FUZZY COMPACT FUZZY DISTANCE SPACE
Abstract
In this paper we recall the definition of fuzzy distance space on a fuzzy set then we define a compact fuzzy distance space and fuzzy totally bounded after that we prove that fuzzy totally bounded fuzzy complete fuzzy distance space is fuzzy compact. Moreover we recall the definition of fuzzy continuous and uniform fuzzy continuous function to prove that fuzzy continuous function and uniform fuzzy continuous functions are equivalent on a fuzzy compact fuzzy distance spaces .Downloads
References
Company, C.F. Romaguera, S. and Tirado, P, "The Bicompletion of Fuzzy Quasi metric spaces" , Fuzzy Sets and Systems , Vol.166 (2011) 56-64.
Dersanambika,K.S. and Aswathy, M.R., "Fixed point theorem in fuzzy metric spaces" , Int.J. contemp Math. Sciences , Vol.6,No.22(2011)1079-1089.
Dubbois, D. and Prade, H." Fuzzy sets and systems, Theory and Application " , Academic Press , Inc. (1980).
Hassan, A.G.," Pseudo- Complete fuzzy locally convex algebras " Ph.D. thesis , AL-Mustansirya University , Baghdad 2002.
George, A. and Veeramani, P."On some results in fuzzy metric spaces", Fuzzy Sets and Systems, Vol.64(1994) 395-399 .
Gregori, V. and Romaguera, S. , "Some properties of fuzzy metric spaces ", Fuzzy Sets and Systems , Vol.115(2000)485-489 .
Gregori , V., Romaguera , S. and sapena ,A. ,"Uniform continuity in fuzzy metric spaces" ,Rend. Ist. Mat. Univ. trieste suppl.2,Vol.32(2001) 81-88.
Gregori, V. and Sapena, A."On fixed point theorems in fuzzy metric spsces", Fuzzy Sets and Systems , Vol.125(2002) 245-253 .
Gregori, V., Romaguera, S. and Sapena,A.,"A characterization of bicomppletable fuzzy quasi metric spaces " , Fuzzy Sets and Systems , Vol. 152(2005) 395-402 .
Gregori,V., Minana, J. and Morillas, S. , "Some question in fuzzy metric spaces " , Fuzzy Sets and Systems Vol.204(2012)71-85 .
Hassan, A, J. "Properties of fuzzy distance on fuzzy set ",M.Sc. Thesis
,University of Technology, 2015.
Klir, G. and Folger, T., "fuzzy sets Uncertainty and information ", prentice , Hall International , Inc (1988) .
Kider,J. ,"Compact standard fuzzy metric space", International J. of Math. Archive ,Vol .5 No.7 (2014) 129-136 .
Kider, J. R. and Hassan, A. J. " Properties of fuzzy distance on fuzzy set ", J. of
Advances in mathematics, Vol.11, No.6, (2015)5286-5299.
Kramosil, D. and Michalek, J., "Fuzzy metric and statistical metric spaces, Kybernetika , Vol.11 (1975) 326-334 .
Lopez, R. and Romaguera, S. ,"The Hausdorfffuzzy metric on compact sets ",Fuzzy Sets and System , Vol.147(2004) 273-283 .
Mihet,D. "A Banach Contraction theorem in fuzzy metric spaces ", Fuzzy Sets and System Vol.144(2004) 431-439 .
Pao-Ming, P. and Ying-Ming, L, "Fuzzy Topology II, products and Quotient spaces " , J.Math Anal. Appl.Vol.77(1980) 20-37 .
Rudin , W., "Functional Analysis"., Tata Mcgraw – Hill publishing company ltd , 1974 .
Wong, C."Fuzzy points and local properties of fuzzy Topology , J. Math .Anal . Appl., Vol.46(1974) 316-328 .
Zadeh, L."Fuzzy sets "Information and control, Vol.8(1965) 338- 353 .
Copyright (c) 2015 Journal of Progressive Research in Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
