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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. TUCS Technical Reports 642, Turku Centre for Computer Science, 2004.

Abstract:

The paper introduces both lattice-theoretical and topological approaches on studying connections between Fuzzy Set Theory and Rough Set Theory or, more precisely, <i>L</i>-sets and modal-like operators. Various results for certain type of <i>L</i>-sets are presented, and it is shown that modal-like operators can be determined by means of <i>L</i>-sets. Moreover, it is shown that a certain subcategory of a category of variable-basis <i>L</i>-sets is isomorphic to the category of Alexandroff topological spaces as well as the category of quasi-ordered sets.

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BibTeX entry:

@TECHREPORT{tJaKo04a,
  title = {A Unifying Study Between Modal-like Operators, Topologies, and Fuzzy Sets},
  author = {Järvinen, Jouni and Kortelainen, Jari},
  number = {642},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2004},
  keywords = {Modal-like operators, quasi-orders, modifiers, rough sets, fuzzy sets, topologies, category theory},
  ISBN = {952-12-1465-1},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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