Neutrosophic Math Tames Cost Risk in Farmland Water Projects

Every large construction project carries a hidden enemy: uncertainty. Budgets balloon, designs change, weather intervenes, and by the time the final account is settled, the numbers on paper rarely match the ones first promised. For farmland water conservancy projects—the irrigation and drainage infrastructure that underpins high-standard agricultural production in China—the stakes are especially high, because public money, food security, and long construction horizons all converge on the same balance sheet. A new study published in Frontiers in Physics proposes an unusually sophisticated answer to this age-old problem, blending fuzzy mathematics with the psychology of human judgment into a single decision-making engine.

The research, conducted by Xiaorong Wu of the Chongqing Qianjiang District Construction Engineering Affairs Center and Xu Chen of Chongqing University of Arts and Sciences, frames engineering cost risk assessment as a multi-attribute group decision-making problem. That formal framing matters. In practice, evaluating the cost risk of a major infrastructure project is never a single-number calculation: multiple experts weigh in, multiple risk categories compete for attention, and the information they provide is often vague, incomplete, or mutually contradictory. The authors argue that under the policy framework of new quality productive forces—China’s push toward innovation-driven, high-efficiency, low-risk construction—these tensions have only intensified, as new technologies and management modes introduce fresh categories of uncertainty into investment budgeting, construction implementation, and post-operation phases.

To capture that uncertainty, the researchers turned to single-valued neutrosophic sets, a mathematical tool introduced by Wang and colleagues in 2010 that extends classical fuzzy logic in a striking way. Where a conventional fuzzy number might say how true a statement is, and an intuitionistic fuzzy number might add how false it is, a neutrosophic number carries three components simultaneously: a truth-membership degree, an indeterminacy-membership degree, and a falsity-membership degree. When an expert says a project’s design risk is ‘moderately high but I am genuinely unsure,’ the triple can encode all three signals at once—confidence, hesitation, and doubt—without forcing the evaluator to collapse their judgment into a single crisp score. The authors argue this avoids the substantial information loss that plagues conventional fuzzy sets when experts confront ambiguous risk factors such as funding volatility, construction management lapses, or policy shifts.

But encoding uncertainty is only half the battle. The other half is how humans actually make decisions under risk, and here the study borrows from one of the most celebrated ideas in behavioral economics: prospect theory, the framework Daniel Kahneman and Amos Tversky developed in 1979 to explain why people fear losses more than they value equivalent gains. Building on that foundation, the TODIM method—an acronym for an interactive, multicriteria decision-making approach proposed by Gomes and Lima in 1992—computes gain-loss dominance degrees between alternatives, explicitly mirroring the risk-averse psychology of real evaluators rather than assuming perfectly rational calculators. The new work goes one step further with a logarithmic refinement, LogTODIM, in which logarithmic functions replace the traditional value function to better fit genuine cognitive patterns and, crucially, to dampen the influence of extreme attribute values that can otherwise distort rankings.

The integrated method, dubbed SVNN-LogTODIM, proceeds through a carefully ordered pipeline. First, each of several experts supplies neutrosophic assessments for every candidate project across every risk attribute, and a weighted aggregation operator fuses these into a single collective matrix. The matrix is then normalized to handle benefit-type and cost-type indicators appropriately. Next comes the weighting stage, and here the authors make a deliberate choice: rather than asking experts how important each risk factor is, they compute attribute weights objectively using Shannon entropy, a measure borrowed from information theory that quantifies how much discriminating information each indicator carries. Attributes whose values vary widely across projects earn larger weights; attributes that look nearly identical everywhere are downweighted. This removes subjective bias from the weighting process entirely.

With weights in hand, the LogTODIM machinery calculates relative weights, dominance degrees, and an overall dominance measure for each alternative, finally producing a ranking in which higher scores indicate lower cost risk. To demonstrate the method, the authors assembled a realistic case study: five candidate farmland water conservancy construction projects evaluated against six risk attributes—engineering design risk, material and equipment cost risk, construction management risk, natural environmental risk, policy and market risk, and supervision and settlement risk. Three domain experts participated: a senior cost engineer with eleven years of experience reviewing high-standard farmland project budgets, an infrastructure risk researcher with nine years in agricultural engineering, and a site project manager with thirteen years of hands-on construction risk control. Each expert provided independent neutrosophic assessments without prior discussion, minimizing groupthink.

