Dual-Indeterminacy Neutrosophic Fusion for Calibrated and

Selective Multi-Source Classification under Source Conflict

Erina Kovachiskaya1,*

1 Faculty of Information Technology and Robotics, Vitebsk State Technological University, Belarus

Received: July 25, 2025 Accepted: September 29, 2025 ⋆ Corresponding author

ABSTRACT

Reliable multi-source AI requires a distinction between two non-equivalent failure modes: within-source ambiguity

and between-source contradiction. This paper formulates dual-indeterminacy neutrosophic fusion (DINF), in which

calibrated posteriors ps ∈ ΔK−1 are transformed into class-wise triples Nk = ⟨Tk, Ik,Fk⟩. Source weights combine

chance-corrected validation reliability, normalized entropy, and a robust Jensen–Shannon consensus discount.

Intrinsic ambiguity U and class-specific contradiction Ck are retained separately and joined by Ik =U +Ck −UCk.

The decision distribution qk ∝ Tk exp(−λIk) therefore penalizes conflict without collapsing neutrosophic evidence

into a probability simplex. Boundedness, permutation invariance, consensus preservation, conflict monotonicity,

log-odds sensitivity, and missing-source neutrality are established. Repeated experiments on three public benchmarks

examine clean data, 30% source dropout, 30% confident contradiction, and 40% mixed failure. Under contradiction,

DINF achieves macro-F1 0.910, NLL 0.445, and selective accuracy 0.939 at approximately 90% coverage; the

corresponding logarithmic-pool values are 0.896, 0.469, and 0.929. The results identify robust agreement discounting

and explicit contradiction-sensitive indeterminacy as complementary mechanisms for calibrated failure-aware fusion.

Keywords: Neutrosophic information fusion Multi-source classification Source conflict Uncertainty decomposition

Calibrated AI Selective prediction Robust decision fusion Sensor failure

1. INTRODUCTION

Let S calibrated sources describe the same item through posteriors

{ps}Ss

=1. A source can be diffuse because its own

observation is weak, or sharply confident while contradicting

the remaining sources. Mean fusion, fixed reliability weights,

entropy weights, and fixed logarithmic pools do not represent

these mechanisms separately; a low-entropy but erroneous

source may therefore dominate the fused decision.

Information-fusion studies identify heterogeneity, conflict,

and changing reliability as persistent challenges [1, 2, 3].

Probability calibration and proper scores are likewise necessary

when predictive confidence changes under shift [4, 5, 6].

Single-valued neutrosophic sets provide independent truth,

indeterminacy, and falsity coordinates [7], but existing operators

commonly encode indeterminacy by one scalar and are

seldom tested under controlled source faults.

This work introduces DINF with

ps 7−→(rs,Hs,Ds,ws) 7−→{Tk,U,Ck, Ik,Fk,qk}Kk

=1.

Its contributions are: (i) Ik =U⊕Ck separates ambiguity from

contradiction; (ii) ws ∝ rs[α +(1−α)(1−Hs)]e−κDs detects

confident outliers without a separate fault classifier; (iii) formal

properties and log-odds sensitivity are derived; and (iv)

public-data experiments quantify calibration, robustness, and

selective prediction under four operating conditions.

The remainder reviews related methods, defines the operator,