# Construction of Quality Indicators Based on Pre-Established Goals: Application to a Colombian Public University

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- The pre-established objectives for each criterion are future estimates, which are not usually precise [15].

## 2. Homogenization and Normalization of the Data Based on the Similarity Measures

#### 2.1. Data Homogenization

- (1)
- The set is ordered: ${s}_{\alpha}>{s}_{\beta}$ if $\alpha $ > $\beta $;
- (2)
- There is a negation operator: neg(${s}_{\alpha})={s}_{\beta}$ such that $\beta =H+1-\alpha $;
- (3)
- There are max. and min. operators: max(${s}_{\alpha},{s}_{\beta}$) = ${s}_{\alpha}$ if $\alpha \ge \beta $, and min(${s}_{\alpha},{s}_{\beta}$) = ${s}_{\alpha}$ if $\alpha \le \beta .$

#### 2.2. Normalization Based on an Ideal

- (a)
- Linearity cannot always be assumed for the manner of approaching or moving away from the ideal. The effect of having values below the ideal may be very different from that of having values greater than the ideal [26].
- (b)
- The normalization proposed in (10) is not very sensitive to the position of the interval $\left[p,\text{}q\right]$ with respect to the ideal $\left[a,\text{}b\right].$

_{1}, and k

_{2}, such that $A\le a\le b\le B$, we define the function ${\eta}_{\left(A,a,b,B;{k}_{1},{k}_{2}\right)}\left(x\right):\text{}\mathbb{R}\to \left[0,1\right]$, given by

_{1}and k

_{2}determine the way to approach or leave from the ideal—for positive values, it is convex and for negative values, it is concave (see Figure 2). In addition, the higher the absolute values of k

_{1}and k

_{2}, ${\eta}_{\left(A,a,b,B;{k}_{1},{k}_{2}\right)}\left(x\right)$, the further we move away from the linear functions $f\left(x\right)=\frac{x-A}{a-A}$ and $g\left(x\right)=\frac{B-x}{B-b}$, which appear in (7).

**Remark**

**1.**

_{1}= 0 (resp. k

_{2}= 0). With this, the functions${\eta}_{\left(A,A,b,B;0,{k}_{2}\right)}\left(x\right)$,${\eta}_{\left(A,a,B,B;{k}_{1},0\right)}\left(x\right)$are as follows:

**Proposition**

**1.**

**Proof.**

**Definition**

**1.**

**Remark**

**2.**

**Example**

**1.**

_{1}= 4, v

_{2}= [4, 9], and v

_{3}= [8, 9].

_{2}= [4, 9] and v

_{3}= [8, 9] using N, we have

_{2}and v

_{3}are transformed into the same value. However, the relationships of $\left[4,9\right]$ and $\left[8,9\right]$ with the ideal are very different: $\left[a,\text{}b\right]\subset \left[4,\text{}9\right]$, whilst $\left[a,\text{}b\right]{\displaystyle \cap}\left[8,\text{}9\right]=\varnothing .$ For this reason, if the actual situation requires it, it may be important to distinguish between both situations.

**Remark**

**3.**

_{2}= [4, 9] and v

_{3}= [8, 9] results in

_{2}= [4, 9] and v

_{3}= [8, 9].

## 3. Ideal Similarity and Multiple-Criteria Decision-Making Methods

_{i}, i = 1,…, n to perform an expensive activity on time and with the appropriate resources and efforts of personnel. To manage it, a value is assigned to each alternative in m criteria, C

_{j}, j = 1,…, m. Depending on the nature of the criteria, an evaluation is carried out using numerical values, intervals, linguistic values, or sets of linguistic values [17]. According to Section 2.1, all of these values could be expressed by means of intervals $\left[{v}_{ij}^{L},{v}_{ij}^{R}\right]\subset \mathbb{R},\text{}1\le i\le n,\text{}1\le j\le m.$ In addition, each criterion, C

_{j}, j = 1,…, m, has a range [A

_{j}, B

_{j}] where the values may vary:

_{j}, b

_{j}] as an ideal (or pre-established goal) for each criterion, so that

_{j}criterion are set [25], a similarity function with the ideal ${f}_{j}$ could be established, like the proposal in (7). From this function, the normalization for each criterion can be performed with the following function:

_{ij}of the interval [0, 1], similarity with the ideal set for the criterion.

