Artificial intelligence systems are increasingly being asked to make decisions from evidence that is incomplete, ambiguous or contradictory. A new mathematical framework aims to improve how such systems combine that evidence by treating information fusion as an optimization problem rather than simply applying a conventional averaging rule. The approach, developed by researchers at Chongqing Technology and Business University in China, combines intuitionistic fuzzy sets, entropy reduction and information diffusion to seek fused results that are both less uncertain and less damaging to the original data. In experiments and a software-development risk assessment, the method produced higher overall fusion-quality scores than several established operators.
Information fusion is the process of combining multiple observations, expert judgments or measurements into a single value that can be used for classification, prediction or decision-making. In many real-world situations, however, the inputs are not clean numerical measurements. An expert may partly support a proposition, partly reject it and still remain unsure. A sensor may provide evidence that is imprecise, while different sources may disagree. Conventional fuzzy sets can represent degrees of membership, but intuitionistic fuzzy sets go further by assigning both a membership degree and a non-membership degree. The remaining portion represents hesitation, or information that cannot confidently be assigned to either side.
For an intuitionistic fuzzy value, the membership degree, non-membership degree and hesitation degree must sum to one. If membership is high and non-membership is low, the evidence favors an option. If both are moderate, the system is uncertain. The hesitation term is calculated as one minus the membership and non-membership degrees, and disappears only when the two degrees together equal one. This three-part representation is useful in artificial intelligence, pattern recognition and multi-criteria decision-making because it distinguishes outright rejection from a lack of knowledge. Yet combining many such values into one has traditionally focused on mathematical properties such as monotonicity, commutativity and boundary conditions, rather than on whether the fusion result is actually informative.
The researchers argue that a fusion operator can possess elegant mathematical properties and still produce a poor answer. Any fusion process necessarily compresses several values into one, which may alter the relationships among the original observations. A result that is highly decisive may therefore be misleading if it has discarded too much of the evidence from which it was produced. Conversely, an operator that preserves the original data very closely may fail to reduce uncertainty at all. The new framework treats these as competing objectives: a useful fusion result should reduce uncertainty while minimizing its deviation from the input information.
To measure information loss, the study introduces a deviation function based on a new distance between intuitionistic fuzzy values. The researchers transform each fuzzy value into a triangular geometric representation and use the coordinates of an associated equilateral triangle to calculate how far the fused value lies from each original value. The distance is weighted according to the hesitation of the values, so that uncertainty is incorporated into the comparison rather than ignored. Information diffusion is then used to estimate how densely the original fuzzy observations are distributed. In technical terms, a normal diffusion function spreads each observation across a monitoring space using Gaussian-like kernels, assigning greater weight to nearby points and less to distant ones.
This diffusion step is designed for situations in which the available sample is incomplete. Instead of treating every observation as equally representative, the method estimates a joint density over the membership and non-membership dimensions. Those estimated densities are normalized and used as probability-like weights in the distance calculation. The resulting deviation score ranges from zero to one: a smaller value indicates that the fused result remains closer to the structure of the original information, while a larger value indicates greater potential information loss. The approach is intended to improve the description of relationships among fuzzy observations when ordinary statistical estimates may be unstable because the sample is small.
The second component is entropy reduction. In information theory, entropy is a measure of uncertainty, and the researchers calculate an intuitionistic fuzzy entropy using both hesitation and the separation between membership and non-membership degrees. They then compare the entropy of the original information with that of the fused value. The difference, called entropy reduction, becomes larger when fusion produces a less uncertain result. It can also be negative, meaning that the supposedly consolidated value is more uncertain than the original information set. The two measures are combined into a Fusion Quality Index, or FQI, defined as an increasing function of entropy reduction and a decreasing function of deviation. The proposed normalized form is the ratio of the natural logarithm of entropy reduction plus two to the natural logarithm of deviation plus three.
Rather than assigning fixed weights to the inputs and accepting the resulting value, the researchers search for the intuitionistic fuzzy value that maximizes the FQI. The candidate membership and non-membership degrees are constrained to remain within the ranges observed in the original data, while their sum must not exceed one. To solve this optimization problem, the study uses particle swarm optimization, a computational method inspired by the collective movement of groups of animals. In the reported simulations, the researchers generated sets of 20 intuitionistic fuzzy values and repeated the process 30 times. They compared the optimized method, called FQO, with five established aggregation operators: intuitionistic fuzzy weighted averaging, intuitionistic fuzzy weighted geometric, intuitionistic fuzzy hybrid geometric, intuitionistic fuzzy Choquet integral and Choquet-integral-based intuitionistic fuzzy arithmetic aggregation.
