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Constrained decomposition integrals: Embedding external conditions into non-additive aggregation
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DOI：10.1016/j.fss.2026.109898.png)
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Abstract
En 中文
The decomposition integral provides a versatile framework for non-additive integration, successfully unifying concepts such as the Choquet and concave integrals. However, its standard formulation lacks the capacity to model scenarios bounded by external physical, logical, or budgetary restrictions. In this paper, we introduce the constrained decomposition integral, a novel generalization that embeds external constraints directly into the underlying optimization problem. We analyze its theoretical properties, demonstrating that under general constraints, the integral preserves monotonicity and acts as an aggregation function. Furthermore, when constraints are linear, the integral retains computational tractability via linear programming and exhibits continuity along with positive homogeneity under homogeneous conditions. To illustrate the practical implications of our framework, we present a workforce scheduling case study and propose a novel scientometric indicator, the consistency-constrained citation index (CCI), which mathematically mitigates the “one-hit wonder” anomaly in research evaluation.
Keywords:
decomposition integral
constrained optimization
non-additive integration
aggregation function
linear programming
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