**Definition**

**2.**

## 4. Construction of Quality Indices

_{0}represents a value below which individuals are not suitable for the task, while S

_{1}represents the threshold above which adaptation is excellent. Considering (20), the institution knows that n

_{1}individuals will perform the task successfully, n

_{2}people will be inadequate, unless they undertake additional training activities ($\beta $ activities per person, $\beta \ge 1$), and n

_{3}individuals can perform the task, although some of them might have some difficulty with it ($\alpha {n}_{3}$ people are adequate, $\alpha \in \left[0,1\right]$).

**Definition**

**3:**

_{1}increases and decreases as n

_{2}increases was constructed in Parada et al. [17]. With A(n), the institution can estimate who is suitable for the activity.

**Definition**

**4:**

**Proposition**

**2:**

- (a)
- It is increasing with respect to n
_{1}with n_{2}and n_{3}being constants. - (b)
- It is decreasing with respect to n
_{2}with n_{1}and n_{3}being constants. - (c)
- When n
_{3}varies, and n_{1}and n_{2}remain constant,

**Definition**

**5:**

**Definition**

**6:**

**Proposition**

**3.**

**Proof.**

**Remark**

**4.**

## 5. Case Study

#### 5.1. Data Used

_{E}): This is obtained from three variables: income from economic dependence, $\mathrm{ED}=[\mathrm{wage}/\mathrm{SMMLV}]$ (where $\u23a1x\u23a4$ is the greatest integer that is less than or equal to x and SMMLV is the current legal minimum monthly wage), the number of siblings (NS), and the position between siblings (PS). The economic dimension indicator is

_{S}= FAD,

_{A}): This is obtained through three valuations [17]: a diagnostic test of UIS Math (DTM), the EFAI-4 numerical ability (NUA), and the 11-Math Knowledge Test (PSO), such that

_{A}, the level of mathematical performance of each student is determined using a linguistic scale, as expressed in Table 2.

_{C}). This is estimated through five tests: verbal reasoning (VR), numerical reasoning (NR), abstract reasoning (ABR), memory (MEM), and spatial awareness (SA). Therefore,

_{H}). This is made up of five variables: anxiety (ANX), depression (DEP), emotional adjustment (EMA), alcohol dependence (ALD), and psychoactive substance abuse (PSA), which are measured using qualitative variables (Table 2):

#### 5.2. Calculation of Indicators

## 6. Discussion

_{i}, as the global assessment for each alternative. This is justified because using (16), regardless of the data set, the ideal and anti-ideal values of the classic TOPSIS method [9] correspond to (1,1, ..., 1) and (0,0, ..., 0), respectively. This fact prevents R

_{i}values from changing when new data are incorporated, that is, the phenomenon known as the rank reversal is avoided [10].

#### 6.1. Comparison with Other Methods

_{1}, n

_{2}, and n

_{3}obtained with the different methods and in different periods.

#### 6.2. Strengths and Weaknesses of Our Proposal

- (1)
- The opinions of the experts, who have been working on the question for years, are taken into account in all parts of the process: the choice of the ideal situation for each dimension, the nature of the data (numbers, intervals or linguistic expressions), the weight given to each dimension, the thresholds S
_{0}and S_{1}that determine the inadequacy and excellence, and the parameters that appear in the indicators. - (2)
- All steps of the method can be calculated with basic tools that any participant in the process can see on their own computer. Specifically, all calculations were performed with Microsoft Excel (see Appendix B).
- (3)
- The indicators are easily interpretable and allow comparison with other achievement indicators of the institution. For example, in the case of the Industrial University of Santander, the values of the proposed indicators are very consistent with the results obtained by its students.

