Neutrosophic Sets and Systems
Abstract
This article presents the Multi-Neutrosophic Ayni Method, a novel framework that integrates Latin American Indigenous philosophies with neutrosophic logic to guide ethical and sustainable AI development. Grounded in ancestral principles such as Ayni, Buen Vivir, In Lak’ech, ch’ixi, and nepantla, this approach models plural, ambiguous, and context-dependent ethical judgments through Multi-Neutrosophic Sets (MNS). A key contribution is the introduction of the Euclidean Multi-Neutrosophic Consensus Measure, which quantifies the degree of alignment among diverse stakeholders' evaluations without erasing epistemic differences. This measure enables the detection of convergence thresholds in intercultural deliberation, offering a rigorous yet flexible tool for decision-making. The method is illustrated through a case study evaluating the deployment of an AI diagnostic system in an Indigenous community. Results show how the iterative application of the Ayni principle—understood as reciprocal ethical negotiation—improves both alignment and legitimacy. This work demonstrates that Indigenous logics, when formalized through neutrosophy, are not only philosophically rich but also operationally valuable for developing just, inclusive, and context-sensitive technologies.
Recommended Citation
Leyva Vázquez, Maikel Y.; Noel Batista Hernandez; Edwin Alberto Callejas; and Florentin Smarandache. "Multi-Neutrosophic Ayni Method Based on Ancestral Logic and N-Alectic Reasoning for Ethical AI and Sustainability." Neutrosophic Sets and Systems 84, 1 (2025). https://digitalrepository.unm.edu/nss_journal/vol84/iss1/1
