Uncertain linguistic fuzzy soft sets and their applications in group decision making

• A novel concept of uncertain linguistic fuzzy soft sets (ULFSSs) is developed.
• Some traditional set operations of such fuzzy soft sets are discussed.
• Some algebra operations and the aggregation process of ULFSSs are studied.
• The application of ULFSSs in decision making is considered.

The aim of this paper is to develop a novel concept of uncertain linguistic fuzzy soft sets (ULFSSs), which applies the notion of uncertain fuzzy set to the soft theory. The relationships between two ULFSSs, including the inclusion relation, the equal relation and the complement relation, are studied based on the binary relations. We also introduce some basic set operations for ULFSSs, such as the ‘AND’ and ‘OR’ operations, the algebra operations. The properties of these operations are also discussed. As an application of this new fuzzy soft set, we propose a ULFSSs-based group decision making model, in which the weights of decision makers are obtained from a non-linear optimization model according to the ‘Technique for Order of Preference by Similarity to Ideal Solution’ (TOPSIS) method and the maximum entropy theory. Finally, an assessment of sound quality problem is investigated to illustrate the feasibility and validity of the approach mentioned in this paper.