Geodesic
On characterizations of finite topological spaces with granulation and evidence theory
Filomat, Tome 33 (2019) no. 19, p. 6425

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DOI

The theory of finite topological spaces can be used to investigate deep well-known problems in Topology, Algebra, Geometry and Artificial Intelligence. To represent uncertainty knowledge of a finite topological space, two kinds of measurement of a finite topological space are first introduced. Firstly, a kind of granularity of a finite topological space is defined, and properties of the granularity are explored. Secondly, relationships between the belief and plausibility functions in the Dempser-Shafer theory of evidence and the interior and closure operators in topological theory are established. The probabilities of interior and closure of sets construct a pair of belief and plausibility functions and its belief structure. And, for a belief structure with some properties, there exists a probability and a finite topology such that the belief and plausibility functions defined by the given belief structure are, respectively, the belief and plausibility functions by the topology. Then a necessary and sufficient condition for a belief structure to be the belief structure induced by a finite topology is presented
DOI : 10.2298/FIL1919425L
Classification : 54A05, 60B05
Keywords: Evidence theory, finite topological space, granularity 
Chang-Qing Li; Yan-Lan Zhang. On characterizations of finite topological spaces with granulation and evidence theory. Filomat, Tome 33 (2019) no. 19, p. 6425 . doi: 10.2298/FIL1919425L
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     author = {Chang-Qing Li and Yan-Lan Zhang},
     title = {On characterizations of finite topological spaces with granulation and evidence theory},
     journal = {Filomat},
     pages = {6425 },
     year = {2019},
     volume = {33},
     number = {19},
     doi = {10.2298/FIL1919425L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL1919425L/}
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