| This paper analyzes regularization constraints in terms of fuzzy logical concepts
for transforming families of fuzzy sets in order to guarantee stable and linguistically interpretable
solutions of fine tuning fuzzy systems. For this purpose, transformations for fuzzy sets are introduced
which are constructed by means of the compositional rule of inference. It is investigated,
under which conditions on these transformations various characteristics of fuzzy partitions and
fuzzy sets like redundancy, convexity and topological aspects keep invariant. However, further
restrictions like the compactness of the set of admissible transformations are required in order to
guarantee stable solutions. It is pointed out that compactness in the uniform sense can be characterized
in terms of purely fuzzy logical concepts that is by means of fuzzy equivalence relations. |