- (1)
- As can be seen in Section 6.1, the proposed method clearly depends on the normalization used and, therefore, on the choice of ideals for each dimension. This makes the consensus among experts decisive in the process.
- (2)
- The weights that have been set for each dimension to determine the solution to the TOPSIS method and; therefore, the values of the indicators. That these weights are accepted by the institution is a key element in the process.
- (3)
- To determine the evolution of the institution, the data handled in each period have not always followed the same criteria, scales, etc. In addition, some data collected over the years cannot be used, for example, because data protection laws prohibit it.

## 7. Conclusions

- Estimate the percentages of students who will not have problems carrying out their studies successfully and those who will need some support.
- Understand each student’s personal situation in order to try to guarantee support for those who need it most.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

2018_1 | Original Numerical Data (Step 1) | Normalized Data (Step 2) | Weighted Normalized Data (Step 3) | Distances (Step 4) | Score (Step 5) | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Students | E | S | H | A | C | E | S | H | A | C | w_{1}E | w_{1}S | w_{1}H | w_{1}A | w_{1}C | D^{+} | D^{-} | R_{i} |

#1 | 1 | 0.5 | 0.55 | [3.5, 4.75] | 6.00 | 1.000 | 0.667 | 0.846 | 0.508 | 1.000 | 0.250 | 0.083 | 0.106 | 0.152 | 0.200 | 0.379 | 0.144 | 0.725 |

#2 | 0.77 | 1 | 0.65 | [3.5, 4.75] | 6.00 | 0.963 | 1.000 | 1.000 | 0.508 | 1.000 | 0.241 | 0.125 | 0.125 | 0.152 | 0.200 | 0.390 | 0.137 | 0.741 |

#3 | 1 | 0.7 | 0.65 | [3.5, 4.75] | 1.00 | 1.000 | 1.000 | 1.000 | 0.508 | 0.000 | 0.250 | 0.125 | 0.125 | 0.152 | 0.000 | 0.342 | 0.242 | 0.586 |

#4 | 1 | 1 | 0.65 | [5.5, 6.25] | 4.00 | 1.000 | 1.000 | 1.000 | 0.962 | 0.714 | 0.250 | 0.125 | 0.125 | 0.289 | 0.143 | 0.444 | 0.057 | 0.886 |

#5 | 1 | 0.5 | 0.55 | [5.5, 6.25] | 5.00 | 1.000 | 0.667 | 0.846 | 0.962 | 0.871 | 0.250 | 0.083 | 0.106 | 0.289 | 0.174 | 0.441 | 0.053 | 0.893 |

#6 | 0.03 | 0.5 | 0.52 | [3.5, 4.75] | 2.00 | 0.038 | 0.667 | 0.800 | 0.508 | 0.287 | 0.009 | 0.083 | 0.100 | 0.152 | 0.057 | 0.209 | 0.315 | 0.399 |

#7 | 1 | 0.7 | 0.52 | [2.0, 2.75] | 3.00 | 1.000 | 1.000 | 0.800 | 0.185 | 0.522 | 0.250 | 0.125 | 0.100 | 0.055 | 0.104 | 0.320 | 0.253 | 0.558 |

#8 | 0.03 | 1 | 0.65 | [3.5, 4.75] | 2.00 | 0.038 | 1.000 | 1.000 | 0.508 | 0.287 | 0.009 | 0.125 | 0.125 | 0.152 | 0.057 | 0.241 | 0.311 | 0.436 |

#9 | 1 | 0.7 | 0.65 | [5.5, 6.25] | 3.00 | 1.000 | 1.000 | 1.000 | 0.962 | 0.522 | 0.250 | 0.125 | 0.125 | 0.289 | 0.104 | 0.434 | 0.096 | 0.819 |

#10 | 1 | 0.7 | 0.65 | [2.0, 2.75] | 6.00 | 1.000 | 1.000 | 1.000 | 0.185 | 1.000 | 0.250 | 0.125 | 0.125 | 0.055 | 0.200 | 0.370 | 0.233 | 0.613 |

## Appendix B

_{1}, n

_{2}, and n

_{3}.

