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A unifying study between modal-like operators, topologies and fuzzy sets
- Source :
-
Fuzzy Sets & Systems . Jun2007, Vol. 158 Issue 11, p1217-1225. 9p. - Publication Year :
- 2007
-
Abstract
- The paper presents the essential connections between modal-like operators, topologies and fuzzy sets. We show, for example, that each fuzzy set determines a preorder and an Alexandrov topology, and that similar correspondences hold also for the other direction. Further, a category for preorder-based fuzzy sets is defined, and it is shown that its equivalent subcategory of representatives is isomorphic to the categories of preordered sets and Alexandrov spaces. Moreover, joins, meets and complements for the objects in this category of representatives are determined. This suggests how to define for fuzzy subsets of a certain universe the lattice operations in a canonical way. [Copyright &y& Elsevier]
- Subjects :
- *TOPOLOGY
*FUZZY sets
*SET theory
*MATHEMATICS
*LATTICE theory
*SPACE
Subjects
Details
- Language :
- English
- ISSN :
- 01650114
- Volume :
- 158
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Fuzzy Sets & Systems
- Publication Type :
- Academic Journal
- Accession number :
- 24610446
- Full Text :
- https://doi.org/10.1016/j.fss.2007.01.011