2026/07/22 by Olaf Frommann
#math.OC #cs.CE
Fuzzy-rule-based scalar objective functions provide a flexible way to encode qualitative preferences, reference regions, and interactions between criteria in multi-criteria optimization and decision making. However, the scalar preference landscape induced by such rules can differ substantially from the intended decision semantics. This paper investigates how membership placement, implicit single-criterion baseline rules, and explicit rule consequents affect the behavior of fuzzy scalar objective functions. Two analytically controlled bi-criteria Pareto fronts and an embedded two-dimensional dominated-reference formulation are used to separate front-selection mechanisms from reference improvement behavior. The study shows that apparent reference following can be caused by flat rule-activation plateaus, whereas genuine reference following requires localized minima with low tie ambiguity. In the dominated-reference setting, global memberships with competing consequents recover robust Pareto tradeoffs but do not necessarily improve each reference design. By contrast, a reference-based three-class rule set consistently improves dominated references, recovers the Pareto set, and avoids plateau-driven selection in the present tests. The results provide diagnostic metrics and practical guidance for constructing fuzzy scalarizations whose optimization behavior is consistent with the intended decision semantics.