# Machine Selection for Inventory Tracking with a Continuous Intuitionistic Fuzzy Approach
## 5 Case Study
### Stage 2: Determine Criteria Weights with CINFU-AHP
The score judgment matrix transforms the IVIFNs into a more straightforward numerical form that can be used for further analysis in the CINFU AHP method. The converted numerical form consists of an interval indicating the general preference for one criterion over another, considering the IVIFN's membership and non-membership degrees. A wider interval implies more uncertainty in the comparison, while a narrower interval reveals a higher degree of consensus. A positive score in the interval suggests that the criterion in the row is preferred over the criterion in the column. Conversely, a negative score in the interval indicates the opposite. The comparison becomes imprecise if the interval spans zero, suggesting no clear preference. After calculating the score judgment matrix, some interesting criteria comparisons were given. The score interval for Speed (C1) vs. Setup Time (C2), (0.222, 0.264) has a positive interval and apparently shows Speed is more important than Setup Time. The narrow range denotes a relatively strong consensus among the experts regarding this preference. The score interval for Setup Time (C2) vs. Ease to Operate and Move (C3), (0.023, 0.139) is positive, albeit it is a narrow one and close to zero, implying a slight preference for Setup Time over Ease of Operation and Move. The closeness to zero and the narrow  
range present a marginal preference and a potential area where expert opinions might be more divergent. The score interval for Ability to Handle Multiple Operations (C4) vs. Lifetime (C6) is (\(-\)0.327, \(-\)0.093). This negative score interval demonstrates that Lifetime was considered more important than Ability to Handle Multiple Operations. This preference might reflect a long-term focus where the machine's durability is prioritized over its versatility. Table 7 presents the interval multiplicative matrix calculated based on Table 6 using Equation (24), which involves transforming the score intervals into their corresponding multiplicative equivalents. The main purpose is to construct a comparable scale reflecting the strength of preference between criteria based on the score judgment matrix. Instead of direct score intervals, the multiplicative matrix emphasizes the factor by which one criterion is considered more important than another. This modification helps capture the preferences' magnitude more effectively and enables the calculation of interval weights for the criteria. If the interval in a cell has values greater than 1, it implies that the criterion in the row is regarded as more significant than the criterion in the column. The larger the values, the stronger the preference. Conversely, if the interval values are less than 1, the criterion in the column is preferred over the criterion in the row. Values closer to zero indicate a stronger preference. If the interval includes the value 1, it suggests an imprecise comparison with no clear choice between the two criteria. After forming the interval multiplicative matrix, some interesting criteria comparisons were given. For criteria C1 (Speed) vs. C2 (Setup Time), the interval is (1.666, 1.836). This interval, with values greater than 1, reinforces that Speed is more important than Setup Time. The magnitude of the values means that Speed is considered approximately 1.7 times more critical than Setup Time. The interval of C2 (Setup Time) vs. C3 (Ease to Operate and Move), (1.055, 1.348), has values greater than 1, showing a weak tendency for Setup Time over Ease of Operation because the values are positive but closer to 1. With values less than 1, the interval multiplicative score for C4 (Ability to Handle Multiple Operations) vs. C6 (Lifetime) (0.471, 0.807) indicates that Lifetime is more critical than Ability to Handle Multiple Operations. Values closer to zero indicate a relatively strong preference for Lifetime.