This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying. It investigates topological notions defined by means of -open sets when these are planted into the frame-work of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). In this paper we introduce some sorts of operations, called general fuzzifying operations from P(X) to , where (X, τ) is a fuzzifying topological space. By making use of them we contract neighborhood structures, derived sets, closure operations and interior operations.
U. H?hle and A. ?ostak, “Axiomatic Foundations of Fixed-Basis Fuzzy Topology,” In: U. H?hle and S. E. Rodabaugh, Eds., Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Vol. 3, Kluwer Academic Publishers, Dordrecht, 1999, pp. 123-272.
S. E. Rodabaugh, “Categorical Foundations of VariableBasis Fuzzy Topology,” In: U. H?hle and S. E. Rodabaugh, Eds., Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Vol. 3, Kluwer Academic Publishers, Dordrecht, 1999, pp. 273-388.
K. M. Abd El-Hakeim, F. M. Zeyada and O. R. Sayed, “Pre-Continuity and D(c, P)-Continuity in Fuzzifying Topology,” Fuzzy Sets and Systems, Vol. 119, No. 3, 2001, pp. 459-471. doi:10.1016/S0165-0114(99)00097-4
T. Noiri and O. R. Sayed, “Fuzzy Open Sets and Fuzzy -Continuity in Fuzzifying Topology,” International Journal of Mathematics and Mathematical Sciences, Vol. 31, No. 1, 2002, pp. 51-63.
M. E. Abd El-Monsef, F. M. Zeyada and A. S. Mashhour, “Operations on Topologies and Its Applications on Some Types of Covering,” Annales de la Société Scientifique de Bruxelles, Vol. 79, 1983, pp. 155-172.