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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