|Title:||L-fuzzy sets and codes||Journal:||Fuzzy Sets and Systems||Volume:||53||Issue:||2||First page:||217||Last page:||222||Issue Date:||25-Jan-1993||Rank:||M21||ISSN:||0165-0114||DOI:||10.1016/0165-0114(93)90175-H||Abstract:||
A decomposition of an L-valued finite fuzzy set (L is a lattice) gives a family of characteristic functions, which can be considered as a binary block-code. Using a previous theorem of synthesis for fuzzy sets, we give conditions under which an arbitrary block-code corresponds to an L-valued fuzzy set. An explicit description of the Hamming distance, as well as of any code distance is also given, all in lattice-theoretic terms. Finally, we give necessary and sufficient conditions under which a linear code corresponds to an L-valued fuzzy set. It turns out that in such case the lattice L has to be Boolean.
|Keywords:||code | Fuzzy set | linear code||Publisher:||Elsevier|
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