Vague LI-Ideals In Lattice Implication Algebras

In order to research the logical system whose proportional value is given lattice, Y. XU proposed the concept of lattice implication algebras. Y.XU, Y.B. Jun and E.H. Roh introduced the notion of LI ¿ ideals of a lattice implication algebras The concept of fuzzy set was intrduced by Zadesh. With the development of fuzzy set, it is widely used in many fields Meanwhile, the deficiency of fuzzy sets are also attract attention. Such as fuzzy set is single function, it cannot express the evidence of supporting and opposing. Based on this reason, the concept of vague set introduced by Gau in 1993. The object of this book is to make a study of vague LI - ideals on lattice implication algebras. We introduce the concept of vague LI ¿ ideals on lattice implication algebra by linking the vague set and LI-ideal theory of Lattice implication algebras. Further we study the relation between VLI ¿ ideal and vague congruence relation of lattice implication algebras.