In this paper,first we introduce n-polygroups and characterize 2-polygroups of order 4 up to isomorphism.Then using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner h...In this paper,first we introduce n-polygroups and characterize 2-polygroups of order 4 up to isomorphism.Then using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner hyperfield of order 4.Moreover,we propose a hyperfield of order 4 which is not as a quotient hyperfield F/G.Finally,some programs written in MATLAB which are based on obtained results compute the number of polygroups,weak polygroups and Krasner hyperfields of order4 up to isomorphism.展开更多
In this paper, we consider the relations among L-fuzzy sets, rough sets and n-ary polygroup theory. Some properties of （normal） TL-fuzzy n-ary subpolygroups of an n-ary polygroup are first obtained. Using the concep...In this paper, we consider the relations among L-fuzzy sets, rough sets and n-ary polygroup theory. Some properties of （normal） TL-fuzzy n-ary subpolygroups of an n-ary polygroup are first obtained. Using the concept of L-fuzzy sets, the notion of ~）-lower and T-upper L-fuzzy rough approximation operators with respect to an L-fuzzy set is introduced and some related properties are presented. Then a new algebraic structure called （normal） TL-fuzzy rough n-ary polygroup is defined and investigated. Also, the （strong） homomorphism of θ-lower and T-upper L-fuzzy rough approximation operators is studied.展开更多
文摘In this paper,first we introduce n-polygroups and characterize 2-polygroups of order 4 up to isomorphism.Then using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner hyperfield of order 4.Moreover,we propose a hyperfield of order 4 which is not as a quotient hyperfield F/G.Finally,some programs written in MATLAB which are based on obtained results compute the number of polygroups,weak polygroups and Krasner hyperfields of order4 up to isomorphism.
基金The second author is supported by National Natural Science Foundation of China （Grant Nos. 60774049, 60875034）, Natural Science Foundation of Education Committee of Hubei Province, China （Grant Nos. D20092901, Q20092907, D20082903, B200529001） and Natural Science Foundation of Hubei Province, China （Grant No. 2008CDB341）
文摘In this paper, we consider the relations among L-fuzzy sets, rough sets and n-ary polygroup theory. Some properties of （normal） TL-fuzzy n-ary subpolygroups of an n-ary polygroup are first obtained. Using the concept of L-fuzzy sets, the notion of ~）-lower and T-upper L-fuzzy rough approximation operators with respect to an L-fuzzy set is introduced and some related properties are presented. Then a new algebraic structure called （normal） TL-fuzzy rough n-ary polygroup is defined and investigated. Also, the （strong） homomorphism of θ-lower and T-upper L-fuzzy rough approximation operators is studied.