- Sub Mathematics_Excel()
- ‘Part0. Create variable sheet
- Sheets.Add.Name = “Var”
- Range(“A1”).FormulaR1C1 = “=COUNTA(Data!C)-3”
- ‘Variable with the number of students
- Dim n As Integer
- n = Cells(1, 1)

- ‘Part1. Set the ideal and the columns
- Sheets(“Data”).Select
- Range(“B3”).FormulaR1C1 = “=MAX(R [3]C[11]:R[1048573]C[11])”
- Range(“B3:F3”).Select
- Selection.FillRight
- ‘Name of each variable
- Range(“H5”).FormulaR1C1 = “E”
- Range(“I5”).FormulaR1C1 = “S”
- Range(“J5”).FormulaR1C1 = “H”
- Range(“K5”).FormulaR1C1 = “A”
- Range(“L5”).FormulaR1C1 = “C”
- Range(“M5”).FormulaR1C1 = “wE”
- Range(“N5”).FormulaR1C1 = “wS”
- Range(“O5”).FormulaR1C1 = “wH”
- Range(“P5”).FormulaR1C1 = “wA”
- Range(“Q5”).FormulaR1C1 = “wC”
- Range(“R5”).FormulaR1C1 = “d-”
- Range(“S5”).FormulaR1C1 = “d+”
- Range(“T5”).FormulaR1C1 = “R”
- Range(“H1”).FormulaR1C1 = “N1”
- Range(“I1”).FormulaR1C1 = “N2”
- Range(“J1”).FormulaR1C1 = “N3”
- Range(“K1”).FormulaR1C1 = “N”

- ‘Part 2. Calculating
- Range(“H6”).FormulaR1C1 = “=+IF(RC[-6]<0.8, RC[-6]/0.8, 1)”
- Range(“I6”).FormulaR1C1 = “=+IF(RC[-6]<0.7,(RC[-6]-0.1)/0.6,1)”
- Range(“J6”).FormulaR1C1 = “=+IF(RC[-6]<0.65,RC[-6]/0.65,1)”
- Range(“K6”).FormulaR1C1 = _”=1/(RC[-5]-RC[-6])*(1/(1-EXP(1))*(RC[-5]-RC[-6]+5*EXP((RC[-6]-1)/5)-5*EXP((RC[-5]-1)/5)))+MAX(0,RC[-5]-6/(RC[-5]-RC[-6]))”
- Range(“L6”).FormulaR1C1 = “=+IF(RC[-5]<6, (1-EXP((1-RC[-5])/5))/(1-EXP(-1)), 1)”
- Range(“M6”).FormulaR1C1 = “=RC[-5]*R2C[-11]”
- Range(“N6”).FormulaR1C1 = “=RC[-5]*R2C[-11]”
- Range(“O6”).FormulaR1C1 = “=RC[-5]*R2C[-11]”
- Range(“P6”).FormulaR1C1 = “=RC[-5]*R2C[-11]”
- Range(“Q6”).FormulaR1C1 = “=RC[-5]*R2C[-11]”
- Range(“R6”).FormulaR1C1 = “=SUMPRODUCT(RC[-5]:RC[-1],RC[-5]:RC[-1])^0.5”
- Range(“S6”).FormulaR1C1 = “=((RC[-6]-R3C2)^2+(RC[-5]-R3C3)^2+(RC[-4]-R3C4)^2+(RC[-3]-R3C5)^2+(RC[-2]-R3C6)^2)^0.5”
- Range(“T6”).FormulaR1C1 = “=RC[-2]/(RC[-2]+RC[-1])”
- Range(“H2”).FormulaR1C1 = “=COUNTIF(R[4]C[12]:R[13]C[12],”“>0,85”“)”
- Range(“I2”).FormulaR1C1 = “=COUNTIF(R[4]C[11]:R[13]C[11],”“<0,45”“)”
- Range(“J2”).FormulaR1C1 = “=RC[1]-RC[-2]-RC[-1]”
- Range(“K2”).FormulaR1C1 = “=COUNTA(C[-10])-3”

