  In 1999, Molodtsov \cite{1} developed the idea of soft set theory, proving it
to be a flexible mathematical tool for dealing with uncertainty. Several
researchers have extended the framework by combining it with other theories of
uncertainty, such as fuzzy set theory, intuitionistic fuzzy soft set theory,
rough soft set theory, and so on. These enhancements aim to increase the
applicability and expressiveness of soft set theory, making it a more robust
tool for dealing with complex, real-world problems characterized by uncertainty
and vagueness. The notion of fuzzy soft sets and their associated operations
were introduced by Maji et al. \cite{7}. However, Molodtsov \cite{3} identified
numerous incorrect results and notions of soft set theory that were introduced
in the paper \cite{7}. Therefore, the derived concept of fuzzy soft sets is
equally incorrect since the basic idea of soft sets in \cite{7} is flawed.
Consequently, it is essential to address these incorrect notions and provide an
exact and formal definition of the idea of fuzzy soft sets. This reevaluation
is important to guarantee fuzzy soft set theory's theoretical stability and
practical application across a range of domains. In this paper, we propose
fuzzy soft set theory based on Molodtsov's correct notion of soft set theory
and demonstrate a fuzzy soft set in matrix form. Additionally, we derive
several significant findings on fuzzy soft sets.
