Common and distinct predictors of non-symbolic and symbolic ordinal number processing across the early primary school years

yes">r (155)=.49,<italic toggle="yes">p<.001 symbolic order processing Grade 1 Grade 2
yes">r (155)=.70, all<italic toggle="yes">p s<.001
toggle="yes">r s .32 vs .18,<italic toggle="yes">z=1.75,<italic toggle="yes">p=.03

A novel MADM algorithm for landfill site selection based on q-rung orthopair probabilistic hesitant fuzzy power Muirhead mean operator

toggle="yes">υ<1,<italic toggle="yes">μ^<italic toggle="yes">q +<italic toggle="yes">υ^<italic toggle="yes">q<=1
pone.0258448.e009">removedGRAPHIC 0<μ<1, 0<υ<1, μ q + υ q<=1,</disp formula><disp formula id="pone.0258448.e010">removedGRAPHIC 0<p l<1, 0<p ¯ m<1, ∑ l=1 | Γ A | p l<=1, ∑ m=1 | Ψ A | p ¯ m<=1
n q 1 / q ] (p ¯ 1 m p ¯ 2 n ∑ m=1 | Ψ h 1 | p ¯ 1 m - ∑ n=1 | Ψ h 2 | p ¯ 2 n) } ⟩</disp formula><disp formula id="pone.0258448.e015">removedGRAPHIC lambda h=<∪ μ l ∈ Γ h { [(1 - (1 - μ l q) lambda) 1 / q ] p l }, ∪ v m ∈ Ψ h { v m lambda (p ¯ m) } ⟩</disp formula><disp formula id="pone.0258448.e016">removedGRAPHIC h lambda=<∪ μ l ∈ Γ h { μ l lambda p l }, ∪ v m ∈ Ψ h { [(1 - (1 - v m q) lambda) 1 / q ] (p ¯ m) } ⟩</disp formula><disp formula id="pone.0258448.e017
toggle="yes">h 1=<italic toggle="yes">h 2,<italic toggle="yes">d (<italic toggle="yes">h 1,<italic toggle="yes">h 2)=0; -<italic toggle="yes">d (<italic toggle="yes">h 1,<italic toggle="yes">h 2)=<italic toggle="yes">d (<italic toggle="yes">h 2,<italic toggle="yes">h 1
j=1, 2, ⋯, l Ψ. - The standardized Euclidean distancebetween<italic toggle="yes">h 1
l=1 | Γ h | p l (μ l q - eta q) 2 ∑ l=1 | Γ h | p l + ∑ m=1 | Ψ h | p ¯ m (1 - υ m q) - eta q) 2 ∑ m=1
toggle="yes">h 1)=0.4083,<italic toggle="yes">S (<italic toggle="yes">h 2)=0.5500
h 1, h 2, ⋯, h n=(1 n ! ⊕ ϑ ∈ S n ⊗ i=1 n n omega ϑ i (1 + T (h ϑ i) ∑ j=1 n omega j (1
r i 1 / q ] (p ¯ ϑ i m) } ⟩</disp formula>Then, we use mathematical induction theory get<disp formula id="pone.0258448.e064">removedGRAPHIC ⊗ i=1
∏ ϑ ∈ S n ∏ i=1 n p ¯ ϑ i m ∏ ϑ ∈ S n ∏ i=1 n ∑ m=1
pone.0258448.e069">removedGRAPHIC (1 n ! ⊕ ϑ ∈ S n ⊗ i=1 n (n ϖ ϑ i h ϑ i r i) 1 ∑ j=1
i=1 n υ i m ϖ i ] (∏ i=1 n p ¯ i m ∏ i=1 n ∑ m=1 | Ψ h i | p ¯ i m) } ⟩</disp formula>Case 2
j=1 i !=j n ∑ l=1 | Ψ h i | p ¯ i m ∑ l=1 | Ψ h j | p ¯ j m } ⟩</disp formula>Case 3
toggle="yes">i=1,2,⋯,<italic toggle="yes">n), then<disp formula id="pone.0258448.e076
M P (h 1, h 2, ⋯, h n)=h</disp formula>Theorem 3. Boundedness Let<italic toggle="yes">h<italic toggle="yes">i (<italic toggle="yes">i=1,2
M P (h 1, h 2, ⋯, h n)<h +</disp formula>Theorem 4. Monotonicity Let<italic toggle="yes">h<italic toggle="yes">i (<italic toggle="yes">i=1,2
toggle="yes">i=1,2,⋯<italic toggle="yes">m ;<italic toggle="yes">j,<italic toggle="yes">k=1,2
h i 1, h i 2, ⋯, h i n</disp formula>- Step8
toggle="yes">h 1)=0.4763,<italic toggle="yes">S (<italic toggle="yes">h 2)=0.4289,<italic toggle="yes">S (<italic toggle="yes">h 3)=0.4845,<italic toggle="yes">S (<italic toggle="yes">h 4)=0.4187,<italic toggle="yes">S (<italic toggle="yes">h 5)=0.4626. - Step 9