New open-source web tool brings uncertainty and group judgment into multi-criteria decisions

Every high-stakes decision, from choosing an energy technology to selecting a container port, involves juggling competing objectives, incomplete data, and the subjective judgments of the people making the call. A team of researchers led by Simone Pagliuca, River Huang, Matteo Cadoni, and Peter Burgherr has now released a free, open-source web application designed to make that juggling act more transparent. The software, called the UP-MAVT Suite, is described in the journal SoftwareX and combines a well-established decision-analysis framework with rigorous uncertainty propagation and native support for group decision-making, all wrapped in an interface that non-experts can use directly from a browser.

The mathematical backbone of the Suite is Multi Attribute Value Theory, or MAVT, a framework grounded in classical value theory that evaluates a finite set of alternatives across multiple criteria. In a typical problem, a small utility choosing between a photovoltaic installation, a gas turbine, and a diesel generator would score each option on capital cost, operating cost, greenhouse gas emissions, and reliability. Because preferences are subjective, MAVT uses value functions that map raw performance values onto a common scale from zero to one, allowing non-linear within-criterion preferences to be captured; for instance, a rent reduction from 1000 to 900 may be valued more than a reduction from 700 to 600. The relative importance of criteria is expressed through weights elicited by trade-off methods, and the overall value of each alternative is computed as a weighted sum of its criteria values.

What distinguishes the UP-MAVT approach is its treatment of uncertainty. Statistics, estimates, unclear input data, multi-actor dynamics, and subjective judgments are inherent sources of uncertainty in any decision process, yet few existing studies address them comprehensively across all model components. UP-MAVT converts deterministic inputs into probabilistic distributions and propagates them, via Monte Carlo sampling, all the way through the aggregation process to the final alternative rankings. This means decision-makers can assess not only the expected outcome of a choice but also how reliable that outcome is. The framework operates in two modes: a strict mode that generates results independently for each decision-maker, and a non-strict mode that aggregates their inputs, enabling both individual diagnosis and collective comparison.

The motivation for building new software came from a systematic gap analysis. A recent review of 25 free multi-criteria decision analysis tools identified two persistent weaknesses: restricted accessibility for non-specialist users and poor uncertainty handling. The authors examined six representative tools in detail. The MAMCA software supports structured engagement of multiple actors through surveys but offers no mechanism for propagating uncertainty. The MCDA Index Tool provides interactive composite indices with sensitivity analysis but no group decision-making. WEB-MAUT-DSS combines weighting methods flexibly but limits uncertainty to interval or discrete representations and offers a practitioner-focused interface. ValueDecisions runs Monte Carlo simulation within MAVT but confines uncertainty to input data, leaving weights and value functions deterministic, and requires data to be uploaded as spreadsheets. Entscheidungsnavi supports collaborative projects but only captures precision intervals rather than full distributions. The pymcdm library is powerful but aimed at programmers, and HELDA, which does propagate probability distributions through Monte Carlo simulation, is distributed only on request as a Java desktop application with stakeholder elicitation relegated to a survey plug-in.

The UP-MAVT Suite closes these gaps with a complete workflow that runs from decision-maker-facing elicitation to final result visualization. Technically, the platform follows a micro-service architecture deployed as a Docker Compose stack with four services: a React frontend built with Chakra UI, a Flask REST backend that handles authentication and session state, a standalone Python worker that executes computationally intensive Monte Carlo simulations, and a MongoDB database that stores case study definitions, elicitation data, and results. The worker polls the database for pending tasks and writes results back, decoupling heavy computation from the web application’s request-response cycle. The core algorithms are shared between web and local use through interchangeable data-loading modules, one reading from the database and one from local CSV files, so the mathematics remains identical regardless of the execution context. The entire codebase is released under the MIT license.

The analysis pipeline unfolds in five steps. First, decision-maker-specific weights are computed from elicited comparisons using the Best-Worst Tradeoff method and its hierarchical extension, PIvot Linked Elicitation BWT, which return uncertain weights by design. In linear mode the solver finds a single feasible weight set; in non-linear mode it produces a feasible weight space, a finite set of weight vectors each satisfying the elicitation constraints equally well, from which the Monte Carlo code samples uniformly at random in every iteration. Second, a non-strict Monte Carlo run compares three aggregation methods: the weighted sum, the geometric mean, and the harmonic mean, presented side by side as heatmaps so practitioners can see the difference between fully and partially compensatory approaches. Third, a strict Monte Carlo run examines the value distributions in detail so the overall scale of uncertainty can be judged. Fourth, a consensus diagnosis assesses the overlap of value distributions across experts, currently by visual inspection, with quantitative consensus metrics planned for future versions. Finally, a non-strict run with 10,000 iterations produces the smooth final heatmaps used to present conclusions.

