| Abstract Hyperstructure theory and fuzzy type theory have both theoreti-cal computer science and mathematical research background dual. Hyperstructure theory has many important applications in pure mathematics and applied mathe-matics. Fuzzy type theory is a kind of higher-order fuzzy logic, which is used in residual lattice as an algebraic structure of truth values. On one side we study the theory of fuzzy hyperlattices further, which enriched its theory. And on another side we study the L-fuzzy filters in EQ-algebras and the category of EQ-algebras and the homomorphisms between them.The arrangement of this thesis is as follows:Chapter One:Preliminaries. The basic concepts and existing results of the the-ories of fuzzy hyperlatticesã€EQ-algebras and category which will be used throughout the thesis are given.Chapter Two:Fuzzy hyperlattices. We study the properties of fuzzy hyperlat-tices. The fuzzy hypercongruences and homomorphisms between two fuzzy hyperlat-tices are discussed further. It is proved that the set of all the fuzzy subhyperlattices of a fuzzy hyperlattice is a complete lattice and the product of two fuzzy hyperlat-tices is also a fuzzy hyperlattice. And a Galois correspondence between the category of all hyperlattices and weak homomorphisms and the category of all fuzzy hyper-lattices and weak homomorphisms is established. Finally, the concept of the strong fuzzy hyperlattices is introduced. An equivalent characteristic of strong fuzzy hy-perlattices is got and a way of how to get a strong fuzzy hyperlattice from a fuzzy hyperlattice is given.Chapter Three:EQ-algebras. First, the concept of L-fuzzy filters in an EQ-algebra is introduced, an equivalent characteristic of L-fuzzy filters is obtained, and it is proved that the set of all L-fuzzy filters is an orderly complete EQ-algebra. Then, the relationships among EQ-homomorphisms, EQ-congruences and L-fuzzy filters are studied, and the basic homomorphism theorems are obtained. Finally, we study the equalizerã€coequalizeã€product and pullback square in the category of all EQ-algebras and the homomorphisms between them, and its completeness is obtained. |