The results were decisive. The analysis ranked the five projects in the order LA2, LA1, LA4, LA5, LA3, with LA2 emerging as the clear optimal choice—the least risky investment under uncertain conditions. To stress-test this conclusion, the authors compared their method against a battery of established alternatives, including the SVNNWA and SVNNWG aggregation operators, the SVNN-CODAS method, the SVNN-EDAS method, and the classical SVNN-TODIM technique. Nearly all approaches agreed on the winner, but the geometric SVNNWG operator produced a subtly different ordering that swapped the positions of LA4 and LA5—an artifact, the authors argue, of geometric aggregation exaggerating the influence of low-performance values. The neutrosophic CODAS and EDAS methods, meanwhile, struggled to distinguish closely matched alternatives and ignored the nonlinear interplay between data and decision-makers’ risk preferences.

Robustness was examined from two further angles. In a parameter sensitivity analysis, the attenuation factor capturing decision-makers’ risk attitudes was swept through values from one to five, covering both strongly loss-averse and mildly risk-seeking psychology. The ranking of the five projects remained unchanged across the entire range, with LA2 holding the top position and LA3 the bottom in every trial—evidence that the method’s conclusions are not artifacts of a particular behavioral assumption. In a second test, the entropy weights were replaced first with simple equal weights and then with weights derived from the MEREC method, which measures how much removing each criterion affects overall performance. Although the three weighting schemes assigned noticeably different numerical values to the six risk indicators, all three produced the identical final ranking, a result the authors present as strong evidence of the model’s stability in the face of reasonable methodological variation.

The practical implications extend well beyond the case study. Cost overruns—the notorious phenomenon in Chinese construction of final accounts exceeding estimates, budgets, and contracts—trace disproportionately to the pre-construction and design phases, where conceptual design decisions can influence ultimate project cost by as much as 95 percent, according to figures cited in the paper. Yet cost control effort has traditionally clustered in the construction and settlement phases, after the decisive choices have already been made. A tool that ranks projects by cost risk before ground is broken, and does so while honestly representing expert hesitation and disagreement, gives project managers and government stakeholders a way to prioritize oversight, allocate contingency funds, and screen candidates at precisely the moment when intervention is cheapest and most effective.

The authors are candid about limitations. The method was validated on a single category of infrastructure—farmland water conservancy projects—so its generalization to urban construction, transportation, or hydraulic engineering remains to be demonstrated. The expert panel comprised only three evaluators, which may limit the comprehensiveness of the group judgment, and the study relies on a single objective weighting scheme rather than a hybrid of subjective and objective approaches. Future work, they suggest, could broaden the project types and expert pools, fuse subjective and entropy-based weights into a composite system, and extend the static, one-time assessment into dynamic models capable of real-time monitoring and early warning as construction unfolds. Even so, the fusion of neutrosophic uncertainty modeling, entropy weighting, and behaviorally grounded TODIM logic offers a compelling template: a decision framework that admits, mathematically, that experts do not know everything—and that ranks risks more honestly because of it.

Subject of Research: A neutrosophic multi-attribute group decision-making method for assessing engineering cost risk in farmland water conservancy construction projects

Article Title: New quality productive forces-empowered neutrosophic group decision-making approach for engineering cost risk assessment: evidence from farmland water conservancy projects

Article References: Wu, X., & Chen, X. (2026). New quality productive forces-empowered neutrosophic group decision-making approach for engineering cost risk assessment: evidence from farmland water conservancy projects. Frontiers in Physics, 14, Article 1964509. https://doi.org/10.3389/fphy.2026.1964509

Image Credits: AI Generated

DOI: 10.3389/fphy.2026.1964509

Keywords: neutrosophic sets, multi-attribute group decision-making, TODIM, prospect theory, engineering cost risk, farmland water conservancy, entropy weighting, sensitivity analysis, fuzzy mathematics, construction management, risk assessment, new quality productive forces