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
We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat an...We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy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.
基金the National Natural Science Foundation of China(60474022)the Key Science Foundation of Education Commission of Hubei Province, China (D200729003+1 种基金D200529001)the research of the third author is partially supported by an RGC grant (CUHK) #2060297(05/07)
文摘We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy
