A New Neutrosophic Confidence Density Model for Statistical Effectiveness Evaluation in Highway and Bridge Project Internal Control

Abstract

This paper proposes a new mathematical model in the field of neutrosophic probability 
and statistics, called the Neutrosophic Confidence Density Function (NCDF). This model 
introduces a three-part probability density system that measures not just the chance of an 
event but also the uncertainty and possible contradiction around it. Traditional 
probability models cannot fully describe situations where data is incomplete or 
conflicting, especially in fields like construction effectiveness evaluation. To support real
world decision-making in highway and bridge project internal control, we apply the 
NCDF to model construction-related effectiveness such as inspection failure, safety issues, 
and quality errors. We also introduce a new operator, the Neutrosophic Confidence 
Integral Operator (NCIO), to combine weighted beliefs and update confidence across 
multiple data sources. 
We define the model mathematically, show how to apply it, and include real examples 
with full calculations. The results show that NCDF and NCIO provide more flexible and 
realistic analysis than classical statistics, especially when dealing with uncertainty and 
conflicting observations in infrastructure projects.

DOI: 10.5281/zenodo.16754423