Abstract
Throughout, X will be a nonempty set. We consider a subset M of X as a crisp fuzzy set, and denote this again by M. We denote the strong α-cut of a fuzzy set μ ε IX by μα, and its weak α-cut by μα*, α ε I.
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References
T.M.G. Ahsanullah and N.N. Morsi, Invariant probabilistic metrizability of fuzzy neighbourhood groups, Fuzzy Sets and Systems 47 (1992) 233–245.
M.A. Amer and N.N. Morsi, Characterizations of some fuzzy topological notions in probabilistic metric spaces, Fuzzy Sets and Systems (1993), to appear.
U. Höhle, Probabilistic metrization of fuzzy uniformities, Fuzzy Sets and Systems 8 (1982) 63–69.
R. Lowen, Fuzzy uniform spaces, J. Math. Anal. Appl. 82 (1981) 370–385.
R. Lowen, Fuzzy neighborhood spaces, Fuzzy Sets and Systems 7 (1982) 165–189.
R. Lowen, Compactness notions in fuzzy neighborhood spaces, Manuscripta Math. 38 (1982) 265–287.
R. Lowen, On the Existence of Natural, Non-topological Fuzzy Topological Spaces (Heldermann-Verlag, Berlin, 1985).
R. Lowen and P. Wuyts, Completeness, compactness and precompactness in fuzzy uniform spaces, Part I, J. Math. Anal. Appl. 90 (1982) 563–581.
A.S. Mashhour and N.N. Morsi, Fuzzy metric neighbourhood spaces, Fuzzy Sets and Systems 45 (1992) 367–388.
A.S. Mashhour and N.N. Morsi, On regularity axioms in fuzzy neighbourhood spaces, Fuzzy Sets and Systems 44 (1991) 265–271.
N.N. Morsi, Nearness concepts in fuzzy neighbourhood spaces and in their fuzzy proximity spaces, Fuzzy Sets and Systems 31 (1989) 83–109.
N.N. Morsi, Dual fuzzy neighbourhood spaces I, Fuzzy Sets and Systems 44 (1991) 245–263.
N.N. Morsi, The Urysohn Lemma for fuzzy neighbourhood spaces, Fuzzy Sets and Systems 39 (1991) 347–360.
P. Wuyts, On the determination of fuzzy topological spaces and fuzzy neighbourhood spaces by their level-topologies, Fuzzy Sets and Systems 12 (1984) 71–85.
P. Wuyts, The RO-property in fuzzy topological spaces, Summary in: Communications IFSA Mathematics Chapter 2 (1988) 36–40.
P. Wuyts and R. Lowen, On separation axioms in fuzzy topological spaces, J. Math Anal. Appl. 93(1983)27–41.
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© 1993 Springer Science+Business Media Dordrecht
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Kandil, A., Hashem, K.A., Morsi, N.N. (1993). A Level-Topologies Criterion for Lowen Fuzzy Uniformizability. In: Lowen, R., Roubens, M. (eds) Fuzzy Logic. Theory and Decision Library, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2014-2_7
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DOI: https://doi.org/10.1007/978-94-011-2014-2_7
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