Authors: | Šešelja, Branimir Tepavčević, Andreja Vojvodić, Gradimir |
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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