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Most of data in a multi attribute decision making (MADM) problem are unstable and changeable, and thus sensitivity analysis can effectively contribute to making proper decisions. Here, we offer a new method for sensitivity analysis of multi-attribute decision making problems so that by changing one element of decision making matrix, we can determine changes in the results of a decision making problem. An analysis is made for simple additive weighting method (SAW) technique, a mostly used multi-attribute decision making techniques, and the corresponding formulas are obtained.

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Effective management, as one of the central pillars of organizational success, hinges on the ability to make informed decisions by appropriately combining and coordinating various elements to achieve desired objectives. In decision-making processes, especially in complex scenarios, decision-makers often rely on a multitude of factors to arrive at the most suitable conclusion. This is particularly true in multi-criteria decision-making (MCDM), where decisions are based on evaluating several criteria rather than a single measure of optimality. The growing body of research over recent decades has delved deeply into MCDM methodologies, yet one fundamental aspect remains: the varying significance of the criteria involved. It is critical to accurately determine the weight or importance of each criterion to ensure optimal decision outcomes.
In this paper, we introduce a novel weighting technique designed to address the challenges of assigning weights in MCDM problems, called the Dispersion-based Weighting Method (DWM). This method builds upon the principles of statistical dispersion and offers an efficient alternative to traditional entropy-based weighting methods. The process involves constructing a criterion matrix, followed by the calculation of the mean, standard deviation, and coefficient of variation for each criterion. The weights are then computed based on these statistical measures, providing a robust and straightforward approach for determining the relative importance of each criterion.
To validate the proposed DWM technique, several numerical examples are presented, demonstrating its practical application and effectiveness. Additionally, we compare the results obtained using DWM with those derived from the well-established Shannon entropy method, which is widely used in MCDM applications. The comparative analysis reveals a strong correlation between the two techniques, while highlighting the advantages of the DWM approach, including:

• Reduced computational complexity
• No requirement for data normalization
• Applicability to both positive and negative data sets

The findings suggest that DWM offers a more accessible, efficient, and versatile alternative to traditional methods, particularly in situations where computational efficiency and handling of diverse data types are crucial.