Filomat 2022 Volume 36, Issue 6, Pages: 2129-2141
https://doi.org/10.2298/FIL2206129S
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Soft outer measure and soft premeasure
Stojanović Nenad (Faculty of Science, University of Kragujevac, Kragujevac, Serbia), nenad6006@gmail.com
Boričić-Joksimović Marija (Faculty of Organizational Sciences, University of Belgrade, Belgrade, Serbia), marija.boricic@fon.bg.ac.rs
Molodtsov introduced the concept of soft set as a new mathematical tool for
dealing with problems treating uncertainties, and, later, Riaz at al.
developed various concepts of soft sets. Here, we study the concept of soft
semiring and soft premeasure and explore their basic properties. We define a
[0,∞]-valued function on some soft set E, that is not a soft σ-algebra, and
then we extend this function to a measure on the soft σ-algebra generated by
E. We also introduce various set functions like soft content and soft
premeasures, and give their basic properties.
Keywords: soft σ-algebra, soft semiring, soft measure, soft premeasure, soft outer measure
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