Class of weak uni-norm operators and aggregation of fuzzy rules

We have demonstrated that strong uni-norm aggregation operators belong to the class of weak triangular norm operators. The new class of operators called weak uni-norm operators was introduced by relaxing condition of associativity of uni-norm operators. This class includes linear weighted averaging of uni-norm operators. Resulting weights are fixed and, thus, this type of aggregation can be used for constructing a fuzzy system with desired properties. A particular application involving linear self-identity operators for defining weights of weak uni-norms was considered, and it was shown that the latter provide additional leverage in fuzzy system modeling technology