TVN-MULTIMOORA

TVN-MULTIMOORA - Üçgensel Değerli Nötrosofik Sayı Ortamında MULTIMOORA

Nötrosofik MULTIMOORA - Üçgensel Değerli Nötrosofik Sayı (TVNN: <(tl,tm,tu),(il,im,iu),(fl,fm,fu)>)

Formül adımları

Analiz motorunun yöntem bildirimindeki (manifest F.steps) adımlar; raporlardaki formüllerle aynı kaynaktır.

Transform K individual SVNN decision matrices into a group TVNN matrix using the triangular-median approach (Eq.45): for each (i,j), lower = mean of ratings ≤ median, middle = median, upper = mean of ratings ≥ median, applied separately for t, i, f components.

$x ̃ i j = < (t l_{i} j, t m_{i} j, t u_{i} j), (i l_{i} j, i m_{i} j, i u_{i} j), (f l_{i} j, f m_{i} j, f u_{i} j) > w h e r e t l_{i} j = a v g (t k_{i} j | t k_{i} j \leq m e d), t m_{i} j = m e d (t i j), t u_{i} j = a v g (t k_{i} j | t k_{i} j \geq m e d); a n a l o g o u s l y f o r i, f$

LaTeX
x̃ij = <(tl_ij,tm_ij,tu_ij),(il_ij,im_ij,iu_ij),(fl_ij,fm_ij,fu_ij)> where tl_ij = avg(tk_ij | tk_ij ≤ med), tm_ij = med(tij), tu_ij = avg(tk_ij | tk_ij ≥ med); analogously for i,f
Apply the TVNWA operator (Ch.18 Eq.27) to the benefit columns (Omega_max) and, separately, to the cost columns (Omega_min) of row i. The two aggregates are kept apart; F3 subtracts one from the other.

$Y_{m} a x_{i} = T V N W A (x_{i} j : j i n O m e g a_{m} a x, w n o r m a l i s e d w i t h i n t h e s i d e); Y_{m} i n_{i} = T V N W A (x_{i} j : j i n O m e g a_{m} i n, w n o r m a l i s e d w i t h i n t h e s i d e); W_{m} a x = s u m (w j : j i n O m e g a_{m} a x), W_{m} i n = s u m (w j : j i n O m e g a_{m} i n)$

LaTeX
Y_max_i = TVNWA(x_ij : j in Omega_max, w normalised within the side); Y_min_i = TVNWA(x_ij : j in Omega_min, w normalised within the side); W_max = sum(wj : j in Omega_max), W_min = sum(wj : j in Omega_min)
Convert Y_max_i and Y_min_i to crisp scores with the score function (Ch.18 Eq.25), weight each by its side's mass, and take the difference: yi = W_max*s(Y_max_i) - W_min*s(Y_min_i). Rank alternatives in descending order of yi.

$y i = W_{m} a x * s (Y_{m} a x_{i}) - W_{m} i n * s (Y_{m} i n_{i})$

LaTeX
yi = W_max*s(Y_max_i) - W_min*s(Y_min_i)
For each criterion j the reference point r*j is the ideal cell of that column, taken in the direction the criterion points.

$r ̃ * j = < (m a x_{i} t l_{i} j, m a x_{i} t m_{i} j, m a x_{i} t u_{i} j), (m i n_{i} i l_{i} j, m i n_{i} i m_{i} j, m i n_{i} i u_{i} j), (m i n_{i} f l_{i} j, m i n_{i} f m_{i} j, m i n_{i} f u_{i} j) >$

LaTeX
r̃*j = <(max_i tl_ij, max_i tm_ij, max_i tu_ij), (min_i il_ij, min_i im_ij, min_i iu_ij), (min_i fl_ij, min_i fm_ij, min_i fu_ij)>
Compute weighted TVNN Hamming distance from each alternative to the reference point for each criterion, then take the maximum.

$d_{i} j = w j \cdot d (x ̃ i j, r ̃ * j) w h e r e d (x 1, x 2) = (1 / 3) (| t l 1 - t l 2 | + | t m 1 - t m 2 | + | t u 1 - t u 2 | + | i l 1 - i l 2 | + | i m 1 - i m 2 | + | i u 1 - i u 2 | + | f l 1 - f l 2 | + | f m 1 - f m 2 | + | f u 1 - f u 2 |); d^{m} a x_{i} = m a x_{j} (d_{i} j)$

LaTeX
d_ij = wj · d(x̃ij, r̃*j) where d(x1,x2) = (1/3)(|tl1−tl2|+|tm1−tm2|+|tu1−tu2|+|il1−il2|+|im1−im2|+|iu1−iu2|+|fl1−fl2|+|fm1−fm2|+|fu1−fu2|); d^max_i = max_j(d_ij)
Rank alternatives in ascending order of d^max_i; lowest distance = best rank.

$r_{i}^{R P} = {r a n k}_{↑} (d_{i}^{max}); best = \arg {min}_{i} d_{i}^{max}$

LaTeX
r^{RP}_i = \mathrm{rank}_{\uparrow}\!\left(d^{\max}_i\right);\quad \text{best} = \arg\min_i d^{\max}_i
Apply the TVNWG operator (Ch.18 Eq.28) to the benefit columns (Omega_max) and, separately, to the cost columns (Omega_min) of row i, each with its weights renormalised within the side. F8 divides one by the other.

$U_{m} a x_{i} = T V N W G (x_{i} j : j i n O m e g a_{m} a x); U_{m} i n_{i} = T V N W G (x_{i} j : j i n O m e g a_{m} i n)$

LaTeX
U_max_i = TVNWG(x_ij : j in Omega_max); U_min_i = TVNWG(x_ij : j in Omega_min)
Convert U_max_i and U_min_i to crisp scores with the score function (Ch.18 Eq.25), then take ui = s(U_max_i) / s(U_min_i) and rank alternatives in descending order of ui.

$u i = s (U_{m} a x_{i}) / s (U_{m} i n_{i})$

LaTeX
ui = s(U_max_i) / s(U_min_i)
Combine three sub-rankings (RS, RP, FMF) using dominance theory: the alternative ranking first (or at highest positions) across all three sub-approaches is selected as best.

$Dominance theory (Brauers-Zavadskas): a^{*} = \arg ⋂_{k \in {R S, R P, F M F}} t o p (r_{i}^{(k)}); ties broken by majority across the three sub-rankings$

LaTeX
\text{Dominance theory (Brauers-Zavadskas):}\;\; a^* = \arg\!\!\!\bigcap_{\,k \in \{RS, RP, FMF\}} \mathrm{top}\!\left(r^{(k)}_i\right);\;\; \text{ties broken by majority across the three sub-rankings}

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: TVN-MULTIMOORA ranks alternatives based on performance scores. Higher score = better rank.