- ‘Set the formula per each column
- Range(Cells(6, 8), Cells(6, 20)).Select
- Selection.AutoFill Destination:=Range(Cells(6, 8), Cells(6 + n − 1, 20))
- Selection.NumberFormat = “0.000”

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**Figure 2.**Representation of ${\eta}_{\left(0,6,7,10;-2,1.5\right)}\left(x\right)$ and ${\mu}_{\left(0,6,7,10\right)}\left(x\right)$. Data from Example 1.

**Figure 3.**Similarity functions of academic, ${\eta}_{A}\left(x\right)$, and cognitive ${\eta}_{C}\left(x\right)$ dimensions.

Data | Original Data | Transformation |
---|---|---|

Type I(real numbers) | $(\mathrm{a})\text{}v\in \mathbb{R}$ | $v\in \mathbb{R}$ (or $\left[v,\text{}v\right]\subset \mathbb{R}$) |

$(\mathrm{b})\text{}v\in S$ | $v\to \mathrm{r}\in \mathbb{R}$ (or $\left[r,\text{}r\right]\subset \mathbb{R}$) | |

Type II(intervals in $\mathbb{R}$) | $(a)\text{}v=\left[{v}^{L},{v}^{R}\right]\subset \mathbb{R}$ | $v\subset \mathbb{R}$ |

$(b)\text{}v=\left\{{v}^{1},{v}^{2},\dots ,{v}^{p}\right\}\subseteq S$ | $v\to \left[1,\text{}p\right]\subset \mathbb{R}$ | |

$(\mathrm{c})\text{}v\in S$ | $v\to {\overline{r}}_{\alpha}\subset \mathbb{R}$ |

(a) Economic dimension (P_{E}): P_{E} = 0.5 ED + 0.3 NS + 0.2 PS | |||||

ED | Value | PS | Value | NS | Value |

1 | 0.1 | >5 | 0.1 | >3 | 0.1 |

2 | 0.2 | Fifth | 0.2 | 3 | 0.3 |

3 | 0.4 | Fourth | 0.4 | 2 | 0.5 |

4 | 0.6 | Third | 0.6 | 1 | 1 |

5 | 0.8 | Second | 0.8 | ||

>5 | 1 | First | 1 | ||

(b) Social dimension (Ps): P_{S} = FAD | |||||

FAD | Value | ||||

$\left[0,\text{}9\right]$ | (Severe situation) | 0.1 | |||

$\left[10,\text{}13\right]$ | (Moderate situation) | 0.5 | |||

$\left[14,\text{}17\right]$ | (Slight situation) | 0.7 | |||

$\left[18,\text{}20\right]$ | (Good situation) | 1 | |||

(c) Academic dimension (P_{A}): P_{A} = 0.5 DTM + 0.25 NUA + 0.25 PSO | |||||

DTM, NUA | Value | PSO | Value | ||

Very Low | 1 | Low Level [0, 30] | 1 | ||

Low | 1.3 | Medium Level (30, 70] | 2 | ||

Low to Medium | 1.6 | High Level (70, 100] | 3 | ||

Medium | 2 | ||||

Medium to High | 2.3 | ||||

High | 2.6 | ||||

Very High | 3 | ||||

(d) Cognitive dimension (P_{C}): P_{C} = 0.2 VR + 0.2 NR + 0.2 ABR + 0.2 MEM + 0.2 SA | |||||

