Soft sets whose soft measure is zero

Abstract

The concept of soft sets is widely used in reasoning when dealing with vague, incomplete, and imprecise information. Since the introduction of the soft set concept by Molodtsov, the theory of soft sets has become the subject of interest for many researchers who have defined new concepts such as soft measure, soft $\sigma$-algebra, and other concepts that are defined in classical measure theory. In the work \cite{2023}, it was shown that with certain extensions, a soft measure can be constructed on the obtained soft $\sigma$-algebra based on soft premeasures on a soft semiring. This study demonstrates that the same conclusion can be reached using a simpler and more natural construction that does not involve the use of a soft exterior measure but rather considers soft sets whose soft measure is zero.