半环中模糊理想的h-闭包

On H-closure of Fuzzy Ideals in Semirings

给出半环中模糊子集的h-闭包的定义。讨论了半环中几类模糊理想的h-闭包的性质。证明了半环中任意两个模糊子集的积(内禀积)的h-闭包与这两个模糊子集的h-积(h-内禀积)的等价性。引入半环的模糊h-广义双理想的定义,并讨论了它与模糊h-双理想的关系。最后用模糊h-左理想、模糊h-右理想、模糊h-理想和模糊h-广义双理想给出h-正则半环的刻画。

In this paper, the concept of h-closure of a fuzzy subset in a hemiring is introduced. Many important properties about the h-closure of several fuzzy ideals are investigated. By this concept the relationsip between the fuzzy h-generalized bi-ideal and the fuzzy h-bi-dieal is discussed. For any fuzzy subsets u and v, it is proved that the h-closure of their product （resp. , intrinsic product） their h-product （resp. h-intrinsic product）. Finally, by the fuzzy left h-ideals, fuzzy right h-ideals, and fuzzy h-generalized bi-ideals the h-hemiregular hemirings are characterized. is equivalent to h-ideals, fuzzy