VR, NR, ABR, MEM and SA | Value | ||||

$\left[40,\text{}80\right]$ (High Risk) | 0.1 | ||||

$\left[81,\text{}90\right]$ (Medium Risk) | 0.5 | ||||

$\left[91,\text{}160\right]$ (Low Risk) | 1 | ||||

(e) Health dimension (P_{H}): P_{H} = 0.25 ANX + 0.2 DEP + 0.2 EMA + 0.2 ALD + 0.15 PSA | |||||

ANX, DEP, EMA | Value | ALD, PSA | Value | ||

$\left[56,\text{}80\right]$ (Serious problems) | 0.1 | Yes | 0.1 | ||

$\left[48,\text{}55\right]$ (problems) | 0.5 | No | 1 | ||

$\left[0,\text{}47\right]$ | 1 |

Dimension | Ranges | Ideals | Weights | ||
---|---|---|---|---|---|

Original * | Transf. | Original | Transf. | ||

Economic | [0, 1] | [0, 1] | [0.8, 1] | [0.8, 1] | 0.25 |

Social | {0.1, 0.5, 0.7, 1} | [0.1, 1] | [0.7, 1] | [0.7, 1] | 0.125 |

Academic | $\left\{\mathrm{VL},\mathrm{L},\mathrm{LM},\mathrm{M},\mathrm{MH},\mathrm{H},\mathrm{VH}\right\}$ | [1, 7] | $\left\{\mathrm{H},\mathrm{VH}\right\}$ | [6, 7] | 0.3 |

Cognitive | $\left\{\mathrm{VL},\mathrm{L},\mathrm{LM},\mathrm{M},\mathrm{MH},\mathrm{H},\mathrm{VH}\right\}$ | [1, 7] | $\left\{\mathrm{H},\mathrm{VH}\right\}$ | [6, 7] | 0.2 |

Health | [0, 0.65] | [0, 0.65] | 0.65 | 0.65 | 0.125 |

Dimension | Range = [A, B] | Ideal = [a, b] | Type of Data | Similarity Function | Weights |
---|---|---|---|---|---|

Economic (E) | [0, 1] | [0.8, 1] | I | ${\mu}_{\left(0,0.8,1,1\right)}\left(x\right)$ | w_{E} = 0.25 |

Social (S) | [0.1, 1] | [0.7, 1] | I | ${\mu}_{\left(0.1,0.7,1,1\right)}\left(x\right)$ | w_{S} = 0.125 |

Academic (A) | [1, 7] | [6, 7] | II | ${\eta}_{\left(1,6,7,7;1,0\right)}\left(x\right)$ | w_{A} = 0.3 |

Cognitive (C) | [1, 7] | [6, 7] | I | ${\eta}_{\left(1,6,7,7;-1,0\right)}\left(x\right)$ | w_{C} = 0.2 |

Health (H) | [0, 0.65] | 0.65 | I | ${\mu}_{\left(0,6.5,0.65,0.65\right)}\left(x\right)$ | w_{H} = 0.125 |

Period | MCDM Results | Quality Indicators Results | ||||||
---|---|---|---|---|---|---|---|---|

n | n_{1} | n_{2} | n_{3} | ${\mathit{E}}_{\mathit{A}}\left(\mathit{n}\right)$ | $\mathit{E}\left(\mathit{n}\right)$ | ${\mathit{E}}_{\mathit{W}}\left(\mathit{n}\right)$ | $\mathit{A}\left(\mathit{n}\right)$ | |

