Homomorphism and isomorphism theorems on fuzzy lattices

Abstract

The idea of homomorphism in various algebraic and fuzzy algebraic structures has been researched by many scholars. In this study, we consider a Fuzzy Lattice and propose a new approach to study the concept of homomorphism on a fuzzy lattice. Some properties of homomorphism on a fuzzy lattice are studied with respect to a fuzzy congruence relation on a fuzzy lattice and the quotient of a fuzzy lattice. Consequently, we construct the first isomorphism theorem of a quotient of fuzzy lattices and apply this theorem to derive the second and third isomorphism theorems. Finally, we establish a one-to-one correspondence between the set of all fuzzy congruence relations which satisfy some condition and the set of all fuzzy congruences on a quotient fuzzy lattice.