- Volume 21 Issue 2
Topos is a set-like category. In topos, the axiom of choice can be expressed as (AC1), (AC2) and (AC3). Category Fuz of fuzzy sets has a similar function to the topos Set and it forms weak topos. But Fuz does not satisfy (AC1), (AC2) and (AC3). So we define (WAC1), (WAC2) and (WAC3) in weak topos Fuz. And we show that they are equivalent in Fuz.
- R. Diaconescu, Axiom of choice and complementation, Proc. Amer. Math. Soc. 51 (1975), no. 1, 176-178
- R. Goldblatt, Topoi, North-Holland, 1984
- P. T. Johnstone, Topos Theory, Academic Press, N. Y., 1977
- A. M. Penk, Two form of the axiom of choice for an elementary topos, J. of Symbolic logic. 40 (1975), no. 2, 192-212
- X. Yuan and E. S. Lee, Categorical analysis of logic operator on fuzzy sets, J. of Math. Anal. and Appl. 177 (1993), 600-607 https://doi.org/10.1006/jmaa.1993.1280
- X. Yuan, H. Li and E. S. Lee, Categories of fuzzy sets and weak topos, Fuzzy Sets and Systems 127 (2002), 291-297 https://doi.org/10.1016/S0165-0114(01)00119-1