三元超半群的(∈,∈∨q)-模糊超理想

(∈,∈∨q)-fuzzy hyperideals of ternary semihypergroups

为探索三元超半群的模糊子集具有的特征,采用(∈,∈∨q)-模糊化方法,给出了三元超半群的左(正、右)(∈,∈∨q)-模糊超理想概念,讨论其相关性质,得到了左(正、右)(∈,∈∨q)-模糊超理想的若干充要条件.(∈,∈∨q)-模糊超理想概念可用于刻画三元超半群的超正则性.研究结果表明:三元超半群的左(正、右)理想在经过(∈,∈∨q)-模糊化之后依然保留了原有的绝大部分性质.

In order to explore the properties of fuzzy subsets of a ternary semihypergroup, the concepts of left（right, lateral） hyperideals of a ternary semihypergroup are fuzzified by using the ＂belongs to＂ relation and ＂quasi coincident with＂ relation between a fuzzy point and a fuzzy subset. As a result, the definition of （∈,∈∨q）- fuzzy left （lateral, right） hyperideals of a ternary semihypergroups is obtained and some of their related properties are studied. Also, it is shown that （∈,∈∨q）- fuzzy left （lateral, right） hyperideals have an application in characterizing hyperregularity of ternary semihypergroups. The result of research indicates that most of the properties which hold in hyperideals can be transformed to （∈,∈∨q） - fuzzy hyperideals.