Abstract
PurposeRecently, F. Smarandache generalized the Atanassov's intuitionistic fuzzy sets and other kinds of sets to neutrosophic sets (NSs). Also, this author introduced a general definition of neutrosophic topology. On the other hand, there exist various kinds of paraconsistent logics, where some contradiction is admissible. The purpose of this paper is to show that a Smarandache's definition of neutrosophic paraconsistent topology is not a generalization of Çoker's intuitionistic fuzzy topology (IFT) or Smarandache's general neutrosophic topology.Design/methodology/approachThe possible relations between the IFT and the neutrosophic paraconsistent topology are studied.FindingsRelations on IFT and neutrosophic paraconsistent topology are shown.Research limitations/implicationsClearly, the paper is confined to IFSs and NSs.Practical implicationsThe main applications are in the mathematical field.Originality/valueThe paper shows original results on fuzzy sets and topology.
Highlights
In various recent papers, Smarandache (1998, 2002, 2003, 2005a) generalizes intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs).In some distinctions between NSs and IFSs are underlined, (Smarandache, 2005a).The notion of IFS defined by Atanassov (1983, 1986) has been applied by Coker (1997) for study intuitionistic fuzzy topological spaces (IFTS)
The notion of IFS defined by Atanassov (1983, 1986) has been applied by Coker
(1997) for study intuitionistic fuzzy topological spaces (IFTS). This concept has been developed by many authors
Summary
In various recent papers, Smarandache (1998, 2002, 2003, 2005a) generalizes intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs).In some distinctions between NSs and IFSs are underlined, (Smarandache, 2005a).The notion of IFS defined by Atanassov (1983, 1986) has been applied by Coker (1997) for study intuitionistic fuzzy topological spaces (IFTS). The notion of IFS defined by Atanassov (1983, 1986) has been applied by Coker (1997) for study intuitionistic fuzzy topological spaces (IFTS). This concept has been developed by many authors
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