Boosting Graduate Employment Quality Assessment with Fuzzy Hierarchical Analysis

Fuzzy Comprehensive Evaluation (FCE) is a multi‑criteria decision method based on fuzzy mathematics, widely used in environmental evaluation, education quality evaluation, risk evaluation, and similar problems.

This paper introduces an important fuzzy comprehensive evaluation method—Fuzzy Hierarchical Analysis—and, with a concrete case, shows its application in evaluating the employment quality of university graduates.

Overview of Fuzzy Comprehensive Evaluation Method

The basic idea of fuzzy hierarchical analysis is to decompose a complex problem into multiple hierarchical sub‑problems, apply fuzzy comprehensive evaluation at each level, and finally obtain a solution for the whole problem.

The specific steps are as follows:

Establish an evaluation index system : Decompose the complex problem into several sub‑problems to form a multi‑level evaluation index system.

Construct a fuzzy judgment matrix : Build the fuzzy judgment matrix according to the relative importance of factors at different levels.

Calculate fuzzy weights : Compute fuzzy weights using eigenvalue decomposition or similar methods.

Establish a fuzzy comprehensive evaluation model : Combine fuzzy weights with the specific evaluations of each factor to build the model.

Comprehensive evaluation and ranking : Perform overall evaluation and ranking of alternatives to select the best option.

Mathematical Model

Related Definitions

Definition 1: If a matrix satisfies certain conditions (omitted), it is called a fuzzy matrix.

Definition 2: If a matrix satisfies certain conditions (omitted), it is called a fuzzy complementary matrix.

Theorem 1: For a fuzzy complementary matrix, summing rows yields a vector; after a specific transformation, the resulting matrix is a fuzzy consistent matrix.

Assume the evaluation index system includes m factors and there are n objects to be evaluated. The steps are:

Construct the evaluation matrix

Construct the fuzzy judgment matrix

Calculate fuzzy weights

Calculate the comprehensive evaluation value

Comprehensive evaluation and ranking

Case Study: Graduate Employment Quality Evaluation

This case applies the fuzzy comprehensive evaluation method to assess the employment quality of graduates from four universities (A, B, C, D) in a certain region.

The evaluation index system includes:

Employment rate

Employment structure

Salary level

Employer satisfaction

Career development

Job‑match degree

Construct the fuzzy judgment matrix, convert it to a fuzzy consistent matrix based on Theorem 1, normalize to obtain fuzzy weights, and then compute the comprehensive evaluation values for each university.

The university with the highest comprehensive evaluation value is considered to have the best employment quality.

Below is the Python code used to calculate the fuzzy weights:

<code>import numpy as

def is_fuzzy_complementary(matrix):
    """
    Check if the given matrix is a fuzzy complementary matrix.
    """
    n = matrix.shape[0]
    for i in range(n):
        for j in range(n):
            if not (0 <= matrix[i, j] <= 1) or not np.isclose(matrix[i, j] + matrix[j, i], 1):
                return False
    return True

def calculate_fuzzy_weights(matrix):
    """
    Calculate the fuzzy weights from a fuzzy complementary matrix.
    """
    R = np.array(matrix)
    if not is_fuzzy_complementary(R):
        raise ValueError("The provided matrix is not a fuzzy complementary matrix.")
    n = R.shape[0]
    # Calculate fi
    f = np.sum(R, axis=1)
    # Perform the transformation to obtain fuzzy consistent matrix F
    F = (f - f.mean()) / (2 * n) + 0.5
    # Normalize to obtain the weights
    weights = F / np.sum(F)
    return weights

# Example fuzzy complementary matrix
R = [
    [0.5, 0.8, 0.6, 0.9, 0.7, 0.6],
    [0.2, 0.5, 0.6, 0.1, 0.8, 0.7],
    [0.4, 0.4, 0.5, 0.4, 0.3, 0.2],
    [0.1, 0.9, 0.6, 0.5, 0.9, 0.7],
    [0.3, 0.2, 0.7, 0.1, 0.5, 0.8],
    [0.4, 0.3, 0.8, 0.3, 0.2, 0.5]
]

# Ensure the matrix is a fuzzy complementary matrix
R = np.array(R)
for i in range(R.shape[0]):
    for j in range(R.shape[1]):
        R[j, i] = 1 - R[i, j]

# Calculate the fuzzy weights
weights = calculate_fuzzy_weights(R)
print("Fuzzy Weights:", weights)
</code>

Reference: Liu Jianfeng, Xia Yang. “A Comprehensive Evaluation Model of Graduate Employment Quality Based on Fuzzy Hierarchical Analysis.” Journal of Suzhou University of Science and Technology (Engineering Edition), 2024, 37(02):75‑80.