Permutability of fuzzy consequence and interior operators and their connection with fuzzy relations

Abstract

This work is structured as follows. In Chapter 1 we brief y introduce some background and we recall the main definitions and results that will be needed. In Chapter 2 we collect several results that show connections between fuzzy relations and fuzzy operators. We also extend some of the known definitions to a more general ones. Chapter 3 is devoted to the analysis of permutability. We start analyzing certain cases of fuzzy relations and fuzzy operators. In particular, fuzzy preorders and indistinguishabilities and fuzzy consequence and interior operators. Then, we relate permutability of fuzzy relations with permutability of the operators that they induce using the different processes defined in Chapter 2. We focus in the cases of fuzzy operators induced by fuzzy preorders and similarities. Finally, we present the conclusions and the possible future work.