The theory of global fuzzy neighborhood structures. I: The general case
The first named author [ibid. 76, No. 2, 205-224, 225-246 (1995; Zbl 0873.54008; Zbl 0873.54009)] characterized fuzzy topologies (stratified fuzzy topologies) as monadic topologies with respect to the partially ordered fuzzy filter monad (homogeneous fuzzy filter monad, respectively). Weakening certain conditions in the definition of monadic topologies, the authors in this paper introduce the concept of global fuzzy neighbourhood structures, which was proved to contain fuzzy topologies and etc. as special cases. Three kinds of global fuzzy neighbourhood structures, corresponding to three kinds of fuzzy filters, are studied systematically; particularly their relationship to fuzzy topologies, stratified fuzzy topologies and the fuzzy neighbourhood space topologies in the sense of \textit{R. Lowen} [ibid. 7, 165-189 (1982; Zbl 0487.54008)] are investigated.
scientific article; zbMATH DE number 1320350
scientific article