Relations in Higher-order Fuzzy Logic III

This contribution is the third and last of a series of talks on relations in higher-order fuzzy logic. The first two [5] have introduced the logical framework (see also [3, 4]) along with a set of basic results that, at first glance, look very familiar. These results, however, have been developed from a much more general basis. Their proofs have been devised independently and resemble closer to proofs known from classical theory than to proofs of results existing in fuzzy set theory. The purpose of this contribution is to establish links between existing results in fuzzy set theory and the results contained in [5]. Moreover, we provide an interpretation to which extent this new framework really adds value and an educated guess what its potential impact on the further development of theory may be.