2014_1 | 454 | 10 | 11 | 433 | 2.20 | 12.59 | 14.66 | 71.99 |

2014_2 | 726 | 4 | 12 | 710 | 0.55 | 6.33 | 7.36 | 72.70 |

2015_1 | 700 | 8 | 47 | 645 | 1.14 | 8.815 | 10.33 | 65.83 |

2015_2 | 964 | 25 | 60 | 879 | 2.59 | 13.37 | 15.59 | 66.82 |

2016_1 | 1248 | 13 | 41 | 1194 | 3.85 | 16.23 | 19.09 | 70.48 |

2016_2 | 343 | 8 | 18 | 317 | 2.33 | 12.60 | 14.87 | 68.07 |

2017_1 | 1262 | 22 | 26 | 1214 | 1.74 | 11.23 | 13.07 | 72.40 |

2017_2 | 936 | 29 | 28 | 879 | 3.10 | 14.87 | 17.34 | 71.40 |

2018_1 | 1047 | 34 | 26 | 987 | 3.25 | 15.31 | 17.80 | 72.16 |

TOPSIS | VIKOR | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Our Norm. | Calibration | Linear Norm. | Our Normaliz | Calibration | ||||||||||||

PERIOD | n | n_{1} | n_{2} | n_{3} | n_{1} | n_{2} | n_{3} | n_{1} | n_{2} | n_{3} | n_{1} | n_{2} | n_{3} | n_{1} | n_{2} | n_{3} |

2014_1 | 454 | 10 | 11 | 433 | 20 | 36 | 398 | 9 | 8 | 437 | 9 | 24 | 421 | 14 | 31 | 409 |

2014_2 | 726 | 4 | 12 | 710 | 8 | 60 | 658 | 21 | 114 | 591 | 4 | 81 | 641 | 4 | 98 | 624 |

2015_1 | 700 | 8 | 47 | 645 | 9 | 151 | 540 | 4 | 79 | 617 | 12 | 89 | 599 | 4 | 147 | 549 |

2015_2 | 964 | 25 | 60 | 879 | 25 | 64 | 875 | 5 | 264 | 695 | 35 | 93 | 836 | 25 | 263 | 676 |

2016_1 | 1248 | 13 | 41 | 1194 | 25 | 70 | 1153 | 38 | 79 | 1131 | 45 | 116 | 1087 | 44 | 119 | 1085 |

2016_2 | 343 | 8 | 18 | 317 | 9 | 16 | 318 | 12 | 35 | 296 | 12 | 19 | 312 | 12 | 24 | 307 |

2017_1 | 1262 | 22 | 26 | 1214 | 21 | 37 | 1204 | 31 | 14 | 1217 | 31 | 27 | 1204 | 31 | 27 | 1204 |

2017_2 | 936 | 29 | 28 | 879 | 38 | 22 | 876 | 2 | 29 | 905 | 2 | 14 | 920 | 2 | 16 | 918 |

2018_1 | 1047 | 34 | 26 | 987 | 32 | 22 | 993 | 41 | 29 | 977 | 84 | 28 | 935 | 176 | 27 | 844 |

TOPSIS | Our Normalization | Calibration | ||||||
---|---|---|---|---|---|---|---|---|

Period | ${E}_{A}\left(n\right)$ | $E\left(n\right)$ | ${E}_{W}\left(n\right)$ | $A\left(n\right)$ | ${E}_{A}\left(n\right)$ | $E\left(n\right)$ | ${E}_{W}\left(n\right)$ | $A\left(n\right)$ |

