Contradiction-Aware Neutrosophic–Fuzzy Sensor Fusion for Reliable

Irrigation Scheduling under Missing and Conflicting Evidence

Riad K. Al-Hamido1,∗

1Department of Mathematics, College of Science, AlFurat University, Deir-ez-Zor, Syria

Abstract

Smart irrigation decisions are often computed from multiple sensor and model channels whose evidence may

be gradual, missing, or mutually contradictory. A conventional fuzzy controller compresses these conditions

into a scalar membership μ ∈ [0, 1], whereas a single-valued neutrosophic representation can retain support,

indeterminacy, and opposition as (T, I, F ). This paper proposes a contradiction-aware neutrosophic–fuzzy

irrigation system (CNFIS) in which three evidence channels for criterion j are summarized by an availability

ratio qj , a robust fuzzy center me j , and a contradiction index cj . The resulting state is

(Tj , Ij , Fj) =

􀀀

qj emj , 1 − qj + qjcj , qj(1 − emj)

which satisfies Tj + Ij + Fj = 1 + qjcj and therefore separates missingness from contradiction without

interpreting the triple as a probability vector. A neutral-prior shrinkage rule sj = (1 − αIj)rj + αIj/2 is

then fused through b d =

j wjsj to estimate normalized irrigation demand, while U =

j wjIj supplies

an explicit re-sensing or abstention signal. The method is evaluated in a fully reproducible Monte Carlo

benchmark containing 30 independent runs of N = 5000 cases under five evidence r egimes; no field measurements

are claimed. At moderate missingness/corruption (pm, pc) = (0.10, 0.10), CNFIS obtains RMSE

0.03318 ± 0.00086 compared with 0.04192 ± 0.00079 for mean fuzzy fusion, a reduction of 20.84%. The reductions

remain 12.63% and 10.57% under severe and extreme regimes, respectively, while the ordinary fuzzy

mean retains a small advantage in clean evidence. At 80% selective coverage, the uncertainty score decreases

CNFIS RMSE from 0.03320 to 0.02825 in the moderate regime. These results support the proposed representation

as a mathematically transparent robustness layer for irrigation systems in which evidence quality, not

only fuzzy demand, must be modeled explicitly.

Keywords: Neutrosophic systems; Fuzzy logic; Smart irrigation; Sensor fusion; Uncertainty; Contradiction;

Missing data; Precision agriculture

1 Introduction

Irrigation scheduling can be expressed as a bounded decision map f : X → [0, 1] in which environmental

measurements x = (x1, . . . , xp) are converted into a normalized water-demand level d = f(x). The mapping

is rarely crisp because a soil-moisture value near a control threshold should not change an irrigation command

discontinuously from d = 0 to d = 1. Fuzzy sets address this gradual transition through a membership

function μA : X → [0, 1],1 and smart-irrigation research has consequently used fuzzy inference to combine

soil, climate, and temporal variables in closed-loop or decision-support configurations.2

The more difficult case i s not vagueness alone but unreliable e vidence. Let x jk denote the k th channel reporting

criterion j, for example a local sensor, a neighboring sensor, or a model-derived estimate. Even when