Decomposed fuzzy sets (DFSs), which have been recently introduced in the field of fuzzy sets are a fuzzy set extension that deals with the membership degree and the non-membership degree of the elements in the set from a functional and dysfunctional point of view in more detail. On the other hand, Pythagorean fuzzy sets (PFSs) are another fuzzy set extension reflecting the hesitancy of decision-makers in a wider area. The main target of this study is to develop a new fuzzy set extension, decomposed Pythagorean fuzzy sets (DPFSs) in order to utilize the properties of DFSs and PFSs together. First, the basic principles and mathematical operators of the DPFSs are developed with their proofs. Then, a new fuzzy multi-criteria decision-making (MCDM) method, DPF- Combinative Distance based Assessment (CODAS) is developed to demonstrate the feasibility and effectiveness of the DPF extension. The developed method is handled in the strategy selection problem for Internet of Things (IoT)-based sustainable supply chain systems. A comprehensive sensitivity analysis is performed on both the criteria weights and the decision makers' weights to verify the stability and effectiveness of the obtained results. In addition, a comparative analysis with decomposed fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Pythagorean fuzzy CODAS and Pythagorean fuzzy TOPSIS methods is presented to show the validity, superiority and advantages of the developed method.