In the realm of multi-criteria decision-making, the Fuzzy Analytic Network Process (FANP) method stands out as a comprehensive and versatile technique. FANP empowers decision-makers to delve into the intricate web of relationships among factors while embracing the inherent uncertainty inherent in expert judgments. Within the framework of the Fuzzy Network Analysis Process, one can seamlessly evaluate a diverse array of both positive and negative criteria. The crux of the matter lies in making comparisons based on preference. In cases of negative criteria, where a lower numerical value indicates superiority, and positive criteria, where a higher numerical value signifies excellence, factors are scrutinized through a lens of preference. To illustrate, if the cost of Project A surpasses that of Project B, Project B emerges as the preferred choice. Moreover, when the quality of Project A outshines that of Project B, the preference for Project A becomes more pronounced.

Another noteworthy attribute of the FANP fuzzy method is its knack for accommodating uncertainty. In scenarios where experts grapple with ambiguity and unpredictability in their assessments, fuzzy numbers like triangular or trapezoidal distributions come to the rescue. The format (l, m, u) characterizes a triangular fuzzy number, with ‘l’ representing the lower bound and ‘u’ symbolizing the upper bound. For instance, in the context of FANP, when comparing Criterion A to Criterion B, you might assign the number (1, 3, 5), effectively attributing a range from 1 to 5 to the criterion in question. To gain a better grasp of this concept, envision students seeking admission to an elite school with a minimum GPA requirement of 17. Yet, the school principal is open to considering a GPA of 16.80. Under these circumstances, it becomes evident that GPAs exceeding 17 are also acceptable. Consequently, this GPA threshold can be represented as a triangular fuzzy number (16.80, 17, 20).

The adaptability of the Fuzzy Analytic Network Process (FANP) method extends to its synergy with other techniques, such as Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (Fuzzy TOPSIS), especially when internal relationships among criteria come into play. Typically, when these relationships are present, FANP takes the reins in calculating the weights of the criteria. Here’s a breakdown of the steps involved in the Fuzzy ANP method:

**Steps of the Fuzzy ANP Method:**

- Define the network structure for the problem.
- Create a tailored fuzzy ANP questionnaire.
- Construct the pairwise comparison matrix.
- Assess inconsistency ratios and attain a consistent pairwise comparison matrix.
- Compute the criteria weights using the Chang method (although alternative techniques are viable).
- Establish the initial supermatrix.
- Calculate the limit supermatrix and extract the final weights.

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