L-Fuzzy Congruences And Ideals Of Semigroups

Let S be a semigroup and L be a complete lattice.In this paper,we study L-fuzzy congruences and L-fuzzy ideals on a semigroup.On this basis,we study properties of L-fuzzy congruences and L-fuzzy ideals on ordinary semigroups and several types special semigroups are discussed.The full text is divided into six chapters,and the main contents are as follows:In Chapter 1,we briefly introduce the research background and significance of fuzzy relations,explain the current research status at home and abroad,and summarize the main work content of this article.In Chapter 2,we give the definition of the L-fuzzy relation,and define the operation between two L-fuzzy relationships,such as "?","?","?" and so on.On this basis,the L-fuzzy congruence on the semigroup is studied,and it is proved that the L-fuzzy congruence? on the semigroup S is for any a,b?S,?-1(1)={(a,b)?S×S|?(a,b)=1} is the congruence on S and ?a=?b(?)?(a,b)=1.In Chapter 3,we define the "?" of two L-fuzzy subsets.The concepts of L-fuzzy ideals and several special L-fuzzy ideals and their equivalent definitions are given.It is proved that every L-fuzzy ideal of the semigroup S is a L-fuzzy interior ideal,and every L-fuzzy left(right)ideal is a L-fuzzy quasi-ideal,Every L-fuzzy bi-ideal is a L-fuzzy generalized bi-ideal,and every L-fuzzy quasi-ideal is a L-fuzzy bi-ideal.In Chapter 4,we introduce the properties of L-fuzzy congruence pairs of regular semigroups,groups,and ?-semigroups.We study the concept of L-fuzzy congruence pairs of inverse semigroups and their properties.In Chapter 5,we introduce some properties of the L-fuzzy ideals of regular,complete regular and intrinsic regular semigroups.In Chapter 6,we summarize the main work of this article and prospects for future work.