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The good development of health care is conducive to improve the value and prospects of society. However, health sectors of Ghana are facing a challenge in providing medical services with expected quality for an ever-increasing number of patients in response to competitive pressures. In such circumstances, the proper evaluation of hospital health-care delivery quality becomes critical. Thus, to achieve this goal, this paper proposes an integrated medical triangular fuzzy MULTIMOORA approach (IMTFMA). We firstly construct the appropriate evaluation criteria system based on the analysis of Ghana's medical services. Then, to properly evaluate the weight of the criteria in a comprehensive manner, we determine the weight of criteria from subjective and objective perspectives. Meantime, we handle the fuzzy evaluation of experts for the criterion importance with the enhanced alpha-level sets method. According to the triangular fuzzy rating for hospitals provided by respondents, we further develop a novel evaluation method based on MULTIMOORA with the axiomatic design for accurately evaluating health-care delivery quality. The research is conducted on 8 selected hospitals, including 4 public and 4 private hospitals in the Greater Accra Region of Ghana, with 24 criteria. 15 experts with rich experience in related fields and 480 respondents assessed the above 8 selected hospitals by questionnaires. According to the outcome of the empirical analysis, even though public hospitals benefit subsidy from the government, they perform abysmally low, whereas private hospitals which are self-sponsored rather perform extremely better than expectation. [ABSTRACT FROM AUTHOR]