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 replaced by condition of positivity (negativity), i.\,e. operations must be only positively (negatively) defined. Weak $B$-operations may not fulfill associativity condition.