On conjectures and consequences in fuzzy logic

Even though the authors´ ultimate goal is to begin with a theoretical study on the concepts of induction, abduction and deduction in the broad framework offered by the theories of fuzzy sets, the paper is nothing else than an experiment focused on two basic preliminary tasks. The first one is to introduce the concept of conjecture, as well as its particular cases hypothesis and consequence, into fuzzy logic (after excluding self-contradictory fuzzy sets). This is done by extending the definitions previously proposed by the authors in the setting of orthocomplemented lattices (Trillas et al., 2000), which appeared to be successful both for orthomodular and boolean lattices. Once these definitions are established, the next step is to study whether they are good enough to capture Zadeh´s compositional operator, which, as it is well known, generates the most common fuzzy inference method