A Dynamic Survey of Soft Set Theory and Its Extensions

TL;DR

This paper provides a comprehensive survey of soft set theory and its various extensions, emphasizing their definitions, constructions, and recent developments across multiple mathematical and application domains.

Contribution

It offers a structured overview of the evolution and current state of soft set theory and its extensions, serving as a foundational reference.

Findings

Extensive overview of soft set variants

Connections to topology and matroid theory

Identification of key research directions

Abstract

Soft set theory provides a direct framework for parameterized decision modeling by assigning to each attribute (parameter) a subset of a given universe, thereby representing uncertainty in a structured way [1, 2]. Over the past decades, the theory has expanded into numerous variants-including hypersoft sets, superhypersoft sets, TreeSoft sets, bipolar soft sets, and dynamic soft sets-and has been connected to diverse areas such as topology and matroid theory. In this book, we present a survey-style overview of soft sets and their major extensions, highlighting core definitions, representative constructions, and key directions of current development.