Вирішення парадоксу Заде: аксіоматична теорія можливостей як фундамент надійного штучного інтелекту

DOI: 10.31673/2412-9070.2025.061215

Abstract

The paper builds a mathematically consistent model for describing uncertainty, which replaces the traditional one-dimensional approach to evaluating events with a dual system of measures - the measure of possibility and the measure of necessity. It is shown that the Zadeh paradox is not a random anomaly, but a critical failure of the conflict resolution mechanism in the Dempster-Shafer theory.
An axiomatic theory of possibility, using dual measures of possibility and necessity, has been presented as a plausible alternative. This approach provides a more honest and complete representation of the uncertain and contradictory state of knowledge. Instead of hiding the conflict, it brings it to the forefront, allowing the system to communicate the fundamental ambiguity of the situation.
An approach to modeling uncertainty for artificial intelligence systems is proposed that combines Dempster-Shafer theory with possibility theory, providing a consistent representation of epistemic uncertainty through confidence intervals and possibility/necessity measures. A modified approach to combining evidence for high-conflict scenarios is developed. A criterion for source consistency and a mechanism for adaptive source weighting in the expert assessment process are proposed.

Keywords: possibility theory; artificial intelligence; reliability; mathematical modeling; uncertainty.