Abstract
Abstract Given a fuzzy bitopological space (X,τ1,τ2), we have used the operator C12:IX→IX defined by C 12 (μ)=τ 1 − cl (μ)∩τ 2 − cl (μ), μ∈I X , which is a supra fuzzy closure operator [Fuzzy Sets and Systems 74 (1995) 353], to generate a family τs which is a supra fuzzy topology [loc. cit., 1995]. So the space (X,τs) is a supra fuzzy topological space associated to the fuzzy bitopological space (X,τ1,τ2). We extend the notions of α.FTi, strong FTi and ultra FTi due to [Fuzzy Sets and System 43 (1991) 95] to the space (X,τs). The properties of fuzzy bitopological spaces have been studied by using their associated supra fuzzy topological spaces. We introduce the notions of α.FP*Ti, S.FP*Ti and U.FP*Ti by using the level supratopology ια(τs) of τs. We investigate the relationship between these notions, the notions FP*Ti [loc. cit., 1995], i=1,2,3,4 and the notions α.FPTi (resp. S.FPTi,U.FPTi) [Fuzzy Sets and Systems 105 (1999) 459]. We give a number of examples, which illustrate that these concepts are not equivalent. Also we extend the notions of α F-continuous (open), strong F-continuous (open) and ultra F-continuous (open) due to [Fuzzy Sets and Systems 38 (1990) 115] to the class of supra fuzzy topological spaces associated to the class of fuzzy bitopological spaces. We study some properties of α.FP*Ti (resp. S.FP*Ti,U.FP*Ti) under these mappings.
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