Research On Algebraic Structures And Weighted Correlation Coefficient Of Vague Soft Set

In abstract algebra,algebraic structures are mathematical structures composed of sets and operations on sets.The algebraic structures generally studied include groups,rings,fields,lattices,modules and field algebras.The algebraic structure of the Vague soft set is to add the relevant content of the soft set on the basis of the algebraic structure and blur it,which is more helpful to deal with the problem of uncertainty.This paper has studied the two algebraic structures of Clifford semigroup and BCK-algebra successively,combined them with Vague soft set,and obtained a series of new conclusions.The correlation coefficients and weighted correlation coefficients of the Vague soft set are also given,so as to better solve practical problems in real life.This article mainly did the following works:In the second chapter,the Vague soft set and the Clifford semigroup are linked together,and a new concept of Vague soft Clifford semigroup is proposed,the equivalence of Vague soft Clifford semigroup and the definition of Vague soft Clifford subsemigroup are given,and the basic algebraic properties of Vague soft Clifford semigroups are introduced.Firstly,it is proved that the intersection and union of any two Vague soft Clifford semigroups are still Vague soft Clifford semigroups.Secondly,it is proved that the Vague soft Clifford semigroup is a semilattice of the group and is a strong semilattice of the group and it is a regular semigroup.Finally,the definition of homomorphism between two Vague soft Clifford semigroups is given,and the homomorphic relationship between Vague soft Clifford semigroups is verified.In chapter three,the Vague soft set is applied to BCK-algebra,the concept of Vague soft BCK-algebra is introduced,and an example is given to help everyone understand the definition of Vague soft BCK-algebra and study its basic algebraic properties,it is concluded that two Vague soft BCK-algebras are still Vague soft BCK-algebras under the intersection and union of Vague sets,and then the Vague ideals on BCK-algebras and Vague soft ideals on BCK-algebras are given.The concept of soft ideals,at the end,illustrates the relationship between Vague soft BCK-algebras and Vague soft ideals on BCK-algebras: every Vague soft ideal on BCK-algebras is a Vague soft BCK-algebra,but not all the Vague soft BCK-algebras are all Vague soft ideals on BCK-algebras.In chapter four,since the correlation coefficient is one of the most widely used indicators in data analysis,the correlation coefficient of the Vague soft set is proposed.Compared with the correlation coefficient of the Vague set previously proposed,the correlation coefficient of the Vague soft set is more advantageous because it considers the case of negative correlation and introduces the idea of parameterization.In order to better solve practical problems in real life,the parameters of the Vague soft set are weighted to give the weighted correlation coefficient of the Vague soft set.Finally,through its application in venture capital problems,the effectiveness and feasibility of the weighted correlation coefficients of Vague soft sets are shown.