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where Y ˜ ij k represents the i th alternative of the j th criteria in the kth decision maker in the normalized matrix.
Also, Y ˜ j k represents the best value (it may have a positive or negative concept) of the j th criteria in view of the k th decision maker in the normalized matrix.
Where each D m denotes the m th dimension; C nm represents the m th criteria in the n th dimension; and ( {T}_c^{ij} ) is the principle eigenvector of the influences of the elements in the i th dimension, as compared to the i th dimension.
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Wi = Weight for the i-th criteria or indicator.
Vi = Score for the i-th criteria or indicator.
(C=left{ {c_1,ldots,c_j,ldots,c_J } right} ): set of criteria, where(c_j )denotes the j-th criterion, (j=1,2,ldots,J).
(W=left( {w_{c_1 },ldots,w_{c_j },ldots,w_{c_J } } right) ): vector of criteria weights, where (w_{c_j } )denotes the weight of the j-th criterion, (j=1,2,ldots,J).
(C^{h}=left{ {c_{j }^h (a_i )} right} ): set of opinions provided by expert (e_h ), where (c_{j }^h (a_i )in R) denotes the preference over thei-th alternative regarding to thej-th criterion, (i=1,2,ldots,I); (h=1,2,ldots,H); (j=1,2,ldots,J).
(E_{ij} =left[ {E_{ij}^L,E_{ij}^U } right] ): be an interval value, where (E_{ij} ) denotes the effective control scope [37] over the i-th alternative with respect to the j-th criterion.
(R_j =left[ {R_j^L,R_j^U } right] ): be an interval value, where (R_j^L, R_j^U ) are preferences, and (R_j )denotes the RP provided by the DM with respect to the j-th criterion.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com