A Novel Enhanced Weighted Product Approach Using Euclidean Normalization and Standard Deviation for Accurate Ranking

Every day, leaders and managers face choices that cannot be solved by looking at a single number. They must hire an employee, pick a supplier, or choose a project by weighing many different factors at once. Some factors are about money, others about skill, and still others about personality or speed. The challenge lies in the fact that these factors are measured in different ways. One might be a salary in dollars, another a test score out of a hundred, and a third a rating of how well someone speaks. When you try to compare these different scales directly, the results can become skewed, favoring the factor with the biggest numbers rather than the one that truly matters most. This is the core problem of multi-criteria decision making: how to balance conflicting and differently measured pieces of information to find the single best option without letting the math distort the reality.

Researchers have long tried to solve this by creating methods that normalize, or standardize, these different scales so they can be compared fairly. However, traditional methods often struggle when the data is messy or when the importance of a factor is decided by human opinion, which can be biased. A team of researchers from Indonesia has now proposed a new way to handle this complexity. They developed a refined version of an existing decision-making tool called the Weighted Product method. By combining a specific way of measuring distance between data points with a mathematical technique that looks at how much the data varies, they created a system that is more stable and objective than previous approaches. Their work suggests that by letting the data itself dictate how important each factor is, rather than relying solely on human judgment, the final rankings of candidates or options become more reliable and resistant to small changes in the input.

The researchers tested their new approach, which they named WP-DISTA, using a real-world scenario: selecting the best job candidates from a pool of nine applicants. In this scenario, each candidate was evaluated on seven distinct criteria, ranging from their level of education and years of work experience to their technical skills, communication abilities, and performance in written tests and interviews. Some of these criteria were beneficial, meaning a higher score was better, while others were costs, where a lower score was preferable. The team fed this data into their new system, which first adjusted all the different scores onto a common scale using a method based on the geometric distance between points, rather than just looking at the highest and lowest values. This step ensured that a criterion with very large numbers, like a test score in the hundreds, did not accidentally overpower a criterion with smaller numbers, like a rating on a scale of one to ten.

Once the data was balanced, the system calculated the importance of each criterion based on how much the candidates differed from one another in that specific area. If a group of candidates all had nearly the same level of education, that factor was given less weight because it did not help distinguish the best from the rest. However, if the candidates varied widely in their technical skills, that factor was given more weight because it was better at separating the strong performers from the weak ones. This process removed the need for a human to guess which factors were most important, replacing subjective opinion with an objective measure of variation. The system then combined these adjusted scores and weights to calculate a final ranking for each candidate, determining who was closest to the ideal set of qualifications.

The results of this new method were striking in their consistency. When the researchers compared the rankings produced by their new system against five other established decision-making methods, the agreement was remarkably high. The new approach matched the results of one of the comparison methods almost perfectly, with a correlation score of 0.9914, and matched another very closely at 0.9742. This high level of agreement suggests that the new method is not producing strange or isolated results, but is aligning with the best practices already in use. More importantly, the researchers tested the stability of their system by slightly changing the importance of the criteria, simulating a situation where a hiring manager might decide that experience is slightly more important than usual. Even with these shifts, the order of the candidates did not change. The top candidate remained at the top, and the lowest remained at the bottom, proving that the system is robust and not easily swayed by minor fluctuations in how the factors are weighted.

In the end, the study demonstrates that a decision-making tool can be made fairer and more reliable by letting the data speak for itself. The new method successfully handled the messy reality of comparing different types of information, ensuring that no single factor dominated the outcome simply because of its scale. By integrating a geometric approach to balancing the data with a mathematical way of determining importance, the researchers created a system that produces clear, stable rankings. This work offers a practical alternative for organizations and individuals who need to make complex choices, providing a way to navigate conflicting criteria with greater confidence that the final decision reflects the true strengths of the options available.