偏序超半群模糊理想类的刻画

On Characterization of Classes of Fuzzy Ideals of Ordered Hyper-Semigroups

本文介绍了偏序超半群左(右)理想、拟理想和双理想的概念,并给出了这些理想的另一种刻画.如果f为偏序超半群H的模糊子集,f称为H的模糊左(右)理想当且仅当f满足条件1)1of≤f(fo1≤f)和2)若x≤y,则f(x)≥f(y);f称为H的模糊拟理想当且仅当满足条件1)fo1∧1of≤f和2)若x≤y,则f(x)≥f(y);f称为H的模糊双理想当且仅当满足条件1)fo1of≤f和2)若x≤y,则f(x)≥f(y).本文结果推广了Kehayopulu的工作.

The concepts of fuzzy left（resp. fuzzy right） ideals, fuzzy quasi-ideals and bi-ideals of ordered hypersemigroups are introduced in this paper, and furtherly, characterizations of them are given. We prove that f is a fuzzy left（resp. fuzzy right） ideal of ordered hypersemigroups if and only if 1） 1of ≤f（resp. fo1≤f） and 2） if x ≤y, then f（x） ≥f（y）. f is a fuzzy quasi-ideal of ordered hypersemigroups if and only if 1） fo1∧1of ≤fx） ≥f（y） and 2） if x ≤y, then f（. f is a fuzzy bi-ideal of ordered hypersemigroups if and only if 1） fo1of ≤f and 2） if x≤y, then f（x） ≥f（y）. As an application of results in this paper, the results of the paper are generalizations of ones of Kehayopulu.