In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly r...In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.展开更多
In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characteriz...In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characterized by the strong fuzzy regularity of the equivalence relation. Finally, the concept of θ-part of fuzzy hypergroup is introduced to determine the necessary and sufficient condition for the equivalence relation θto be transitive.展开更多
Quotient canonical(m,n)-hypermodules over Krasner(m,n)-hyperrings are studied as a generalization of the well-known algebraic hyperstructures.In this work,we prove that if N is a normal(m,n)-ary subhypermodule,then th...Quotient canonical(m,n)-hypermodules over Krasner(m,n)-hyperrings are studied as a generalization of the well-known algebraic hyperstructures.In this work,we prove that if N is a normal(m,n)-ary subhypermodule,then the m-ary hyperoperations defined on the quotient canonical(m,n)-ary hypermodule[M:N^(*)]are m-ary operations and the relation N^(*)is a strongly regular relation.Further,in this case,it is shown that the scalar hyperoperation is just an operation.展开更多
基金Supported by the National Natural Science Foundation of China(10861007)
文摘In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.
文摘In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characterized by the strong fuzzy regularity of the equivalence relation. Finally, the concept of θ-part of fuzzy hypergroup is introduced to determine the necessary and sufficient condition for the equivalence relation θto be transitive.
文摘Quotient canonical(m,n)-hypermodules over Krasner(m,n)-hyperrings are studied as a generalization of the well-known algebraic hyperstructures.In this work,we prove that if N is a normal(m,n)-ary subhypermodule,then the m-ary hyperoperations defined on the quotient canonical(m,n)-ary hypermodule[M:N^(*)]are m-ary operations and the relation N^(*)is a strongly regular relation.Further,in this case,it is shown that the scalar hyperoperation is just an operation.
