Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation… (More)

Among various approaches to fuzzy logics, we have chosen two of them, which are built up in a similar way. Although starting from diierent basic logical connectives, they both use interpretations… (More)

Sachs (Can J Math 14:451–460, 1962) showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an… (More)

This contribution is concerned with the compactness of fuzzy logics, where we concentrate on the three standard fuzzy logics—Łukasiewicz logic, Gödel logic, and product logic.

Mamdani controller was successfully used in many applications. One of its interpretations is that it uses a fuzzy relation as an approximation of the desirable input–output correspondence. We analyze… (More)

A defuzzification function assigns to each fuzzy set a crisp value in a way that this value may intuitively be understood as the “centre” of the fuzzy set. In the present paper, this vague concept is… (More)

Triangular norms are associative operations which represent conjunctions in fuzzy logic. They were also studied in the context of probabilistic metric spaces. It is known that each continuous… (More)