TOPSIS-RAD: Ranking According to Desires
Leonardo Fernandes Costa, Helder Gomes Costa, Diogo Lima, Brunno Rodrigues
Abstract
Traditional TOPSIS derives its reference points -- the Positive Ideal Solution () and Negative Ideal Solution () -- from the observed alternative set, making rankings susceptible to misalignment with decision-maker (DM) requirements, sensitivity to outlier performances, and rank reversal. This paper proposes TOPSIS-RAD, which addresses these issues by incorporating two arrays of DM-defined reference levels. Vetoed Performance Levels () exclude non-viable alternatives before normalisation, preventing them from distorting the ranking frontiers. Desired Performance Levels () cap performances at the DM's desired level before normalisation, anchoring the in explicit aspirations rather than dataset extremes. Three toy examples demonstrate each mechanism: reshapes normalisation boundaries by removing a non-viable alternative; fixed frontiers stabilise rankings by limiting the influence of performances well above the desired level. The method preserves the familiar distance-based structure of TOPSIS while grounding the ranking in stable, DM-specified boundaries. Limitations and future research directions are also discussed.
AI Impact Assessments
(1 models)Scientific Impact Assessment: TOPSIS-RAD: Ranking According to Desires
1. Core Contribution
TOPSIS-RAD proposes two modifications to the classical TOPSIS multi-criteria decision-making (MCDM) method: (1) Vetoed Performance Levels (VPL), which exclude alternatives failing minimum acceptable thresholds before normalization, and (2) Desired Performance Levels (DPL), which cap performances at decision-maker-specified aspiration levels before normalization. Together, these mechanisms replace data-driven PIS/NIS with fixed, DM-defined reference points, addressing three well-known TOPSIS weaknesses: misalignment with DM preferences, sensitivity to outliers, and rank reversal.
The core idea is conceptually straightforward — anchor normalization boundaries in exogenous reference levels rather than dataset extremes. This is not entirely new; the paper itself acknowledges that Chen et al. (2011), Kong (2011), García-Cascales & Lamata (2012), and de Farias Aires & Ferreira (2019) all proposed fixed reference points. TOPSIS-RAD's incremental contribution is the combination of a veto screening mechanism with performance capping, implementing a satisficing logic where exceeding an aspiration threshold earns no additional credit.
2. Methodological Rigor
The algorithmic description is detailed and clearly presented, with step-by-step formalization. However, the validation is limited to three toy examples with 10 alternatives and 4 criteria, all using equal weights and benefit-only criteria. This is a significant weakness:
The rank-reversal immunity claim is demonstrated by a single insertion test (A11), which is illustrative but not a formal proof. A rigorous treatment would require proving that the closeness coefficients are invariant to set composition under fixed VPL/DPL, which follows directly from the fixed normalization bounds but is never formally stated as a theorem.
3. Potential Impact
The practical utility of TOPSIS-RAD is plausible in regulated or procurement contexts where minimum thresholds and aspiration levels are naturally defined. The web application (Visual TOPSIS-RAD) adds accessibility. However, several factors limit impact:
4. Timeliness & Relevance
Rank reversal in MCDM remains an active research topic, as evidenced by recent publications cited in the paper. The problem is genuine and practically relevant. However, the specific solution proposed here — fixed external reference points — is well-trodden ground in the TOPSIS literature. The paper's positioning would benefit from engagement with the broader reference-point MCDM literature beyond the brief mention in Section 6.3, including methods like TODIM, PROMETHEE with reference profiles, or goal programming approaches.
5. Strengths & Limitations
Strengths:
Limitations:
Overall Assessment
TOPSIS-RAD presents a modest, well-motivated but incrementally novel extension to TOPSIS that combines pre-screening veto filters with aspiration-level capping. The conceptual contribution is sound but not deep, and the empirical validation is insufficient for a methods paper. The work would benefit substantially from real-world applications, formal proofs, and comprehensive sensitivity analysis. As presented, it reads as a preliminary methodological note rather than a complete research contribution.
Generated Jun 8, 2026
Comparison History (27)
Paper 1 is more novel and timely, addressing a fast-growing, high-impact area: stateful governance and provenance for AI coding agents. Its local-first, event-sourced design plus a deterministic pre-action “memory-as-governance” gate has clear real-world applicability and could influence tooling, reproducibility, and safety practices across software engineering and AI agent research. While its evaluation is limited (self-study, small n), it provides an implemented open-source system. Paper 2 is a sensible TOPSIS variant but appears incremental with toy examples and narrower cross-field impact.
