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In order to incorporate linguistic information into decision making, it is necessary to apply computing with words (CW) techniques. Traditional CW models use only single and simple linguistic terms to represent both input and output, which limits the flexibility in information processing. Recent researches on computing with comparative linguistic expression, including extension models, has partially overcome this limitation. Nonetheless, the flexibility of linguistic information expression remains limited due to the discrete distributions of primary terms. A complete CW framework should include both encoding and decoding technologies for linguistic information, but previous researches have primarily focused on fuzzy encoding approaches, while ignoring fuzzy decoding techniques for linguistic expressions. To improve the accuracy and interpretability of CW in dealing with linguistic expressions, this research proposes a novel model called 2-tuple comparative linguistic expression (2-TCLE). To establish a framework for studying fuzzy representations of linguistic expressions, both fuzzy encoding and decoding approaches for 2-TCLE will be presented in a systematic manner that are performed to match each other. A novel linguistic computational model for dealing with 2-TCLE is presented and then applied to solve a multi-criteria group decision making case study. • A novel model named 2-TCLE is proposed. • Fuzzy encode approach for 2-TCLE is studied. • Fuzzy decode approach for 2-TCLE is studied. • A novel CW model dealing with 2-TCLE is provided. • The proposed CW model is applied to MCGDM. [ABSTRACT FROM AUTHOR]