Abstract
This research report focuses on the algebraic structure of the class of multisets equipped with their set operations. First the authors introduce the method to define a join operation in BCK-algebra without boundedness. Next, we define a subtraction on the set of natural numbers, and show that it forms a linear BCK-algebra. According to the above result and already-known theory of BCK-algebra, we define join and meet operations from the subtraction. Furthermore, we show that difference, union, and intersection of multisets can be defined through the above subtraction, join and meet operations, respectively. As the main result of the research, we prove that the class of multisets forms a commutative BCK-algebra with condition (S).
