New Insights into Binary Soft Set Theory: Revisions, Extensions, and Foundations
DOI:
https://doi.org/10.5281/zenodo.21154605Keywords:
Binary soft set, Binary soft set operations, Binary soft subsetAbstract
The concept of binary soft sets was first introduced by Açıkgöz and Taş (2016). However, certain deficiencies exist in both the fundamental concepts and the operational aspects of their framework. In this study, these shortcomings are addressed by revisiting the foundational concepts of binary soft set theory and updating existing definitions where necessary. Furthermore, several new concepts regarding binary soft sets are introduced. In this context, the definition, examples, and tabular/matrix representations of binary soft sets, the concepts of empty, absolute, and relative null/whole binary soft sets with respect to a fixed parameter set are proposed. This is followed by the introduction of binary soft subsets/supersets, support sets, complements, α,β-intersections/unions, and upper/lower α,β-inclusion sets. Finally, we propose various binary soft set operations, including restricted/extended operations, AND/OR-products, and Cartesian products. To ensure a deeper understanding, all the developed concepts are enriched with illustrative examples.
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