Applying Fuzzy Comprehensive Evaluation: Steps and Real‑World Case

1 Fuzzy Comprehensive Evaluation

When evaluation factors or objects are inherently vague, fuzzy evaluation methods are needed. Let the set of evaluation indicators be the indicator set, the set of linguistic terms be the comment set, and the weight vector of the indicator set represent the relative importance of each indicator.

2 Evaluation Steps

The general steps of fuzzy comprehensive evaluation are:

Step 1: Determine the indicator set and its weight vector, usually obtained from public statistics, surveys, or expert scoring.

Step 2: Construct the comment set composed of linguistic terms.

Step 3: Build the single‑indicator evaluation vectors and combine them into the evaluation matrix.

Step 4: Synthesize the fuzzy comprehensive evaluation result vector by applying an appropriate operator to the evaluation matrix.

Step 5: Derive the evaluation conclusion, often using the maximum membership principle to select the grade corresponding to the largest component of the result vector.

3 Case Study

A university sets a rule that a teacher can be promoted to professor if the combined proportion of "good" and "fairly good" exceeds 50%. Different weights are assigned for teaching‑oriented and research‑oriented professor positions. A seven‑member evaluation panel assessed a teacher, and the votes were converted into membership degrees to form the comprehensive evaluation matrix. Using the weighted sum operator, the overall evaluation value shows that the "good" and "fairly good" categories together exceed 50%, so the teacher qualifies for promotion as a teaching‑oriented professor.

Reference

Si Shou‑kui, Sun Xi‑jing. Python Mathematics Experiments and Modeling .