Validation was thorough. The team replicated two published case studies along with an uncertainty-augmented variation and an analytically tractable case. A convergence study showed that Monte Carlo error reaches the range of ten to the power of minus three to minus two by 1000 iterations and is guaranteed to fall below ten to the power of minus three by 10,000 iterations for the largest cases. Since the third decimal place is treated as the last practically significant digit, 1000 iterations suffice for exploratory analysis while 10,000 serve as the default for final results. Scalability benchmarks showed memory use remains in the low megabytes, leaving runtime, driven mainly by the number of criteria and secondarily by the number of decision-makers, as the practical bottleneck. The software is backed by an automated test suite comprising 378 tests for the Flask backend with 71 percent statement coverage, 126 tests for the React frontend, and 59 tests for the Monte Carlo and PILE-BWT solver worker with 88 to 89 percent coverage.

To demonstrate the workflow, the authors replicated a port selection case study ranking seven European container ports, including Piraeus, Koper, Genoa, Antwerp, Rotterdam, Hamburg, and Gdansk, on six criteria ranging from terminal handling charges and ISPS fees to customs service, port reputation, satisfaction with terminal operations, and the number of container terminals. In the deterministic validation, value functions were elicited as piecewise-linear functions through guided mid-value splitting and weights through a slider-based trade-off interface with consistency feedback. The computed weights aligned with the reference study within rounding error, confirming correct implementation. In the uncertainty demonstration, deterministic performance values were replaced with probability distributions drawn from six supported families: discrete, normal, uniform, triangular, trapezoidal, and histogram. One criterion was treated as qualitative, with decision-makers ranking alternatives by drag-and-drop and adjusting tier gaps with sliders, supplemented by a self-declared confidence level that widens the value function to reflect subjective uncertainty. A second decision-maker with slightly different preferences showcased the group capability.

The outputs are designed for interpretation rather than mere computation. The strict Monte Carlo mode produces probability density functions of each alternative’s value, overlaid across experts, while the non-strict mode generates a ranking heatmap in which each cell indicates the probability that a given alternative achieves a specific rank. This distributional richness is precisely what the authors argue is missing from earlier approaches, which typically reduce full probability distributions to summary statistics or rank-based outputs. By embedding uncertainty directly within the value-theory structure of MAVT, the Suite captures subtleties that deterministic or simplified methods overlook, while preserving a framework with a long track record in environmental planning, wastewater policy, infrastructure scenarios, logistics, and energy-sector life cycle assessments.

The practical significance is the integration of two capabilities rarely found together: comprehensive uncertainty handling across all model components and native group decision-making with remote, asynchronous participation. Researchers gain a reproducible open-source platform, and practitioners gain stakeholder engagement comparable to dedicated multi-actor tools while obtaining fuller uncertainty quantification. The developers acknowledge limitations, including the empirical heuristic that converts confidence levels into value-function ranges without formal mathematical justification, and the absence of quantitative consensus thresholds. Future work will add quantitative parameters for characterizing results, more aggregation methods, enhanced visualization and export tools, quantitative consensus metrics, and additional weight-elicitation methods such as the classical swing technique. For now, the Suite stands as an unusually complete answer to a question that plagues every complex decision: not just which option looks best, but how confident we can honestly be that it is.

Subject of Research: An open-source web application for multi-criteria group decision analysis under uncertainty using MAVT and Monte Carlo simulation

Article Title: UP-MAVT suite: A web application for multi-criteria group decision analysis under uncertainty

Article References: UP-MAVT suite: A web application for multi-criteria group decision analysis under uncertainty. (n.d.). https://doi.org/10.1016/j.softx.2026.103112

Image Credits: AI Generated

DOI: 10.1016/j.softx.2026.103112

Keywords: multi-criteria decision analysis, MAVT, uncertainty propagation, Monte Carlo simulation, group decision-making, open-source software, web application, weight elicitation, Best-Worst Tradeoff, decision support systems, value functions, reproducibility