AI 中文总结
研究模糊标量目标函数中规则诱导行为，通过特定方法区分前沿选择与参考改进行为，揭示参考遵循原因及不同规则集表现，为构建符合决策语义的模糊标量化提供诊断指标与实践指导。
AI 中文摘要
基于模糊规则的标量目标函数为在多准则优化和决策中编码定性偏好、参考区域以及准则间相互作用提供了一种灵活方式。然而，此类规则诱导的标量偏好格局可能与预期决策语义有很大差异。本文研究隶属度放置、隐式单准则基线规则和显式规则结果如何影响模糊标量目标函数的行为。使用两个分析控制的双准则帕累托前沿和一个嵌入式二维主导参考公式来区分前沿选择机制和参考改进行为。研究表明，明显的参考遵循可能由平坦的规则激活平台引起，而真正的参考遵循需要具有低平局模糊性的局部最小值。在主导参考设置中，具有竞争结果的全局隶属度可恢复稳健的帕累托权衡，但不一定能改进每个参考设计。相比之下，基于参考的三类规则集在当前测试中始终能改进主导参考、恢复帕累托集并避免平台驱动的选择。结果为构建优化行为与预期决策语义一致的模糊标量化提供了诊断指标和实践指导。
英文摘要
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.
CommentsPreprint, 19 pages, 5 figures
