Ridesharing has emerged as an alternative transportation mode along road networks around the world. Rideshare matching problem is vital to improve the sustainable development of ridesharing systems. This paper aims to address the stable two-sided satisfied matching problem considering the participants’ psychological perception. First of all, we investigate the elements that influence passengers’ and drivers’ ridesharing experience by means of semi-structured research interviews and questionnaire survey. Two ridesharing perception evaluation systems are originally established to get the preference orders of passengers and drivers separately. Then, rideshare matching-related definitions are stated and rideshare matching linguistic information processing is also elaborated in detail based on preference utility function, disappointment function, as well as elation function. Furthermore, we propose a stable two-sided satisfied matching model on account of fuzzy linguistic information processing about ridesharing, which is able to reflect participants’ psychological factors. To verify the validity of our model, we present a two-sided matching case based on hypothetical rideshare matching platform. The analytical results indicate that the use of stable two-sided satisfied matching method based on fuzzy linguistic information enables to substantially satisfy both drivers’ and passengers’ expectation and improve the sustainability of ridesharing systems.