DOI QR코드

DOI QR Code

FUZZY EQUIVALENCE RELATIONS AND FUZZY FUNCTIONS

  • 발행 : 2009.03.01

초록

In this paper, by using the definition of fuzzy equivalence relations introduced by Dib and Youssef, we obtain fuzzy analogues of many results concerning ordinary equivalence relations. Moreover, we investigate fuzzy analogues of many results concerning relationships between ordinary equivalence relations and ordinary functions. In particular, we obtain the fuzzy-canonical decomposition of a fuzzy function.

키워드

참고문헌

  1. J. C. Bezdck and J. D. Harris. Fnzzy partitions and relations; an axiornatic basis fof clustering, Fuzzy Sets and Systems 1 pp. 111-127, 1978 https://doi.org/10.1016/0165-0114(78)90012-X
  2. K. A. Dib and Nabil L. Youssef, Fuzzy cartesian product, fuzzy relations and fuzzy functions, Fuzzy Sets and Sustems 41 pp. 299-315, 1991 https://doi.org/10.1016/0165-0114(91)90134-C
  3. M. A. Ercer, Functions, equivalence relations, quotient spaces and subsets in fuzzy set theory, Fuzzy Sets and Systems 3 pp.75-92, 1980 https://doi.org/10.1016/0165-0114(80)90006-8
  4. J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 8 pp.145-174, 1967
  5. K. Hur, H. W. Kang and K.C. Lee, Fuzzy equivalence relations and fuzzy partitions, Honam Math. J. 28(3) pp.291-315, 2006
  6. V. Murali, Fuzzy equivalence relations, Fuzzy Sets and Systems, 30 pp.155-163, 1989 https://doi.org/10.1016/0165-0114(89)90077-8
  7. W. C. Ncmitz Fuzzy relations and fuzzy functions, Fuzzy Sets and Systems 19 pp.177-191, 1986 https://doi.org/10.1016/0165-0114(86)90036-9
  8. L. A. Zadeh, Fuzzy sets, Inform. and Control 8 pp.338-353, 1965 https://doi.org/10.1016/S0019-9958(65)90241-X