With the increasing risk to human health and environmental issues, the selection of appropriate management and treatment of healthcare waste has become a major problem, especially in developing countries. There are various alternatives to dispose of health care waste. The important is to assess the best alternative among them. The assessment of each alternative should be done based on public health, psychological, economic, environmental, technological, and operational aspect. The selection of the best health care waste treatment (HCWT) alternative is a complicated, multi-criteria decision-making (MCDM) problem involving numerous disparate qualitative and quantitative features. Hence, in this research article, the MCDM method is presented for estimating and choosing the best alternative of HCWT by COPRAS technique in a Pythagorean fuzzy set (PFS). Here, in this paper, first of all, a new entropy measure on PFSs is proposed and its validity is studied. Thereafter, the MCDM technique Complex Proportional Assessment (COPRAS) is discussed in which the criteria weights are assessed by the proposed entropy measure and score function to enhance an efficacy and efficiency of the proposed technique. Furthermore, the above-defined technique is employed to resolve the real-life problem to obtain the best treatment alternative to disposal of the health care waste. Finally, sensitivity analysis is presented to rationale the proposed viewpoint for prioritizing HCWT alternatives.