Fuzzy Relation Equations in Residuated Lattices

We would like to underline the following statement of Goguen [5]: “The importance of relations is almost self-evident. Science is, in a sense, the discovery of relations between observables... Difficulties arise in the so-called “soft” sciences because the relations involved do not appear to be “hard”, as they are, say, in classical physics. A thoroughgoing application of probability theory has relieved many difficulties, but it is clear that others remain. We suggest that further difficulties might be cleared up through a systematic exploitation of fuzziness”.