Abstract
We discuss construction of fuzzy implication and also correlation between negation and implication operators defined on fuzzy values. Two structures for fuzzy implications are studied: the lattice of Step-Ordered Fuzzy Numbers (SOFNs) and the Boolean algebra \(\mathfrak {B}\) of membership degrees for metasets. Even though these two approaches stem from completely different areas it turned out that they lead to similar applications and results. Both of them emerged from research conducted by W. Kosinski and can be applied not only in the most popular application field which is approximate reasoning but also for designing decision-support systems, enriching methods and techniques of opinion mining, or modeling fuzzy beliefs in multiagent systems.
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