Refined n-Valued Neutrosophic Markov Decision Processes for Quality Evaluation of Talent Cultivation in Vocational Education under Emerging Productive Forces

Abstract

Emerging Productive Forces (EPF) including artificial intelligence, green 
manufacturing, and digital platforms change skill requirements faster than classical 
curriculum planning can adapt. Standard Markov Decision Processes (MDPs) assume 
precise transition probabilities and rewards, which under-represent structural 
indeterminacy in new technologies and fast-evolving job roles. This paper develops a 
Refined n-Valued Neutrosophic Markov Decision Process (r-nMDP) for optimal 
vocational curriculum control. In r-nMDP, transition kernels and rewards are expressed 
as n-valued refined neutrosophic triplets (T,I,F) representing suitability, indeterminacy, 
and mismatch, respectively. Building on neutrosophic probability and its n-valued 
refinement, we define a Neutrosophic Bellman Operator, prove its contraction and fixed
point uniqueness under a weighted triplet norm, and establish policy improvement in a 
neutrosophic partial order. We also introduce a Neutrosophic Curriculum Efficiency 
Index (NCEI) to evaluate and compare policies with explicit penalties on indeterminacy 
and mismatch. A fully calculated case study with five skill states and three curriculum 
actions under EPF shocks demonstrates that r-nMDP policies reduce indeterminacy by 
20–30% while improving skill–demand alignment by 15–20% compared with a classical 
MDP baseline. The framework offers a rigorous, uncertainty-aware foundation for 
designing resilient vocational training strategies in the era of EPF.

DOI: 10.5281/zenodo.16884581