Teaching assessment at the university has attracted the interest of the university and its stakeholders for many years. However, since assessing teaching qualities involves elements of uncertainty and unreliability, considerable teaching assessment systems appear to have not been able to achieve their objectives in real-life circumstances. The situation becomes crucial if the university uses an inappropriate approach that insufficiently appraises the factors of competing criteria and ideal solutions. This paper implements the premise that it may simultaneously evaluate both factors. It used the Fuzzy Delphi Method (FDM) in conjunction with the Z-number approach to reduce the degree of ambiguity in the selection of the faculty members who did well in their teaching assessments. The FDM method provides six comprehensive step-by-step procedures, which include categorizing the nature of input datasets, the construction of a decision matrix, fuzzy averaging, defuzzification processes, and the rating for the assessment. Meanwhile, the pair component in the Z-number used by this method was proven to have dealt efficiently with uncertainties and a degree of reliability. A numerical example from a case study has been used to highlight the ability and feasibility of the proposed method. The outcomes demonstrated that this approach could more precisely address the uncertainty associated with human judgment. It also offered some level of assurance for each assessment procedure. As a result, it provides university decision-makers (DMs) with an effective procedure to address the issue, particularly in teaching assessment.