Operations on Multisets and Fuzzy Multisets

Abstract

This paper presents a comprehensive redefinition of Yagar's bag theory [5] by introducing novel notations and adopting the terminology of multisets. The primary objective of this study is to provide a solid foundation for understanding multisets, catering to those interested in delving into the core principles of this concept. We compare two variants of multisets: fuzzy multisets and crisp multisets, and explore their distinct characteristics. Additionally, we investigate various operations on multisets, including those involving fuzzy multisets. Furthermore, we discuss the significance of multiset relations in the context of data set theory.