2014_1 | 2.20 | 12.59 | 14.66 | 71.99 | 4.41 | 16.92 | 20.14 | 65.00 |

2014_2 | 0.55 | 6.33 | 7.36 | 72.70 | 1.10 | 8.38 | 10.05 | 63.80 |

2015_1 | 1.14 | 8.815 | 10.33 | 65.83 | 1.29 | 7.91 | 10.04 | 48.65 |

2015_2 | 2.59 | 13.37 | 15.59 | 66.82 | 2.59 | 13.11 | 15.56 | 66.27 |

2016_1 | 3.85 | 16.23 | 19.09 | 70.48 | 2.00 | 11.63 | 13.75 | 67.51 |

2016_2 | 2.33 | 12.60 | 14.87 | 68.07 | 2.62 | 13.45 | 15.82 | 68.94 |

2017_1 | 1.74 | 11.23 | 13.07 | 72.40 | 1.66 | 10.88 | 12.71 | 71.13 |

2017_2 | 3.10 | 14.87 | 17.34 | 71.40 | 4.06 | 17.16 | 19.91 | 72.55 |

2018_1 | 3.25 | 15.31 | 17.80 | 72.16 | 3.06 | 14.90 | 17.30 | 72.66 |

VIKOR | Linear | Our Normalization | Calibration | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Period | ${E}_{A}\left(n\right)$ | $E\left(n\right)$ | ${E}_{W}\left(n\right)$ | $A\left(n\right)$ | ${E}_{A}\left(n\right)$ | $E\left(n\right)$ | ${E}_{W}\left(n\right)$ | $A\left(n\right)$ | ${E}_{A}\left(n\right)$ | $E\left(n\right)$ | ${E}_{W}\left(n\right)$ | $A\left(n\right)$ |

2014_1 | 1.98 | 12.02 | 13.96 | 72.89 | 1.98 | 11.61 | 13.70 | 67.94 | 3.08 | 14.28 | 16.95 | 66.13 |

2014_2 | 2.89 | 12.64 | 15.62 | 55.27 | 0.55 | 5.75 | 7.00 | 60.07 | 0.55 | 5.62 | 6.90 | 57.28 |

2015_1 | 0.57 | 5.85 | 7.12 | 59.92 | 1.71 | 10.01 | 12.23 | 58.46 | 0.57 | 5.30 | 6.72 | 49.09 |

2015_2 | 0.52 | 4.71 | 6.14 | 42.85 | 3.63 | 15.08 | 18.11 | 62.63 | 2.59 | 10.60 | 13.73 | 43.36 |

2016_1 | 3.04 | 14.26 | 16.89 | 66.79 | 3.61 | 15.08 | 18.08 | 63.07 | 3.53 | 14.87 | 17.86 | 62.75 |

2016_2 | 3.50 | 14.72 | 17.72 | 61.90 | 3.50 | 15.42 | 18.18 | 67.96 | 3.50 | 15.20 | 18.04 | 66.01 |

2017_1 | 2.46 | 13.48 | 15.59 | 73.96 | 2.46 | 13.34 | 15.50 | 72.46 | 2.46 | 13.34 | 15.50 | 72.46 |

2017_2 | 0.21 | 3.88 | 4.55 | 70.54 | 0.21 | 3.95 | 4.59 | 72.84 | 0.21 | 3.94 | 4.58 | 72.53 |

2018_1 | 5.82 | 20.53 | 23.80 | 71.91 | 8.02 | 24.21 | 27.94 | 73.05 | 16.81 | 35.58 | 40.47 | 75.33 |

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## Share and Cite

**MDPI and ACS Style**

Liern, V.; Parada-Rico, S.E.; Blasco-Blasco, O.
Construction of Quality Indicators Based on Pre-Established Goals: Application to a Colombian Public University. *Mathematics* **2020**, *8*, 1075.
https://doi.org/10.3390/math8071075

**AMA Style**

Liern V, Parada-Rico SE, Blasco-Blasco O.
Construction of Quality Indicators Based on Pre-Established Goals: Application to a Colombian Public University. *Mathematics*. 2020; 8(7):1075.
https://doi.org/10.3390/math8071075

**Chicago/Turabian Style**

Liern, Vicente, Sandra E. Parada-Rico, and Olga Blasco-Blasco.
2020. "Construction of Quality Indicators Based on Pre-Established Goals: Application to a Colombian Public University" *Mathematics* 8, no. 7: 1075.
https://doi.org/10.3390/math8071075