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A Unifying Study Between Modal-Like Operators, Topologies, and Fuzzy Sets

Jouni Järvinen, Jari Kortelainen, A Unifying Study Between Modal-Like Operators, Topologies, and Fuzzy Sets. Fuzzy Sets and Systems 158(11), 1217−1225, 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.

(Preliminary version as TUCS Technical Report 642)

BibTeX entry:

@ARTICLE{jJaKo07a,
  title = {A Unifying Study Between Modal-Like Operators, Topologies, and Fuzzy Sets},
  author = {Järvinen, Jouni and Kortelainen, Jari},
  journal = {Fuzzy Sets and Systems},
  volume = {158},
  number = {11},
  pages = {1217−1225},
  year = {2007},
}

Belongs to TUCS Research Unit(s): Algorithmics and Computational Intelligence Group (ACI), FUNDIM, Fundamentals of Computing and Discrete Mathematics

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