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Novel concepts of soft sets with applications. (English) Zbl 1368.54006

Summary: We introduce different concepts of soft sets, including soft \(\sigma\)-ring, soft algebra, and soft \(\sigma\)-algebra. We present different types of set functions, including soft finitely subadditive, soft countably sub-additive, soft finitely additive, soft countably additive and soft monotone. We study the concept of soft outer measure and soft Lebesgue outer measure. We also describe interesting applications of soft mappings to decision-making.

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
54A40 Fuzzy topology
11B05 Density, gaps, topology
54D30 Compactness
06D72 Fuzzy lattices (soft algebras) and related topics
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