arXiv:2207.10783v2 Announce Type: replace
Abstract: In this article, we propose two quantitative methods for calculating weight vectors for incomplete pairwise comparison matrices using reference values. Both procedures are extensions of arithmetic and geometric heuristic estimation (HRE) methods. The proposed solutions allow flexible selection of the number of reference alternatives and the range of comparisons, from the acceptable minimum to a complete set. In this paper, we prove that the newly introduced geometric HRE method for incomplete data is optimal. For this method, we also prove the existence of a feasible solution. In the paper, we also provide sufficient conditions for the existence of a solution for the second arithmetic variant of the HRE method. We illustrate the presented methods with numerical examples.
Translating AI research into reality: summary of the 2025 voice AI Symposium and Hackathon
The 2025 Voice AI Symposium represented a transition from conceptual research to clinical implementation in vocal biomarker science. Hosted by the NIH-funded Bridge2AI-Voice consortium, the



