Characterizations and soft star-operations of soft fractional ideals on integral domains

The Molodtsov-conceived concept of soft sets provides a robust mathematical approach for managing uncertainty. This study explores the positive outcomes resulting from the application of soft set theory techniques, paving the way for innovative research methodologies in soft multiplicative ideal theory. The paper delves into the operations that lead to themselves within the realm of undeniable soft fractional ideals. Introducing the notion of soft star-ideals, we illustrate the construction of a complete lattice derived from the collection of all soft star-operations on integral domains. Furthermore, we provide characterizations for pseudo-principal domains, principal ideal domains, and greatest common divisor domains in relation to soft star-operations of undeniable soft fractional ideals.