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arxiv: 2604.25958 · v1 · submitted 2026-04-27 · 🧮 math.GM

Recognition: unknown

Introduction of Over/Under/Off Masses

Florentin Smarandache
Authors on Pith no claims yet

Pith reviewed 2026-05-07 17:02 UTC · model grok-4.3

classification 🧮 math.GM
keywords over/under/off massinformation fusionuncertain theoriesneutrosophic setsfuzzy logicevidence combinationwildfire evacuationcoverage gaps
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The pith

Over/under/off masses extend uncertain set and logic concepts to information fusion.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends the over/under/off framework previously applied to sets, logic, and probability in fuzzy and neutrosophic theories directly to masses used in information fusion. It presents this as a new tool for combining evidence from multiple uncertain sources. The extension is illustrated through three practical scenarios involving real-world data streams. A sympathetic reader would care if the approach provides a systematic way to represent and combine over-assigned, under-assigned, or indeterminate belief masses without inventing entirely separate structures.

Core claim

For the first time the over/under/off concepts from sets, logic, and probability are carried over to masses, producing over-masses (values above 1), under-masses (values below 0), and off-masses (indeterminate values) that can be used when fusing information from heterogeneous sources.

What carries the argument

The Over/Under/Off Mass, the direct transfer of over, under, and off assignments to belief masses in evidence combination.

If this is right

  • Satellite, IoT, and social-media data can be fused during wildfire evacuation and resource allocation by allowing masses to exceed 1 or fall below 0.
  • Coverage gaps can be represented explicitly through off-masses that capture indeterminacy.
  • Contradictory or erroneous reports in security monitoring can be discounted by assigning under-masses or off-masses.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same construction might be tried in other fusion frameworks that already use numerical masses, such as Bayesian updating or possibility theory.
  • If the extension works, existing software libraries for evidence combination could be modified by simply relaxing the [0,1] bounds on mass values.
  • Empirical tests on archived multi-source datasets would be needed to measure whether the added flexibility improves or merely complicates the fusion output.

Load-bearing premise

The over/under/off distinctions already defined for sets and logic carry over to masses in fusion without requiring additional axioms, proofs, or empirical checks.

What would settle it

Implement the proposed over/under/off masses in a standard fusion algorithm for one of the described scenarios and show that fusion error or decision quality does not change compared with ordinary masses.

read the original abstract

In this paper, for the first time, we extend the Over/Under/Off Set/Logic/Probability used in uncertain theories (such as: fuzzy, neutrosophic and extensions) to the Over/Under/Off Mass that could be used in Information Fusion. The approach is exemplified in three scenarios: (1) wildfire evacuation and resource allocation with satellite, IoT, and social media; (2) coverage gaps where indeterminacy must be managed; and (3) security monitoring where contradictory or erroneous reports are discounted.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript claims to introduce, for the first time, an extension of the Over/Under/Off framework from sets, logic, and probability (as used in fuzzy, neutrosophic, and related theories) to Over/Under/Off Masses suitable for information fusion, and illustrates the idea through three narrative scenarios involving wildfire evacuation/resource allocation, coverage gaps with indeterminacy, and security monitoring with contradictory reports.

Significance. If a rigorous formalization were supplied, the extension could provide a structured way to represent and combine over-assigned, under-assigned, and off-assigned mass values in fusion problems, potentially aiding applications with conflicting or incomplete sensor data. As written, however, the contribution remains at the level of a conceptual suggestion without definitions, operators, or consistency checks against existing mass-function theories.

major comments (2)
  1. [Abstract] Abstract: the central claim that the Over/Under/Off concepts are extended to masses is asserted without any definition of an Over/Under/Off mass function, any statement of the power-set construction, any normalization condition, or any fusion rule that would replace or augment Dempster’s rule or similar operators.
  2. [Scenarios] The three scenarios (wildfire, coverage gaps, security monitoring) are presented only as narrative descriptions; no assignment procedure for the over/under/off components of a mass, no example mass tables, and no demonstration of how fusion would proceed under the new structure are supplied, so the claimed usability in information fusion cannot be evaluated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. We agree that the manuscript, as currently written, introduces the Over/Under/Off Mass concept primarily at a conceptual and narrative level. We will prepare a major revision that supplies the missing formal elements while preserving the original illustrative intent.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the Over/Under/Off concepts are extended to masses is asserted without any definition of an Over/Under/Off mass function, any statement of the power-set construction, any normalization condition, or any fusion rule that would replace or augment Dempster’s rule or similar operators.

