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- W2062087746 abstract "We introduce and develop topologies whose members are dynamic sets à la Zeleny. This development spawns the notions of phase and co-phase spaces, fuzzy dual, dynamic dual, and co-fuzzy dual with the following results being obtained: Result A . The notion of fuzzy dual provides a unifying framework for the diverse fuzzification schemes of Hutton-Gantner-Steinlage-Warren, Klein, and Lowen. Result B . The dynamic duals of the fuzzy real lines are both homeostatic and coheterostatic. Result C . The fuzzy real lines, re-interpreted as fuzzy duals of R with the usual Euclidean topology T , induce on R , via the notion of co-fuzzy dual, a class of canonical, stratified fuzzy topologies {CO R L }. E.g., if L is a DeMorgan algebra and α ϵ L c -{1}, then the α-compactness of A ⊂ R is equivalent to the ordinary compactness of A w.r.t. T ; and if L is a Hutton algebra, ( R , L , CO R L ) is metrizable in the sense of Hutton and Erceg with Erceg metric d ( L ) such that d(L) (p r 1 , p s 1 )=¦r − s¦ (where p r is the crisp point or impulse with support r ), i.e., d ( L ) extends the Euclidean metric on R ." @default.
- W2062087746 created "2016-06-24" @default.
- W2062087746 creator A5015958599 @default.
- W2062087746 date "1988-04-01" @default.
- W2062087746 modified "2023-10-18" @default.
- W2062087746 title "Dynamic topologies and their applications to crisp topologies, fuzzifications of crisp topologies, and fuzzy topologies on the crisp real line" @default.
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- W2062087746 doi "https://doi.org/10.1016/0022-247x(88)90189-8" @default.
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