The mathematical backbone of the library is Dempster–Shafer Theory, sometimes called evidence theory or the theory of belief functions. Unlike classical probability, which requires every ounce of belief to be pinned to individual hypotheses, Dempster–Shafer Theory lets a source declare that its confidence covers a set of possibilities. A doctor reading a patient’s symptoms may be able to say the evidence points to a group of possible diseases without being able to split that support among them individually. This ability to represent partial knowledge and outright ignorance explicitly, rather than being forced to divide belief artificially, is what has made the theory attractive for sensor fusion, medical expert systems, target recognition in defense applications, and robotics.

Classical Dempster–Shafer Theory, however, rests on an assumption that rarely holds perfectly in the messy real world: that the possible hypotheses are mutually exclusive and exhaust all options. Categories can overlap, and information sources can generate extreme conflict. To handle overlapping hypotheses, researchers developed Dezert–Smarandache Theory, an extension built on a structure called the hyper-power set, which includes not just unions of hypotheses but also their intersections. A second, more notorious problem arises with Dempster’s original combination rule, which normalizes conflict away. In Zadeh’s famous counterexample, two sources strongly support two different hypotheses, and after normalization a third hypothesis that both sources consider nearly impossible ends up absorbing all the belief. That kind of counterintuitive result spurred a family of alternative fusion rules, including Yager’s rule, the transferable belief model of Smets, the Dubois–Prade rule, and the proportional conflict redistribution rules PCR5 and PCR6.

Building such machinery from scratch for every study is time-consuming and error-prone, and the authors found that existing tools each covered only fragments of the picture. The two existing Python packages and two R packages focus on classical Dempster–Shafer Theory, while the two MATLAB frameworks date from 2008 and 2010. According to a feature comparison conducted by the authors, no other modern tool combines classical DST, free and constrained Dezert–Smarandache models, a symbolic proposition parser, the hyper-power set, the DSmH fusion rule, and PCR5 within one interface. evidencelib, currently at version 1.2.0 under the MIT license, fills that gap. Its computational core is pure Python with zero runtime dependencies, requiring only Python 3.10 or newer, with optional Matplotlib support for visualization. It is installable from the Python Package Index, documented online, and validated by a test suite running in continuous integration on Python 3.10 through 3.14 with strict static type checking and an enforced coverage threshold of at least 90 percent.

Architecturally, the library is organized into five interconnected components. The Frame component defines the frame of discernment in one of three model variants: classical DST, the free DSm model in which all hypotheses may intersect, or hybrid models in which selected intersections are explicitly forbidden by constraints. A parser converts textual propositions into symbolic objects without executing arbitrary code, and the Proposition component encodes hypotheses as integer bitmasks over Venn regions, so that union, intersection, and containment reduce to single integer operations. The MassFunction component does the heavy lifting, offering belief, plausibility, commonality, and conflict measures; uncertainty metrics such as Deng entropy, fractal-based belief entropies, information volume, nonspecificity, and strife; the full menu of fusion rules; and round-trip import and export through dictionaries, JSON, and CSV, plus publication-ready LaTeX table output.

Two worked examples in the paper show what the library can do. The first is a weld inspection decision with three mutually exclusive outcomes: accept the component, repair it, or reject it. Visual inspection strongly supports acceptance with a mass of 0.70, while ultrasonic testing strongly supports repair with 0.65, producing a conjunctive conflict of 0.455 — a deliberately high value that exposes the differences between conflict-handling strategies. Smets’ rule parks the conflicting mass on the empty set, Dempster’s rule normalizes it away, Yager’s rule transfers it to total ignorance, Dubois–Prade shunts it to the union of the contested hypotheses, and PCR5 redistributes it proportionally. The choice of rule changes the operational outcome: under Dempster’s rule the pignistic probability of acceptance is 0.539, clearing an illustrative decision threshold of 0.50, but under Yager’s rule it falls to 0.445, which under the example’s policy would trigger an additional inspection. The same evidence, the same hypotheses — yet a different action, purely because of how conflict is managed.

The second example leaps into territory classical theory cannot reach: diagnosing a pump that may suffer electrical, mechanical, and hydraulic faults simultaneously. In the free DSm model, these fault types may co-occur, and the hyper-power set for three hypotheses contains 19 propositions. Fusing readings from motor-current, vibration, and pressure-and-flow analysis with the conjunctive DSmC rule assigns the largest mass, 0.2925, to the intersection of electrical and mechanical faults, revealing a dominant electromechanical state with an additional hydraulic contribution rather than forcing a single diagnosis. The generalized pignistic transformation then distributes probability over the seven disjoint Venn regions, with the three-way fault intersection receiving 0.425.

The pump case also demonstrates the hybrid model’s power. If maintenance knowledge rules out a purely electrical fault co-occurring with a purely hydraulic one, a single constraint deletes those regions, shrinking the hyper-power set from 19 propositions to 13. Refusing the same data with the DSmH rule, which redistributes the support of forbidden intersections to the disjunctions of the involved propositions, sharpens the diagnosis: the electromechanical region’s pignistic probability rises from 0.257 to 0.521, and the Deng entropy of the fused assignment drops from 5.8371 to 4.5523 — a quantified measure of how a structural constraint reduces total uncertainty. Because the sources and masses are identical, every difference is attributable solely to the model constraint, making the library a natural laboratory for testing how modeling assumptions shape conclusions.

The tool has real limits, and the authors are candid about them. The free DSm hyper-power set grows explosively: with six hypotheses it contains 7,828,353 propositions, so complete free-model enumeration is recommended only up to five hypotheses, with larger problems requiring constrained hybrid models or classical DST. Venn diagram visualization caps out at three hypotheses, the implementation processes finite batches rather than streams, and the dependency-free pure-Python core, while maximally portable, avoids NumPy vectorization and is therefore not built for high-throughput workloads. The library also takes mass functions as input; deriving those masses from raw sensor data and modeling source reliability remain the user’s responsibility.

Even so, the significance is considerable. By turning the choice of hypothesis model and combination rule into a parameter of analysis rather than a fixture of hand-written code, evidencelib lets researchers directly study how modeling assumptions and conflict handling affect belief measures, uncertainty metrics, decision rankings, and final actions. For anyone building sensor networks, diagnostic systems, or any pipeline where imperfect sources must be reconciled, it promises to shorten the path from idea to reproducible, publishable result. The authors plan adaptive conflict-redistribution rules and more efficient fusion for large numbers of sources in future releases, and hint at an optional accelerated backend — keeping the core lean while the evidence gets heavier.

Subject of Research: Evidence modeling and fusion under uncertainty using Dempster–Shafer and Dezert–Smarandache theories

Article Title: evidencelib: A python library for evidence modeling and fusion under uncertainty

Article References: Śniegowski, S., Świder, A., Shekhovtsov, A., & Sałabun, W. (2026). evidencelib: A python library for evidence modeling and fusion under uncertainty. SoftwareX, 36, Article 103019. https://doi.org/10.1016/j.softx.2026.103019

Image Credits: AI Generated

DOI: Not provided

Keywords: evidencelib, Dempster–Shafer theory, Dezert–Smarandache theory, evidence fusion, uncertainty quantification, belief functions, conflict redistribution, sensor fusion, decision support, Python software, information fusion, open-source library