Multi-granular Decision Synthesis Based on Linguistic Evaluations

Decision makers may adopt linguistic evaluations at different linguistic granularities to describe and assess the same object, which may yield inconsistent decision outcomes. To model and synthesize such multi-granular linguistic evaluations, this paper introduces the notion of a multi-granular linguistic-valued decision formal context, which provides a structured representation of object-attribute relations expressed by linguistic evaluations. Moreover, recognizing that attributes may contribute unequally to the final decision, we embed attribute importance weights into the multi-granular formal context and construct an attribute importance weight-driven multi-granular linguistic-valued decision formal context, thereby elucidating how attribute importance weight shapes decision outcomes across granularities. Building on this framework, we develop a multi-granular decision synthesis algorithm based on linguistic evaluations, which consistently integrates evaluation information across different granularities under uncertain linguistic environments and thus offers effective support for decision making and selection.