To understand why this work matters, it helps to start with the Belief Rule Base itself. The BRB is a semi-quantitative prediction method grounded in expert knowledge, and it has already demonstrated significant potential in diagnosing heart-related conditions. Unlike a black-box neural network, a BRB encodes its reasoning as a set of interpretable rules that combine expert judgment with data-driven inference. Inputs are mapped onto reference values, and an evidential reasoning approach, often abbreviated as ER, fuses the resulting evidence to produce a diagnosis with degrees of belief rather than a single brittle yes-or-no answer. That transparency is precisely what makes BRB models attractive for medicine, where clinicians need to understand why a system flagged a patient as high risk.

But there has long been a catch. In a traditional BRB, the model’s structure, including the reference values that anchor its rules, is determined largely by expert knowledge. In practical diagnostic applications, the researchers note, determining the BRB model structure based solely on expert knowledge presents substantial challenges. Experts may disagree, the number and placement of reference values can be arbitrary, and a poorly chosen structure can degrade the accuracy of the entire system. The new study tackles this weakness head-on by making the structure itself adaptive rather than fixed by hand.

The first pillar of the new method addresses the reference value selection problem. Instead of relying on clinicians to pick the thresholds that define, say, low, moderate, and high cholesterol, the team employs the K-Means clustering algorithm with an improved initial centroid selection strategy to automatically generate stable reference values from the data. K-Means is a classic unsupervised learning technique that partitions data points into clusters, but its performance is notoriously sensitive to where the initial cluster centers, or centroids, are placed. A bad initialization can trap the algorithm in a poor solution, producing unstable clusters and therefore unstable reference values. By improving how those initial centroids are chosen, the researchers ensure that the reference values generated for the BRB are consistent and reliable, giving the diagnostic model a solid data-driven foundation.

With stable reference values in hand, the framework then constructs multiple BRB models using the reference value sets derived from the clustering results. This is where the structure-adaptive character of the method becomes apparent. Rather than committing to a single hand-designed architecture, the system generates a family of candidate models, each built on a different clustering-derived structure. The evidential reasoning approach is then used for model inference across these candidates, and a comprehensive evaluation framework assesses performance across both complexity and accuracy dimensions. That dual-axis evaluation is a notable design choice: it enables flexible adjustments aligned with decision-makers’ requirements. A hospital deployment that prizes interpretability and low computational cost can favor a simpler model, while a research setting chasing maximum diagnostic accuracy can select a more complex one. The framework does not force a one-size-fits-all trade-off; it makes the trade-off explicit and tunable.

The second pillar of the method is the engine that tunes all of these models: a multi-strategy improved whale optimization algorithm, which the authors call MSIWOA. The whale optimization algorithm is a metaheuristic inspired by the bubble-net hunting behavior of humpback whales, which spiral upward through schools of prey. In its standard form, candidate solutions mimic this spiral movement and a shrinking encirclement pattern to search a problem space. Like many bio-inspired optimizers, however, the basic algorithm can stagnate prematurely, converging on a suboptimal set of parameters before it has fully explored the landscape. For a task as delicate as calibrating the parameters of a Belief Rule Base, premature convergence can mean the difference between a sharp diagnostic tool and a mediocre one.

The multi-strategy improvements are designed to counter exactly that weakness. By combining several modification strategies, the MSIWOA balances exploration, the broad search for promising regions of the parameter space, with exploitation, the fine-tuning of solutions within those regions. Applied to the SA-BRB, the optimizer searches for the parameter settings, including rule weights and belief degrees, that minimize diagnostic error while respecting the structural constraints of the model. The result is a BRB whose rules are not merely transcribed from expert opinion but refined against real patient data, while still retaining the interpretable rule-based form that makes the model auditable. It is a hybrid philosophy: let data determine the skeleton of the model through clustering, and let optimization polish its parameters through an improved swarm search.

The researchers validated the approach through heart disease case studies, and the results, according to the paper, confirm both the effectiveness and the practicality of the proposed model. The significance of that validation extends beyond cardiology. Heart disease diagnosis is a canonical benchmark problem in medical machine learning, and a method that succeeds there, while remaining transparent, is a strong candidate for adaptation to other conditions where early detection matters and where clinicians demand explainability. The authors frame early diagnosis and prevention as playing a critical role in mitigating the impact of heart disease, and their framework is explicitly aimed at that early stage, where subtle patterns in patient indicators must be weighed against uncertainty and incomplete information.

What sets this work apart in a crowded field of diagnostic AI is its refusal to choose between accuracy and interpretability, or between expert knowledge and data-driven automation. Deep learning models routinely achieve impressive classification scores but offer little insight into their reasoning, which limits their acceptance in high-stakes clinical settings. Purely expert-driven systems are transparent but brittle, vulnerable to the biases and blind spots of the people who built them. The structure-adaptive BRB occupies a middle path: expert knowledge still shapes the semi-quantitative reasoning framework, but the most error-prone structural decisions, the choice of reference values and the tuning of parameters, are delegated to clustering and to the improved whale optimizer. The comprehensive evaluation framework then lets the end user decide where on the complexity-accuracy spectrum the deployed model should sit.

The study, published open access on 6 October 2026 and citable under DOI 10.1007/s40747-026-02549-0, was supported in part by the Natural Science Foundation of Heilongjiang Province and several institutional programs at Harbin Normal University, where most of the authors are based, with Manlin Chen contributing from Changchun University of Technology. The work arrives at a moment when health systems worldwide are searching for decision-support tools that can triage cardiovascular risk earlier and more reliably, particularly in settings where specialist expertise is scarce. A diagnostic model that can generate its own stable reference values, adapt its structure to the data at hand, and be tuned for either speed or precision could lower the barrier to deploying such tools. If the SA-BRB framework’s promise holds up in broader clinical testing, the humble rule base, long overshadowed by deep neural networks, may prove that sometimes the smartest way forward in medical AI is not a bigger black box, but a better-structured, self-tuning window into the reasoning itself.

Subject of Research: A structure-adaptive Belief Rule Base model optimized with an improved whale optimization algorithm for heart disease diagnosis

Article Title: A heart disease diagnosis method based on structure-adaptive Belief Rule Base and multi-strategy-improved whale optimization algorithm

Article References: Sun, X., Fu, W., Ma, N., Duan, X., & Chen, M. (2026). A heart disease diagnosis method based on structure-adaptive Belief Rule Base and multi-strategy-improved whale optimization algorithm. Complex & Intelligent Systems. https://doi.org/10.1007/s40747-026-02549-0

Image Credits: AI Generated

DOI: 10.1007/s40747-026-02549-0

Keywords: heart disease, Belief Rule Base, whale optimization algorithm, K-Means clustering, evidential reasoning, machine learning, medical diagnosis, decision support systems, data mining, artificial intelligence, cardiovascular models, expert systems