Fuzzy bicompletable quasi-fuzzy distance space


  • Jehad Kider Mathematics
  • Aisha J. Hassan






Fuzzy Distance Space, Quasi-Fuzzy Distance Space, Fuzzy Bicompletable Quasi-Fuzzy Distance Space.


In this paper we introduce the definition of quasi-fuzzy distance space then we discuss several properties of this space after we give an example to illustrate this notion. Then we show that the existence of a quasi-fuzzy distance space which is not fuzzy bicompletable. Here we prove that every fuzzy bicompletable quasi-fuzzy distance space admits a unique [up to fuzzy isodistance] fuzzy a bicompletion.


[1] Company, C.F. Romaguera, S. and Tirado, P, (2011) "The Bicompletion of Fuzzy Quasi metric spacesâ€, Fuzzy Sets and Systems, Vol.166, 56-64. http://dx.doi.org/10.1016/j.fss.2010.12.004.

[2] Dersanambika, K.S. and Aswathy, M.R., (2011) "Fixed point theorem in fuzzy metric spacesâ€, Int.J. contemp Math. Sciences, Vol.6, No.22, 1079-1089.

[3] Dubbois, D. and Prade, H. (1980)" Fuzzy sets and systems, Theory and Applicationâ€, Academic Press, Inc.

[4] Hassan, A.G., (2002)" Pseudo- Complete fuzzy locally convex algebras†Ph.D. thesis, AL-Mustansirya University, Baghdad.

[5] George, A. and Veeramani, P. (1994)"On some results in fuzzy metric spaces", Fuzzy Sets and Systems, Vol.64, 395-399. http://dx.doi.org/10.1016/0165-0114(94)90162-7.

[6] Gregori, V. and Romaguera, S., (2000) "Some properties of fuzzy metric spaces ", Fuzzy Sets and Systems, Vol.115, 485-489. http://dx.doi.org/10.1016/S0165-0114(98)00281-4.

[7] Gregori, V., Romaguera , S. and sapena ,A. ,(2001)"Uniform continuity in fuzzy metric spaces" ,Rend. Ist. Mat. Univ. trieste suppl.2, Vol.32, 81-88.

[8] Gregori, V. and Sapena, A. (2002)"On fixed point theorems in fuzzy metric spsces", Fuzzy Sets and Systems, Vol.125, 245-253. http://dx.doi.org/10.1016/S0165-0114(00)00088-9.

[9] Gregori, V., Romaguera, S. and Sapena,A.,(2005)"A character-ization of bicomppletable fuzzy quasi metric spaces " , Fuzzy Sets and Systems , Vol. 152, 395-402 http://dx.doi.org/10.1016/j.fss.2004.09.006.

[10] Gregori,V., Minana, J. and Morillas, S.(2012) , "Some ques-tion in fuzzy metric spaces " , Fuzzy Sets and Systems Vol.204,71-85 http://dx.doi.org/10.1016/j.fss.2011.12.008.

[11] Hassan, A, J. (2015) "Properties of fuzzy distance on fuzzy setâ€, M.Sc. Thesis, University of Technology, 2015.

[12] Klir, G. and Folger, T., (1988) "fuzzy sets Uncertainty and information ", prentice, Hall International, Inc.

[13] Kider, J. (2014),"Compact standard fuzzy metric space", International J. of Math. Archive, Vol .5 No.7, 129-136.

[14] Kider, J. R. and Hassan, A. J. (2015) “Properties of fuzzy distance on fuzzy set ", J. ofAdvances in mathematics, Vol.11, No.6, 5286-5299.

[15] Kramosil, D. and Michalek, J., (1975) "Fuzzy metric and statistical metric spaces, Kybernetika, Vol.11, 326-334.

[16] Lopez, R. and Romaguera, S., (2004)"The Hausdorff fuzzy metric on compact sets ", Fuzzy Sets and System, Vol.147, 273-283. http://dx.doi.org/10.1016/j.fss.2003.09.007.

[17] Mihet, D. (2004)"A Banach Contraction theorem in fuzzy metric spaces ", Fuzzy Sets and System Vol.144, 431-439. http://dx.doi.org/10.1016/S0165-0114(03)00305-1.

[18] Pao-Ming, P. and Ying-Ming, L, (1980) "Fuzzy Topology II, products and Quotient spacesâ€, J. Math Anal. Appl.Vol.77, 20-37. http://dx.doi.org/10.1016/0022-247X(80)90258-9.

[19] Rudin, W., (1974) "Functional Analysis". Tata Mcgraw – Hill publishing company ltd.

[20] Wong, C. (1974)"Fuzzy points and local properties of fuzzy Topology, J. Math .Anal. Appl., Vol.46, 316-328. http://dx.doi.org/10.1016/0022-247X(74)90242-X.

[21] Zadeh, L (1965)."Fuzzy sets "Information and control, Vol.8, 338- 353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X.

View Full Article: