Abstract
T-and @aT-compositions, i.e., composite operations of sup-T and [email protected]T, and relationships among -, @aT-operators and t-norm are considered. It is shown that, if a composite fuzzy relational equation by T-composition has solutions, then a greatest one exists, and that if a similar equation by @aT-composition has solutions, a greatest or least one exists, and unlike in T-compositions, it may have no lower solutions even if it has a greatest. Furthermore, the equivalence of the - and @aT-operator, and the equipollence between t-norms and @aT-operators are also shown. These results may be applicable to fuzzy inference under compositional rules of inference.
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