Modeling temporal uncertainty using dynamic fuzzy soft sets: a framework for longitudinal decision-making with time-varying criteria

Decision making processes in the modern world are characterized by dynamics as far as evaluation criteria, relevant information, and human judgment itself change over time. Classical fuzzy soft set approaches, even when extended to the time series, suffer from inflexibility due to the fixed structure of parameters. In order to solve this problem, the novel approach, called the Dynamic Fuzzy Soft Set (DFSS) concept, is formulated in this paper. In contrast to previous approaches, DFSS allows parameters to be added, removed or to change their status in terms of importance. This makes the DFSS approach more applicable to longitudinal decision making processes and to situations when the structure of parameters evolves. The framework is elaborated within the rigorous mathematical formulation including definition of basic DFSSconstructs, corresponding algebraic operations, and structural properties compatible with classical fuzzy soft set theory. Relations and mappings are defined for dynamic fuzzy soft structures as well. An important property of DFSS framework distinguishing it from other approaches is a proper treatment of temporal evaluation and temporal aggregation without structural biases. Examples illustrating differences in the behavior of DFSSframeworkcompared to temporal fuzzy soft approaches are provided together with a case study demonstrating application of the proposed approach to educational decision making process.