Combining belief functions and fuzzy membership functions
Bibliographic record
Abstract
In several practical applications of data fusion and more precisely in object identification problems, we need to combine imperfect information coming from different sources (sensors, humans, etc.), the resulting uncertainty being naturally of different kinds. In particular, one information could naturally been expressed by a membership function while the other could best be represented by a belief function. Usually, information modeled in the fuzzy sets formalism (by a membership function) concerns attributes like speed, length, or Radar Cross Section whose domains of definition are continuous. However, the object identification problem refers to a discrete and finite framework (the number of objects in the data base is finite and known). This implies thus a natural but unavoidable change of domain. To be able to respect the intrinsic characteristic of uncertainty arising from the different sources and fuse it in order to identify an object among a list of possible ones in the data base, we need (1) to use a unified framework where both fuzzy sets and belief functions can be expressed, (2) to respect the natural discretization of the membership function through the change of domain (from attribute domain to frame of discernment). In this paper, we propose to represent both fuzzy sets and belief function by random sets. While the link between belief functions and random sets is direct, transforming fuzzy sets into random sets involves the use of α-cuts for the construction of the focal elements. This transformation usually generates a large number of focal elements often unmanageable in a fusion process. We propose a way to reduce the number of focal elements based on some parameters like the desired number of focal elements, the acceptable distance from the approximated random set to the original discrete one, or the acceptable loss of information.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.011 | 0.020 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.005 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".