**7. Conclusions**

A novel method for MADM problems under a linguistic term environment was proposed, combining shadowed sets and Pythagorean fuzzy sets. We defined Pythagorean shadowed numbers and subsequently described their operation rules and basic properties. Based on the operation rules, the score function of Pythagorean shadowed numbers was deduced, and a numerical example was provided to illustrate the computing process. Bearing the above results in mind, we proposed a new MADM approach to deal with linguistic terms. A supplier selection example was used to demonstrate the feasibility of our method. Compared with the linguistic term subscript method and the linguistic scale function method, a data-driven method was adopted to construct the shadowed set models for linguistic terms, which can avoid information loss or information distortion to a grea<sup>t</sup> extent. The comparative analysis shows that our method can provide more reasonable and accurate decision-making results by depicting linguistic terms in a more precise manner.

In future research, the proposed method can be extended to other types of shadowed sets, for example, left-shoulder, right-shoulder, non-cored, etc. Additionally, applications in other fields are also worth exploring with our approach.

**Author Contributions:** Methodology, H.W.; Writing—Original Draft Preparation, S.H.; Formal Analysis, C.L.; Investigation, X.P.; Writing—Review & Editing, H.W.

**Funding:** NSFC (No. 61402260, 61473176), and partly by the Taishan Scholar Project of Shandong Province.

**Acknowledgments:** The authors would like to thank the National Natural Science Foundation of China (No. 61402260, 61473176) and the Taishan Scholar Project of Shandong Province for the financial support.

**Conflicts of Interest:** The authors declare no conflict of interest.
