Rule-Induced Behavior of Fuzzy Scalar Objective Functions for Reliable Multi-Criteria Decision Making

Olaf Frommann

arXiv:2607.20731v1 Primary: math.OC Secondary: cs.CE

Abstract

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.

Disclosure

“vendored FuzzyGoal 1.2.0 dependency snapshot are archived on Zenodo at https://doi.org/10.5281/zenodo.21310754. Declarations No specific funding was received for conducting this study. The author declares no relevant competing interests. Generative AI assistance was used for language editing, documentation structuring, drafting support, and consistency checks; the author reviewed and validated the final manuscript and remains fully responsible for its content. References [1] Richard”
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Structural counts

Pages 19 pdf

Theorems 0 source

Lemmas 0 source

Propositions 0 source

Corollaries 0 source

Definitions 0 source

Displayed equations 53 source

Bibliography entries 20 source

Appendix pages 0 estimated

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Appendix pages include the first PDF page with an explicit Appendix heading through the final page.