The results showed that FQO achieved the strongest overall fusion quality. It was slightly weaker than the Choquet-based methods on one measure of deviation in the randomized comparison, but it had a marked advantage in entropy reduction and in the combined FQI. Only FQO, weighted averaging and hybrid geometric aggregation produced positive average entropy reduction in that experiment; the other operators increased uncertainty on average. Pairwise one-sided Wilcoxon tests conducted on the 30 simulated results indicated that the optimized method outperformed the alternatives in FQI. The findings also revealed a fundamental tension: operators that suppress deviation more aggressively may reduce uncertainty less effectively. According to the researchers, this trade-off explains why a composite measure is more informative than judging fusion methods by information preservation or uncertainty reduction alone.
The team also tested the framework on a software-development risk assessment involving six competing projects and three broad categories of risk: product engineering, the development environment and project constraints such as resources, contracts and interfaces. These assessments are difficult to express as precise probabilities because they depend on expert judgments and incomplete information. After aggregating the risk evidence with the new method, FQO recorded the lowest average deviation, at 0.0859, and the lowest dispersion in that measure, indicating both limited information loss and comparatively stable performance. Its average entropy reduction was 0.1038, whereas several existing methods produced negative values. The resulting FQI was 0.6597, higher than the approximately 0.6 level reported for the other operators. When the six projects were ranked using the study’s intuitionistic fuzzy ordering relation, the fifth option emerged as the preferred choice.
The findings do not establish that the method will improve every AI system or every decision involving uncertain information. The experiments rely on simulated intuitionistic fuzzy data, and the authors acknowledge that their quality indicators capture only two aspects of what “good” information fusion might mean. Other factors could matter, including robustness to outliers, fairness among information sources, sensitivity to the diffusion bandwidth and the consequences of errors in the final application. The study also reports no newly generated or analyzed dataset beyond the experimental and case-study procedures described. Nevertheless, the framework offers a measurable way to ask a question often left implicit in fuzzy decision-making: not merely whether an aggregation rule is mathematically valid, but whether it makes the evidence clearer without erasing what the evidence contained. The researchers suggest that future versions could be applied to heterogeneous data in computer vision, traffic monitoring, autonomous systems, finance, engineering and environmental governance, where the quality of a fused judgment can shape the decisions made downstream.
Intuitionistic fuzzy information fusion optimized through entropy reduction, information-loss measurement and information diffusion theory.
Intuitionistic Fuzzy Information Fusion Optimized Through Entropy Reduction and Information Loss Measures Integrated with Diffusion Theory
Rong, S., Yan, L., & Yahan, W. (2026). Intuitionistic fuzzy information fusion optimized through entropy reduction and information loss measures integrated with diffusion theory. Cognitive Computation, 18, Article 104. https://doi.org/10.1007/s12559-026-10626-2
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https://doi.org/10.1007/s12559-026-10626-2
intuitionistic fuzzy sets, information fusion, entropy reduction, information loss, information diffusion, artificial intelligence, decision-making, particle swarm optimization
Subject of Research: Technology and Engineering
Subject of Research: Technology and Engineering
Article Title: Diffusion Theory Optimizes Intuitionistic Fuzzy Fusion, Cutting Entropy and Information Loss
Article References: Rong, S., Yan, L., & Yahan, W. (2026). Intuitionistic Fuzzy Information Fusion Optimized Through Entropy Reduction and Information Loss Measures Integrated with Diffusion Theory. Cognitive Computation, 18(1), Article 104. https://doi.org/10.1007/s12559-026-10626-2
Image Credits: AI Generated
DOI: 10.1007/s12559-026-10626-2
Keywords: advanced mathematical frameworks for AI evidence processing, decision-making under contradictory information, entropy reduction in AI decision-making, evidence fusion optimization, fusion quality assessment, fuzzy logic and information theory, handling incomplete and ambiguous evidence, improving data reliability in artificial intelligence, information diffusion in fuzzy systems, Intuitionistic fuzzy sets, risk analysis using fuzzy fusion, uncertainty minimization in data fusion
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SCIENMAG. (August 28, 2026). Diffusion Theory Optimizes Intuitionistic Fuzzy Fusion, Cutting Entropy and Information Loss. https://scienmag.com/diffusion-theory-optimizes-intuitionistic-fuzzy-fusion-cutting-entropy-and-information-loss/
SCIENMAG. “Diffusion Theory Optimizes Intuitionistic Fuzzy Fusion, Cutting Entropy and Information Loss.” Scienmag, 28 August 2026, https://scienmag.com/diffusion-theory-optimizes-intuitionistic-fuzzy-fusion-cutting-entropy-and-information-loss/. Accessed 28 August 2026.
SCIENMAG. “Diffusion Theory Optimizes Intuitionistic Fuzzy Fusion, Cutting Entropy and Information Loss.” Scienmag. August 28, 2026. https://scienmag.com/diffusion-theory-optimizes-intuitionistic-fuzzy-fusion-cutting-entropy-and-information-loss/
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