Weaker forms of continuity in Sostak's fuzzy topology
An extension of Chang's fuzzy topology was defined by \textit{D. P. Šostak} in [Rend. Circ. Mat. Palermo, II. Ser. Suppl. 11, 89-103 (1985; Zbl 0638.54007)]. Let \((X, \tau)\) be a fuzzy topological space in Šostak's sense. Let for \(r \in (0,1], \lambda \in [0,1]^X\) the operators \(C_\tau, I_\tau\) be defined in the following way: \(C_\tau (\lambda, r) = \land \{ \mu ; \lambda \leq \mu, \tau (1-\mu) \geq r \}\) and \(I_\tau (\lambda, r) = \lor \{ \mu ; \lambda \geq \mu, \tau (\mu) \geq r \}\). A fuzzy set \(\lambda \in [0,1]^X\) is called \(r\)-fuzzy semi-open if there exists a fuzzy set \(\mu\), \(\tau (\mu) \geq r\) such that \(\mu \leq \lambda \leq C_\tau (\mu , r)\). It is \(r\)-fuzzy strongly semi-open if \(\mu \leq \lambda \leq I_\tau (C_\tau (\mu , r),r)\). It is \(r\)-fuzzy preopen if \(\lambda \leq I_\tau (C_\tau (\lambda , r),r)\), \(r\)-fuzzy semi-preopen if \(\lambda \leq C_\tau (I_\tau (C_\tau (\lambda , r),r),r)\) and it is \(r\)-fuzzy regular open if \(\lambda = I_\tau (C_\tau (\lambda , r),r)\). In a dual way the closed counterparts are defined. Mutual relations between these systems of fuzzy sets are studied as well as their topological properties. Similar definitions are also given for mappings between these systems. The paper contains a number of misprints.
scientific article; zbMATH DE number 1942799