We introduce the concept of T-fuzzy subhypermodules of hypermodules with respect to triangular norms and obtain some results. In particular, we define a probabilistic version of hypermodules using random sets and show...We introduce the concept of T-fuzzy subhypermodules of hypermodules with respect to triangular norms and obtain some results. In particular, we define a probabilistic version of hypermodules using random sets and show that fuzzy hypermodules defined in triangular norms are consequences of probabilistic hypermodules under certain conditions.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 ( No.60474022)the Key Science Foundation of Education Committee of Hubei Province,China (No.2004Z002 D200529001)
文摘We introduce the concept of T-fuzzy subhypermodules of hypermodules with respect to triangular norms and obtain some results. In particular, we define a probabilistic version of hypermodules using random sets and show that fuzzy hypermodules defined in triangular norms are consequences of probabilistic hypermodules under certain conditions.
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.
