IDEAL FUZZY RING

Abstract

At this time the research on the ideal ring not only exist in the structure but can be combined with the concept of fuzzy set is the ideal fuzzy ring. This study proves the properties that express the relationship between ideal ring and ideal fuzzy ring. The study was conducted by studying literature from various sources, both books and journals that support and relevant to the review conducted. Based on the research, it is found that the ideal properties of fuzzy ring is if μμ ideal fuzzy in ring R and μμ (𝑥𝑥) <μμ (𝑦𝑦) for each 𝑥𝑥, 𝑦𝑦∈𝑅𝑅 apply μμ (𝑥𝑥-𝑦𝑦) = μμ (𝑥𝑥) = μμ (𝑦𝑦-𝑥𝑥). The properties that express the relationship between the ideal ring and the ideal fuzzy ring are a fuzzy subset is the fuzzy ideal in R if and only if the subset level μμ𝑡𝑡 is ideal in R, if I is ideal in R then there is μμ which is the ideal fuzzy ring in R such that μμ𝑡𝑡 = 𝐼𝐼 and the similarity nature of the two subset levels of a fuzzy subset in the ring are the same if and only if there is no 𝑥𝑥∈𝑅𝑅 such that 𝑡𝑡1≤μμ (𝑥𝑥) <𝑡𝑡2, and if μμ is ideal fuzzy in ring R then the ideal level of μμ is μμ𝑡𝑡0⊆μμ𝑡𝑡1⊆ ⋯ ⊆μμ𝑡𝑡𝑛𝑛 = 𝑅𝑅