Quantum model regression for generating fuzzy numbers in adiabatic quantum computing

This paper addresses the problem of inherent fuzziness in real -world data, arising from uncertainties, complexities, and limitations of traditional statistical methods. We introduce a pioneering method leveraging Adiabatic Quantum Computing (AQC), based on an adiabatic quantum regression model, to generate fuzzy numbers-ideal tools owing to their extension of real numbers and robust arithmetic properties. This innovative approach overcomes challenges in Quantum Machine Learning (QML) and limitations of Noisy Intermediate -Scale Quantum (NISQ) computers, providing a solution superior to conventional statistical methods and addressing the crucial issue of exponential power increase. Unique to this work, we offer rare closed -form expressions to produce fuzzy numbers through AQC and emphasise the integration of random variables and fuzzy numbers to encapsulate uncertainty fully. We propose a novel transformation of the Cumulative Distribution Function (CDF) into triangular and trapezoidal fuzzy numbers using AQC, enabling a comprehensive description of probability distributions of random variables. Experimental results are detailed, demonstrating the significant applicability and breakthroughs of this research in addressing data fuzziness.