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Some properties of B -operations

Bohdan Butkiewicz (2007)

Kybernetika

In the paper the problem of mathematical properties of B -operations and weak W B -operations introduced by the author for interpretation of connectives “and”, “or”, and “also” in fuzzy rules is considered. In previous author’s papers some interesting properties of fuzzy systems with these operations were shown. These operations are weaker than triangular norms used commonly for a fuzzy system described by set of rules of the type if – then. Monotonicity condition, required for triangular norms, is...

Some relations on the lattice of varieties of completely regular semigroups

Mario Petrich (2002)

Bollettino dell'Unione Matematica Italiana

On the lattice L C R of varieties of completely regular semigroups considered as algebras with the binary multiplication and unary inversion within maximal subgroups, we study the relations K l , K , K r , T l , T , T r , C and L . Here K is the kernel relation, T is the trace relation, T l and T r are the left and the right trace relations, respectively, K p = K T p for p l , r , C is the core relation and L is the local relation. We give an alternative definition for each of these relations P of the form U P V U P ~ = V P ~ ( U , V L ( C R ) ) , for some subclasses P ~ of C R ....

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