Powerset Theory of Fuzzy Soft Sets
This study proves that fuzzy soft sets also give rise to a powerset theory, which is also defined by a monad, and describes the construction of fuzzy soft relations as an example of the use of monads in fuzzysoft sets.
Abstract
Fuzzy powerset theory is defined by a monad, and therefore it can be applied in computer science. Fuzzy soft sets generalize fuzzy sets and have considerable application potential in, for instance, decision-making and optimization. In this study, we prove that fuzzy soft sets also give rise to a powerset theory, which is also defined by a monad. As in the case of fuzzy sets, in fuzzy soft set theory, it is possible to use several theoretical constructions requiring the existence of a powerset theory and monads. We describe the construction of fuzzy soft relations as an example of the use of monads in fuzzy soft sets.