Similarity preservation in fuzzy relational systems: Extension for hedges.

We present results on how formulas of fuzzy logic preserve similarity. The basic question can be put as follows: Does an input-output mapping, which is defined by logical formulas and which maps fuzzy sets to fuzzy sets, preserve similarity and to what extent? That is, can we estimate similarity degrees of the output fuzzy sets in terms of similarity degrees of the input fuzzy sets? In the present paper, we extend previously published results. Our extension consists in that we take truth-stressing hedges, i.e. truth functions of connective ldquovery truerdquo, into account. We present the similarity-estimation results and provide an example of application of our results.