As a concept put forward by Prof Zadeh, Z-numbers have become a research hotspot in fuzzy theory. Different from the previous fuzzy sets, Z-numbers possess a stronger ability in expressing uncertainty because of the unique structure. The chief purpose of this paper is to research linguistic uncertain Z-numbers with a rectangular coordinate system. Taking into account the shortcomings of previous studies, the rectangular coordinate system is firstly adopted to address linguistic Z-numbers. Based on the new expression, arithmetic operations are defined. After summarizing the drawbacks of the previous aggregation operators, a novel approach named linguistic uncertain Z-numbers weighted averaging aggregation operator based on the rectangular coordinate system (LUZWAAORCS) is defined. Subsequently, the Minkowski distance measure of linguistic uncertain Z-numbers is proposed and the rationality is proven by a theorem. Follow that, a score function considering the Minkowski distance measure and technique for order preference by similarity to an ideal solution (TOPSIS) is suggested to quantify the information in different Z-numbers. Besides, an innovative Cosine similarity is defined to measure the similarity. Simultaneously, several examples are used to describe the proposed innovations. As far as our latest knowledge is concerned, Z-numbers have never been researched with a rectangular coordinate system, so this may be another door to process Z-number-based information.