Abstract
Fuzzy topology has used a definition which has an L-topological space consisting of a crisp set of fuzzy subsets of a crisp set. The notion of a topological space object in SET(L) provides a generalization of this concept to that of a fuzzy set of fuzzy subsets of a fuzzy set. This chapter extends the introduction given in [2] and provides connections with more mainstream fuzzy topology.
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References
J. Adé.mek, H. Herrlich, G. E. Strecker, Abstract and Concrete Categories: The Joy of Cats, Wiley Interscience Pure and Applied Mathematics, John Wiley & Sons (Brisbane/Chicester/New York/Singapore/Toronto), 1990.
U. Höhle, L. N. Stout, Foundations of fuzzy sets, Fuzzy Sets and Systems 40 (2) (1991), 257–296.
R. Lowen, Fuzzy topological spaces and fuzzy compactness, Journal of Mathematical Analysis and its Applications 56 (3) (1976), 621–633.
B. Schweitzer, A Sklar, Probabilistic Metric Spaces, North Holland (Amsterdam), 1983.
A. P. Sostak, Two decades of fuzzy topology: basic ideas, notions, and results, Russian Math. Surveys 44 (6) (1989), 125–186.
L. N. Stout, Topology in a topos II: E -completeness and E -cocompleteness, Manuscripta Mathematica, 17 (1975), 1–14.
L. N. Stout, Quels sont les espaces topologiques dans les topos? Annales des sciences mathématiques de Québec II (1) (1978), 123–141.
L. N. Stout, Fuzzy logic from a second closed structure on a quasitopos, in Proceedings of the Third IFSA World Congress (1989), 458–461, IFSA ( August 1989, Seattle).
L. N. Stout, The logic of unbalanced subobjects in a category with two closed structures, Chapter 3 in: S. E. Rodabaugh, E. P. Klement, U. Höhle, eds, Application Of Category To Fuzzy Sets, Theory and Decision Library—Series B: Mathematical and Statistical Methods, Volume 14, Kluwer Academic Publishers (Boston/Dordrecht/London), 1992, pp. 73–105.
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Stout, L.N. (2003). Fully Fuzzy Topology. In: Rodabaugh, S.E., Klement, E.P. (eds) Topological and Algebraic Structures in Fuzzy Sets. Trends in Logic, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0231-7_10
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DOI: https://doi.org/10.1007/978-94-017-0231-7_10
Publisher Name: Springer, Dordrecht
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