Civil Engineering Construction Progress Monitoring Assessment using  Hyper-Fermatean Neutrosophic Sets (HFNS): A New Method

Chunmei Yao; Huimin Zhao

Authors

Chunmei Yao School of Civil Engineering and Architecture, Anhui Water Conservancy Technical College , Hefei, 231603, Anhui, China
Huimin Zhao School of Civil Engineering and Architecture, Anhui Water Conservancy Technical College , Hefei, 231603, Anhui, China

Keywords:

Neutrosophic theory, Construction Monitoring, Civil Engineering, Fermatean Neutrosophic Sets

Abstract

Effective civil construction monitoring requires robust methods to handle uncertainty
and indeterminacy arising from incomplete data, expert subjectivity, and variable environmental
conditions. Traditional neutrosophic frameworks, including Interval-Valued Fermatean
Neutrosophic Sets (IVFNS), offer limited capability in modeling deep, multi-layered uncertainties
often present in complex civil infrastructure projects. In response to this gap, we propose a novel
extension, termed Hyper-Fermatean Neutrosophic Sets (HFNS), which introduces hyper
dimensional structures to represent multiple levels of truth, indeterminacy, and falsity
components. We formally define HFNS, develop new aggregation and advanced scoring
functions, and design a de-neutrosophication operator to translate HFNS data into actionable
decisions. Our framework is applied to a public case study from a civil construction company
civil construction, where we compare HFNS with classical Neutrosophic models. The
quantitative and qualitative analyses demonstrate that our methodology can offer a new solution
to advance monitoring of civil construction in civil engineering.

DOI: 10.5281/zenodo.15843598