Lattice Valued Intuitionistic Fuzzy Homomorphisms Of Universal Algebras

The theory of intuitionistic fuzzy homomorphism is an important part of in-tuitionistic fuzzy set theory. Basing on the values in a MV-algebra intuitionistic fuzzy sets, and using the concept of L-intuitionistic fuzzy relations, this paper shows an in-depth research on the related problems of intuitionistic fuzzy homo-morphisms. The main contents are as follows:Firstly, we give the definition of L-intuitionistic fuzzy relations and part intuitionistic fuzzy functions, and acquire some equivalent characterizations of the intuitionistic fuzzy functions. By using some concepts of intuitionistic fuzzy functions, we introduce the concept of uniform intuitionistic fuzzy relations. Then we do some rearch on the equivalent expression problem of the uniform intuition-istic fuzzy relations, bring the concept of (part) uniform F-intuitionistic functions, and then prove some fundamental properties of such functions.Next, we introduce the concept of uniform intuitionistic fuzzy relation mor-phisms and intuitionistic fuzzy congruences in the universal algebras, and attest the equivalent characterization theorems of uniform intuitionistic fuzzy relation morphisms. We also study the relationship between uniform intuitionistic fuzzy relation morphisms and intuitionistic fuzzy congruences.Thirdly, we present the concept of intuitionistic fuzzy homomorphisms, dis-cuss its basic properties, and obtain some equivalent conditions of the intuition-istic fuzzy homomorphisms. We study the relationship between intuitionistic fuzzy homomorphisms and intuitionistic fuzzy congruences, show the intuition-istic fuzzy homomorphism theorem and isomorphism theorem in the universal algebras.