The defuzzified crisp weights may not perfectly total 1.0 (or 100%). Create a final column to normalize them: = Crisp_Weight / SUM(All_Crisp_Weights)
Note: In modern Excel, you can use the =GEOMEAN() function directly across the specific cells in the row. Step 3: Compute Fuzzy Weights
Fuzzy weights must be normalized so their defuzzified values sum to 1. Without normalization, comparisons across matrices are meaningless.
Identify the goal, criteria, and alternatives.
A standard FAHP template consists of several key worksheets or sections: 1. Linguistic Scale Setup
: A grid where you enter your expert judgments. Because each entry is a TFN, every "cell" in your matrix will actually need three Excel columns.
Next, calculate each criterion's synthetic extent value. This involves dividing the row sum by the total matrix sum using fuzzy arithmetic (division of TFNs).
In standard AHP, the Consistency Ratio (CR) is straightforward. In Fuzzy AHP, calculating the CR is mathematically complex and not standardized. Many Excel templates the consistency check entirely, which invalidates the scientific rigor of the analysis. A good template must include a fuzzy consistency index calculation.
Finally, the template should present results in a clean, easy‑to‑read format:
Apply data bars to the final normalized weights column. This gives users an instant, visual breakdown of priority rankings. If you need help building this template, let me know: How many criteria your model needs to handle.
To build an Excel template, you must first establish the conversion scale. The standard Saaty scale translates into Triangular Fuzzy Numbers as follows: Linguistic Variable Traditional Scale Fuzzy Number Reciprocal Fuzzy Number Equally Important Moderately More Important Strongly More Important Very Strongly More Important Extremely More Important Intermediate values 2, 4, 6, 8 Reciprocal values Mathematical Architecture of the Excel Template
