Complex Neutrosophic Measures with αψ-Regularization for Teaching Quality of University Ideological and Political Courses in the New Media Era

Abstract

This paper introduces a novel mathematical framework that extends complex 
neutrosophic sets through the development of a phase-coherent complex neutrosophic 
measure (PCN-measure) combined with an αψ-regularization scheme. The PCN-measure 
assigns to each measurable set a triplet of complex values truth, indeterminacy, and falsity 
expressed in polar form with amplitude and phase. Amplitudes are aggregated using σ
additivity, while phases are combined through circular-mean addition, ensuring 
invariance under global phase shifts. A new distance function is defined that integrates 
amplitude differences with wrapped phase distances, generalizing existing d-equality 
concepts in complex neutrosophic theory. To address topological regularity, a variational 
functional is introduced that penalizes phase discontinuities while preserving αψ
connectedness, and its minimizers are shown to retain structural coherence under stated 
conditions. The framework further proposes a phase-locked aggregation operator (PLA) 
that balances proximity in the new metric with topological connectedness, yielding 
unique solutions up to global phase shifts. While the contributions are primarily 
theoretical, the design is motivated by the cyclic and interconnected nature of 
performance indicators in university ideological and political education in the new media 
era. An illustrative example demonstrates the computation of PCN-measures, phase
coherent distances, and PLA minimizers, supported by numerical results with explicit 
parameter interpretations. 

DOI: 10.5281/zenodo.16934651