    Authors: The referee is correct that the abstract and body currently assert the extension without supplying the required mathematical apparatus. In the revised manuscript we will add an explicit definition of an Over/Under/Off mass function on the power set, state the normalization condition that the sum of all mass components equals one, and introduce a fusion operator that extends Dempster’s rule to accommodate over-, under-, and off-assigned masses. revision: yes

  2. Referee: [Scenarios] The three scenarios (wildfire, coverage gaps, security monitoring) are presented only as narrative descriptions; no assignment procedure for the over/under/off components of a mass, no example mass tables, and no demonstration of how fusion would proceed under the new structure are supplied, so the claimed usability in information fusion cannot be evaluated.

    Authors: We accept that the scenarios remain purely descriptive and therefore do not yet allow evaluation of the fusion procedure. The revision will include, for each scenario, (i) a concrete assignment procedure that partitions sensor reports into over-, under-, and off-mass components, (ii) numerical mass tables, and (iii) a step-by-step application of the proposed fusion rule showing how the combined mass is obtained. revision: yes

Circularity Check

0 steps flagged

No circularity: purely conceptual extension with no equations or derivations

full rationale

The manuscript asserts a novel extension of Over/Under/Off concepts to masses for information fusion and illustrates it with three narrative scenarios. No equations, axioms, normalization conditions, fusion operators, or formal definitions appear in the provided text. Consequently there are no derivation steps, fitted inputs, self-citations, or renamings that could reduce to the paper's own inputs by construction. The central claim remains an unformalized suggestion rather than a mathematical result, so the circularity patterns do not apply.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the assumption that the extension from sets/logic/probability to masses is valid and applicable to information fusion, with no free parameters or supporting evidence detailed in the abstract.

axioms (1)
  • domain assumption Over/Under/Off concepts from set, logic, and probability theories can be extended to masses for information fusion.
    This is the core premise stated in the abstract without further justification.
invented entities (1)
  • Over/Under/Off Mass no independent evidence
    purpose: To represent and manage uncertainty in information fusion tasks
    New term introduced as the target of the extension.

pith-pipeline@v0.9.0 · 5370 in / 1274 out tokens · 64766 ms · 2026-05-07T17:02:58.011705+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

4 extracted references

  1. [1]

    Journal of Mathematics and Informatics ,

    F. Smarandache, Operators on Single-Valued Neutrosophic Oversets, Neutrosophic Undersets, and Neutrosophic Offsets, “ Journal of Mathematics and Informatics ,” Vol. 5, 2016, 63 -67, Published on 29 June 2016, https://fs.unm.edu/SVNeutrosophicOverset-JMI.pdf; https://hal.archives-ouvertes.fr/hal-01340833

    2016

  2. [2]

    Smarandache, A Unifying Field in Logics: Neutrosophic Logic

    F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics , ProQuest Info & Learning, Ann Arbor, MI, USA, pp. 92 -93, 2007, https://fs.unm.edu/eBook-Neutrosophics6.pdf; first edition reviewed in ZentralblattfürMathematik (Berlin, Germany): https://zbmath.org/?q=an:01273000

    2007

  3. [3]

    Shafer, A mathematical theory of evidence, Princeton Univ

    G. Shafer, A mathematical theory of evidence, Princeton Univ. Press, 1976

    1976

  4. [4]

    Smarandache, An introduction to DSmT, Published in Florentin Smarandache & Jean Dezert (Editors): Advances and Applications of DSmT for Information Fusion (Collected works), Vol

    Jean Dezert, F. Smarandache, An introduction to DSmT, Published in Florentin Smarandache & Jean Dezert (Editors): Advances and Applications of DSmT for Information Fusion (Collected works), Vol. I, American Research Press, Rehoboth, 2004, Chapter I, pp. 3-35; https://fs.unm.edu/IntroductionToDSmT.pdf Received: Oct 19, 2025. Accepted: April 15, 2026

    2004