A Study On The Falling Shadow And Soft Set Theory Of Hemirings

In this thesis, we investigate some properties and structures of hemirings byusing fuzzy sets, falling shadows and soft sets, the whole thesis is divided into fourchapters.The first chapter provides a brief overview of the history and current status ofresearch fuzzy sets, falling shadows and soft sets. Parts of the main research contentof this article are simply introduced.The second chapter presents falling fuzzy ideals, then we extend it to fallingfuzzyh-ideals, furthermore, their inference relations are introduced.Based on prefect positive correlations and independent probability spaces, thecharacterizations of h-hemiregular hemirings are obtained via falling fuzzyideals(h-ideals, h-bi-ideals, h-quasi-ideals) in third chapter.In fourth chapter, we put forward three kinds of (M,N)-soft intersectionh-ideals based on the soft intersection hemirings. The relationships among them areinvestigated. Moreover, the h-hemiregular hemirings are characterized by thesekinds of (M,N)-soft intersection h-ideals.