Attribute-typed Gamma transformations in fuzzy soft sets for benefit, cost, linguistic and threshold criteria in multi-criteria clinical decision-making

Abstract Gamma soft set models convert raw attribute data into fuzzy memberships through a single transformation for all attributes, so they cannot express attributes whose desirability peaks at a target value. We propose the attribute-typed fuzzy Gamma soft set (AT-FGSS), in which a typing map assigns each attribute one of four types (benefit, cost, linguistic or threshold) and selects a matching transformation. Threshold attributes use a Gaussian target-proximity function whose tolerance is fixed by a half-membership calibration rule. We prove its algebraic properties and define intuitionistic and interval-valued extensions. It is applied to antihypertensive regimen selection in type 2 diabetes, using illustrative assessments from three expert panels, and to a non-clinical example; all results come from deposited code. The case-study ranking is stable under changes of tolerance, weights and input noise, and matches baseline methods once threshold attributes are given their target direction; guidance from the American Diabetes Association and the Eighth Joint National Committee supports only part of it. In about 23, 000 simulated problems with known ground truth, AT-FGSS identified the best alternative more often than six baselines when alternatives straddled the targets (84.9% versus at most 64.9%), in all 15 design variations, but not when the true preference was one-sided.