Paper 1 introduces a novel methodological contribution (TOPSIS-RAD) that addresses well-known limitations of a widely-used MCDM method (TOPSIS), including rank reversal and sensitivity to outliers, with clearly defined mechanisms (VPL and DPL). This has broad applicability across operations research, engineering, and management science. Paper 2 is a replication/complementary study of PlanGPT with relatively incremental findings (LLM planner is no better than greedy search), which, while useful, primarily confirms existing skepticism about LLM-based planning rather than introducing new methods or surprising insights.
Paper 2 offers a concrete, incremental but publishable methodological contribution to a widely used multi-criteria decision-making method (TOPSIS), with clear problem framing (outliers, rank reversal, DM misalignment), explicit mechanism (VPL/DPL), and immediate applicability across engineering, management, and policy. Its rigor is easier to validate (properties, sensitivity, comparisons) and the topic is timely for decision analytics. Paper 1 is ambitious and potentially impactful, but reads more like a high-level framework proposal with anticipated results and unclear formalization/evaluation, making near-term scientific impact less certain.
Paper 2 proposes a concrete methodological improvement to TOPSIS, a widely-used multi-criteria decision-making method, addressing well-known practical problems (rank reversal, outlier sensitivity). It has clear applicability across operations research, engineering, management science, and any field using MCDM. Paper 1 is a philosophical argument about AI consciousness that, while timely, primarily advocates for a specific metaphysical position (Biological Idealism) without empirical methodology or testable contributions, limiting its scientific impact to philosophical discourse rather than broader scientific advancement.
Paper 2 has higher potential impact: it tackles timely, high-demand problems in tool-using LLM agents for real customer-service workflows, with broad applicability across AI, HCI, and software systems. It contributes both conceptual framing (declarative vs imperative orchestration as policy classes in a Dec-POMDP) and empirical evidence across multiple models and retrieval regimes, highlighting retrieval as the dominant bottleneck—an actionable insight for system design. Paper 1 is a solid incremental method in MCDM/TOPSIS with narrower cross-field reach and more limited validation (toy examples).
Paper 2 presents a novel algorithmic contribution (BiXDFBnB) that addresses a well-known challenge in bidirectional search—making front-to-front heuristics practical by reducing overhead. It adapts an existing framework (SFBDS) to maximization problems, demonstrates empirical improvements on multiple problem types (LSP, Snakes, CIB), and contributes to fundamental algorithmic research with broader applicability. Paper 1 proposes a variant of TOPSIS (a well-established MCDM method) with incremental modifications (VPL/DPL), demonstrated only on toy examples, limiting its demonstrated impact and methodological rigor.
Paper 2 is likely higher impact: it tackles a timely, high-interest problem (post-deployment self-improvement of LLM agents without supervision) with broad applicability across AI, software engineering, and autonomous systems. The proposed framework is more novel and general, and it reports empirical results across multiple benchmarks/agents with transfer and verifier-alignment analyses, suggesting stronger methodological rigor and real-world relevance. Paper 1 is a useful incremental extension to TOPSIS for decision analysis, but its scope and cross-field impact are narrower and the evidence appears limited to toy examples.
Paper 1 addresses a critical and highly timely challenge in AI safety—monitoring internal reasoning in frontier models. Its large-scale benchmarking and introduction of quantifiable metrics (time and token horizons) offer broad, immediate implications for AI development, oversight, and policy. In contrast, Paper 2 presents an incremental, albeit useful, methodological adjustment to a traditional decision-making algorithm (TOPSIS) validated only on toy examples, limiting its impact to a specialized sub-field of operations research.
Paper 1 has higher potential scientific impact due to a more technically novel and timely contribution: a fully engineered GPU-accelerated pseudo-Boolean SAT solver using JAX features (vectorisation, autodiff, JIT, sharding) plus tailored numerical/DFT techniques to address stability and scaling. This targets a core computational problem with broad downstream applications (verification, planning, optimization, AI) and can influence both SAT/constraint solving and GPU/ML-compiler-based algorithm design. Paper 2 is a practical refinement of TOPSIS; useful in decision analysis but more incremental and narrower in cross-field methodological impact.
Paper 2 proposes a concrete methodological improvement (TOPSIS-RAD) to a widely-used multi-criteria decision-making method, addressing well-known practical problems like rank reversal and outlier sensitivity. It offers a specific, implementable technique with clear applications across operations research, engineering, and management. Paper 1 is a philosophical/historical review synthesizing known ideas about probability, fuzzy logic, and deep learning without introducing new methods or empirical findings. While intellectually interesting, review-style epistemological essays typically generate fewer citations and less follow-on research than novel methodological contributions to active research areas.