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on the fuzzy metric places

R. Srinivasan,K.Renganathan

Published in International Journal of Advanced Research in Mathematics and Applications

ISSN: 2350-028X          Impact Factor:1.2         Volume:1         Issue:1         Year: 08 January,2014         Pages:1-39

International Journal of Advanced Research in Mathematics and Applications

Abstract

Zadeh [Zadeh , 1965] introduced the concepts of fuzzy sets in1965 , and in the next decade Kramosil and Michalek [Kramosil & Michalek ,1975] introduced the concept of fuzzy metric space with the help of continuous t norms in1975 which opened an avenue for further development of analysis in such spaces which have very important applications in quantumphysics particularly in connections with both string and   theory which were given and studied by EI Naschie [El Naschie ,1998] . George and Veeramani [George &Veeramani ,1994,1997] modified the concept of fuzzyPmetric space introduced by Kramosil and Michalek also with the help of continuous t  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 r is replaced by fuzzy number r (either triangular fuzzy number or singleton fuzzy set). For more details see [Kramosil &Michalek, 1975] [Erceg, 1979], [Grabiec, 1988], [Kaleva & Seikkala, 1984].

Kewords

Fuzzy Metric Space, Triangular Fuzzy number, Operations of Fuzzy numbers, Fuzzy Pseudo-Metric, Fuzzy mapping

Reference

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