In fuzzy set theory, while handling multi-attribute decision making problems, there are few conditions imposed on weight vectors (weight vector for attributes, for experts), that each component of these vectors must be greater than zero, taken from [0,1], and the sum of their components must be equal to one.
When the sum of weights is equal to 1 in fuzzy set-based MCDM, it is typically associated with normalization. Normalization ensures that the weights are scaled to a common scale, making them comparable and facilitating their interpretation in the decision-making process. Normalization is particularly important when dealing with multiple criteria that may have different units or scales.
Here's a brief explanation of why the sum of weights is often normalized to 1:
In fuzzy set-based MCDM, fuzzy numbers or linguistic terms may be used to represent uncertainties and imprecise information associated with the decision-making process. The normalization of weights is done while considering these uncertainties to provide a more comprehensive representation of the decision-maker's preferences.
It's worth noting that there are various methods for determining these weights, and the choice of method may depend on the specific characteristics of the decision problem and the preferences of the decision-maker.
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