Some observations on left absolutely flat monoids.
In the paper the problem of mathematical properties of -operations and weak -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...
On the lattice of varieties of completely regular semigroups considered as algebras with the binary multiplication and unary inversion within maximal subgroups, we study the relations , , , , , , and . Here is the kernel relation, is the trace relation, and are the left and the right trace relations, respectively, for , is the core relation and is the local relation. We give an alternative definition for each of these relations of the form for some subclasses of ....