International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Fuzzy Mappings and Fuzzy Equivalence Relations

  • Lim, Pyung-Ki (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University) ;
  • Choi, Ga-Hee (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University) ;
  • Hur, Kul (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
  • Received : 2011.07.12
  • Accepted : 2011.09.21
  • Published : 2011.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

Equivalence relations and mappings for crisp sets are very well known. This paper attempts an investigation of equivalence relations and mappings for fuzzy sets. We list some concepts and results related to fuzzy relations. We give some examples corresponding to the concept of fuzzy equality and fuzzy mapping introduced by Demirci [1]. In addition, we introduce the notion of preimage and quotient of fuzzy equivalence relations. Finally, we investigate relations between a fuzzy equivalence relation and a fuzzy mapping.

Keywords

Acknowledgement

Supported by : Wonkwang University

References

  1. M.Demirci, "Fuzzy functions and their fundamental properties", Fuzzy Sets and Systems, vol.106, no. 2, pp. 239-246, 1999. https://doi.org/10.1016/S0165-0114(97)00280-7
  2. J.A.Gouen, "L-fuzzy sets", J.Math.Anal.Appl., vol.18, no. 1, pp. 145-17, 1967. https://doi.org/10.1016/0022-247X(67)90189-8
  3. V.Murali, "Fuzzy equivalence relations", Fuzzy Sets and Systems, vol.30, pp. 155-163, 1989. https://doi.org/10.1016/0165-0114(89)90077-8
  4. W.C.Nemitz, "Fuzzy relations and fuzzy functions", Fuzzy Sets and Systems, vol.19, no. 8, pp. 177-191, 1986. https://doi.org/10.1016/0165-0114(86)90036-9
  5. S.V.Ovchinnikov, "Structure of fuzzy binary relations", Fuzzy Sets and Systems, vol.6, no. 2, pp. 169-195, 1981. https://doi.org/10.1016/0165-0114(81)90023-3
  6. C.C.Pinter, "Set Theory", Kyung Moon Publishers, 2002.
  7. P.M.Pu and Y.M.Liu, "Fuzzy topology II. Product and quotient spaces", J.Math.Anal.Appl. vol.77, no. 2, pp. 20-37, 1980. https://doi.org/10.1016/0022-247X(80)90258-9
  8. T.H.Yalvac, "Fuzzy sets and functions on fuzzy space", J.Math.Anal.Appl. vol.126, pp. 409-423, 1989.
  9. L.A.Zadeh, "Fuzzy sets", Inform. and Control, vol.8, pp. 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X
  10. L.A.Zadeh, "Similarity relations and fuzzy ordering", Inform. Soi, vol.3, pp. 117-200, 1971.