The purpose of this paper is to develop a generic model for the patient priority criterion in the transplantation of a specific organ. Our model is based on graded logic and the LSP evaluation method. We include medical, social, and ethical attributes with the intention to develop a complete list of evaluation attributes that can be customized for use in a variety of social environments. Specific medical aspects of decision model are developed for the case of liver transplantation. The proposed methodology can be customized for other organs. This is the reason why we hope that the proposed approach can provide necessary sophistication, explainability, and applicability in all social environments where the goal is to improve the results of organ transplantation process by developing and using advanced decision models.