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Characterizing closure systems in the graded setting - CMMSE
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  • Manuel Ojeda-Hernandez,
  • Inma Cabrera,
  • Pablo Cordero,
  • Emilio Muñoz-Velasco
Manuel Ojeda-Hernandez
University of Malaga

Corresponding Author:[email protected]

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Inma Cabrera
Universidad de Málaga
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Pablo Cordero
University of Malaga
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Emilio Muñoz-Velasco
Universidad de Málaga
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Abstract

Closure systems play a major role in both pure and applied mathematics. This paperpresents an extension of the notion of closure system, which is done adapting theidea of meet-subsemilattice to a complete fuzzy lattice. This extension is carried outon two levels, first as crisp sets and then as fuzzy sets. In both cases, the one-to-onerelations between closure operators and closure systems that hold in the classicalcase are extended properly to this framework. Furthermore, a novel characterizationfor a closure system is established.