Ternary fuzzy soft sets

In this paper, incorporating the concepts of fuzzy sets and ternary soft sets, the ternary fuzzy soft sets could be introduced in formal context (information system). These ternary fuzzy soft sets, by integrating the idea of fuzzy set into ternary soft set, can symbolize the objects universe based on the degree of object with or without an attribute. In comparison to intuitionistic fuzzy soft sets and soft intuitionistic fuzzy sets, ternary fuzzy soft sets offer a simpler approach. We describe and demonstrate ternary fuzzy soft sets through some instances and reveal the practice of ternary fuzzy soft set vividly via Mind Mapping. Additionally, we define soft operations and the related attributes among the ternary fuzzy soft sets. Meanwhile, \((\alpha ,\beta )\) $(\alpha ,\beta )$ -Level ternary fuzzy soft set is launched with the decomposition theorem for ternary fuzzy soft sets studied.