This chapter is devoted to fuzzy structures — systems of fuzzy relations and functions on a set. We introduce and investigate basic structural notions connected with fuzzy structures, and basic relationships between fuzzy structures and a language of fuzzy predicate logic. As a matter of fact, what is developed here belongs traditionally to so-called model theory, in our case to model theory for fuzzy logic. However, this chapter is not to be understood to be a treatise on model theory for fuzzy logic. Rather, we present only notions and results that are more or less directly connected to fuzzy relational modeling. Notions and results of this chapter will be used in the subsequent chapters where several special fuzzy structures will be investigated.
KeywordsMembership Degree Residuated Lattice Fuzzy Relational Relation Symbol Truth Degree
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