It's impossible to be negative in any way.

Dear Husam

Why?

Thank you Dear Husam Jasim Mohammed

Can you tell me why?

Dear Erfan, can you explain how you do this weighting in detail?

Hi dear Thanh-Tuan Dang

I use the "Preference selection index" who is an objective weighting method and for some of the parameters, it gave me negative weights.

The article "Weighting Methods for Multi-Criteria Decision Making Technique" of ODU, G.O. August 2019, May help you

Thank you, dear Jridi Ichraf

Dear Erfan

Regarding PSI I suggest revising your calculation since weights in this method are the ratio between (1 - deviations from the mean), a positive number, and the total sum of deviations, also positive

Dear Nolberto Munier

Yes, the sum of deviations is always positive but what if this number is higher than 1(1 - a number higher than 1)? In this case, the PSI gave us a negative weight. Am I Right?

No, because it is supposed that the deviation is a fraction since it is normalized

Dear Nolberto Munier

I use this article as a reference for my calculations. And it's also saying that this method can give negative weights.

Dear Erfan

Honestly. I don't know the answer to your question, perhaps because I don't work with weights in MCDM problems

However, common sense forces me to ask this question: How can one imagine a negative weight for criteria? Which would be the meaning?

Even if there were, which is their influence in evaluating alternatives? None, because weights are not meant to evaluate alternatives (except objective weights), but just used to make a balance or trade-off between criteria, since all of them add up to 1

I read the paper you mention where the authors assert negativity, as you say, but an assertion needs a justification. Where is it?.

The fact that neither entropy nor SD produces negative weights seems to indicate that they don't exist.

As you probably know Linear Programming doesn't use weights, however, internally, in each iteration tit produces something similar that allows qualifying criteria to select a dominated alternative for deletion, and it is justified.

Thank you Nolberto Munier

Suggest reviewing this paper for MCDM methods:

https://www.sciencedirect.com/science/article/abs/pii/S092583881732827X