Exploring Key Results on Soft Multigroups

Abstract

In (1999), Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. In (2011), Alkhazaleh et al introduced the notion of soft multiset as a generalization of Molodtsov’s soft set. In the work of Nazmul and Samanta (2015), the concept of Soft multigroup was introduced. This paper continues the study of soft multigroup which has been explored over some time. Onoyima et al. (2024) defined the idea of a soft multigroupoid but the definition was incomplete. We propose the complete definition of soft multigroupoid and the necessary and sufficient condition for a soft multigroupoid to be a soft multigroup was given. It is shown that the union of two soft multigroups is again a soft multigroup if they are comparable. Finally, more results in the framework of soft multigroup were established.