Strong negations and restricted equivalence functions revisited: an analytical and topological approach. (English) Zbl 1522.03067
Summary: Throughout this paper, our main idea is to analyze the concepts of a strong negation and a restricted equivalence function, that appear in a natural way when dealing with theory and applications of fuzzy sets and fuzzy logic. Here we will use an analytical and topological approach, showing how to construct them in an easy way. In particular, we will also analyze some classical functional equation related to those key concepts.
MSC:
| 03B52 | Fuzzy logic; logic of vagueness |
Keywords:
fuzzy sets; strong negations; restricted equivalence functions; admissible distances; implication operators; real valued functionsSoftware:
BSDSReferences:
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