The increasing integration of AI software into various aspects of our daily lives has amplified the importance of evaluating the quality of these intelligent systems. The rapid proliferation of AI-based software projects and the growing reliance on these systems underscore the urgency of examining their quality for practical applications in both industry and academia. This systematic literature review delves into the study of quality assessment metrics and methods for AI-based systems, pinpointing key attributes and properties of intelligent software projects that are crucial for determining their quality. Furthermore, a comprehensive analysis of this domain will enable researchers to devise novel methods and metrics for effectively and efficiently evaluating the quality of such systems. Despite its importance, this area of development is still relatively nascent and evolving. This paper presents a systematic review of the current state of the taxonomy of quality assessment for AI-based software. We analyzed 271 articles from six different sources that focused on the quality assessment of intelligent software systems. The primary objective of this work is to provide an overview of the field and consolidate knowledge, which will aid researchers in identifying additional areas for future research. Moreover, our findings reveal the necessity to establish remedial strategies and develop tools to automate the process of identifying appropriate actions in response to abnormal metric values.