The Measures Of Fuzzy Subrings And Fuzzy Ideals

In this paper, we mainly deal with the measure of fuzzy subrings including the T-fuzzy subring degree based on a general t-norm, and the fuzzy subring degree of a fuzzy set based on the t-norm minimum. Meanwhile some preliminary results on the T-fuzzy ideal degree are obtained.Firstly, we give the definition of the fuzzy subring degree, study its equivalent versions and the fuzzy subring degrees of the intersection of fuzzy subsets, and investigate the relationships between the fuzzy subring degrees of the image and preimage of a fuzzy subset under a morphism. Then we deal with the fuzzy subring degree based on a general t-norm. Some equivalent versions are presented particularly when the involved fuzzy subset is a T- fuzzy sub-semiring. Under the condition ’TT ??,we discuss the relationships between the T-fuzzy subring degrees of two fuzzy subsets, their intersection under T’and their direct product and the relationships between the fuzzy subring degrees of the image and preimage of a fuzzy subset under a morphism.Finally, we introduce the concepts of T-fuzzy left ideal degree, the T-fuzzy right ideal degree and T-fuzzy ideal degree under a general t-norm andinvestigate their connections. Furthermore, the T-fuzzy ideal degrees of the intersection of two fuzzy subsets and the image of a fuzzy subset under a morphism are also studied.