadeh [Zadeh, 1965] introduced the concepts of fuzzy sets in 1965, and in the next decade Kramosil and Michalek [Kramosil and Michalek, 1975] introduced the concept of fuzzy metric space with the help of continuous norms in1975 which opened an avenue for further development of analysis in such spaces which have very important applications in quantum physics particularly in connections with both string and theory which were given and studied by EI Naschie [El Naschie, 1998].

George and Veeramani [George and Veeramani, 1994, 1997] modified the concept of fuzzy metric space introduced by Kramosil and Michalek also with the help of continuous norms.

In this search we will define in different way the fuzzy metric space by given definitions about the fuzzy families, the fuzzy field, the fuzzy space, and other concepts based on that every real number is replaced by fuzzy number (either triangular fuzzy number or singleton fuzzy set).

For more details see [Kramosil and Michalek, 1975] [Erceg, 1979], [Grabiec, 1988], [ Kaleva and Seikkala,1984.]