*2.4. Simulation Process*

To proceed with the calculations, the software FuzzyLog© was used, which allows the elaboration and work with models based on the mathematics of uncertainty to recover the so-called forgotten effects in the causality relations. This program facilitates the values' insertion and automatically solves the incidence matrices' calculation, showing all the results directly in their different versions and variants in graphic and numerical form for their corresponding analysis. Researchers have validated this tool's effectiveness as robust, reliable, and easy to operate [13,56].

The research used the simulation process proposed by the authors [16], which consisted of four stages: (1) Analysis of a real-world problem, (2) Development and validation of the conceptual model, (3) Codification and verification of the model, and (4) Experimental development and simulation results.

The first stage of the simulation process corresponds to the five Latin American countries' case analysis presented in Section 2.2.

The second stage consisted of developing and validate the conceptual model, beginning with identifying the study variables. Two sets of interrelated elements have been proposed from the literature review that act as causes and effects. Three academic specialists on the subjects validate the 22 variables that are the study object in the simulation. They are professors and researchers in Brazil, Colombia, and Spain.

In this case, the set of causes represents the five innovation helixes and is presented as: *C* = {*<sup>c</sup>*1, *c*2, *c*3, *c*4, *<sup>c</sup>*5}. Table 1 presents a set of causes.


**Table 1.** The five helices of innovation.

Source: Own elaboration based on [10]. C/c: Cause.

The set of effects constitutes the SDGs and is presented as: *E* = {*<sup>e</sup>*1,*e*2,*e*3,*e*4,*e*5,*e*6,*e*7,*e*8,*e*9,*e*10,*e*11,*e*12,*e*13,*e*14,*e*15,*e*16,*e*17}. Table 2 presents a set of effects.

**Table 2.** The 17 Sustainable Development Goals.


Source: Own elaboration based on [8]. E/e: effect.

The third stage was to code and verify the model proposed. All variables were inserted into the FuzzyLog© software provided by Anna María Gil-Lafuente, and a review of the data performed. Lastly, with the appropriate programming, the simulation was carried out.

Finally, in the experimental development stage, the specialists estimated the direct incidence between the two sets of causes and effects shown in the matrix *M*- . The assigned value belongs to the interval [0, 1], where zero means the lowest value, and the closer to 1, the higher the incidence rate. After collecting the assessments of each specialist, an average is calculated to obtain the consolidated outcome. Figure A1 shows the results.

Next, the same specialists evaluated the incidences between the causes and between the effects. The specialists sent the answers by e-mail in spreadsheet format. An average was then calculated to aggregate the values. As a result, the matrix between causes and the matrix between effects is generated, represented in Figures A2 and A3, respectively.

With the three matrices *M*- , *A*-, and *B*-, the accumulated effects matrix was calculated *M*- ∗. Figure A4 presents the results of the matrix calculation *A*- ◦ *M*- ◦ *B*- = *M*- ∗.

Finally, the Forgotten Effects Matrix was calculated: *F*- = *M*- ∗ − *M*- . Figure A5 shows the results.

The results of the Forgotten Effects Matrix indicated the effects not observed or forgotten during the assessment stage. The higher the value, the greater the degree of forgotten effect. Therefore, values closer to the number 1 deserve special attention from the decision-maker. The most relevant results of the simulation are presented below.

#### **3. Results of Simulation Applying the Forgotten Effects Theory**

This section presents the main results applying the Forgotten Effects Theory. The selection criterion used was to detail one result for each helix due to this publication's page limit. These five results presented are sufficient to validate the model. The incidences chosen should be between 0.8 (almost full incidence) and 0.9 (practically full incidence) [57]. Future studies may explore other application results.

Table 3 shows these cause-effect relationships that presented high incidences of 0.8 and 0.9 and recovered with the model's application.


Source: Own elaboration based on [54]. SDGs: sustainable development goals.

Firstly, Figure 10 shows the non-existence of a relationship between political capital (H1) and Gender Equality (SDG 5). However, it can be seen that the interposed element (SDG16) Peace, Justice, and Strong Institutions potentiated this relationship to 0.8. The figure also shows the path traveled with all incidents. Therefore, the result indicates that to achieve SDG5 political capital and strong institutions are needed to promote gender equality.

**Figure 10.** Relation between Political Capital (H1) and Gender Equality (SDG5).

Secondly, Figure 11 presents the relationship between the Human Capital (H2) and Climate Action (SDG13) variables. The result shows no direct relationship between the variables, but the interposed element (SDG9) Industry, Innovation, and Infrastructure potentiated this relationship to 0.9. Also, the figure presents all existing incidences. Therefore, the result shows the importance of H2 to reach the SDG13. In this case, investment in R&D strengthens the industry with sustainable production, reducing global warming.

**Figure 11.** Relation between Human Capital (H2) and Climate Action (SDG 13).

Thirdly, Figure 12 shows the relationship between the Economic Capital (H3) and Climate Action (SDG 13) variables. The result shows no direct relationship between the variables, but the interposed element (SDG9) Industry, Innovation, and Infrastructure potentiated this relationship to 0.9. The figure also presents all existing incidences. Soon the result shows the importance of the H3 to reach the SDG13. In this case, the economic stimuli will increase the opportunities for SDG9 with sustainable solutions and thus allow to face climate change.

Fourthly, Figure 13 shows the relationship between the Ecological Capital (H4) and Zero Hunger (SDG2) variables. At first, this relationship did not exist, but the interposed elements (H3) Economic capital and (SDG1), No poverty, potentiated this relationship to 0.9. The figure also shows the path traveled with all incidents. Then, the result indicates that to reach SDG1, and it is necessary to involve the H4; for example, the use of clean energy will expand employment opportunities and, as a consequence, contribute to the reduction of poverty and hunger.

Fifthly, Figure 14 presents the relationship between the Social Capital (H5) and Peace, Justice, and Strong Institutions (SDG16) variables. The result showed no direct relationship between the variables, but the interposed element (SDG10) Reducing Inequality potentiated this relationship to 0.9. Also, the figure presents all existing incidences. Therefore, the result shows the importance of H5 to reach the SDG16. Therefore, social protection policies' adoption contributes to achieving greater equality, peace, and social justice progressively.

In summary, the results reinforce the existing links between the helices and the SDGs (Table A5). The algorithm's application allowed the identification of forgotten effects that can impact the scope of sustainable development. It is up to the decision-maker to use the simulation results or adjust the model and apply it in their country or company.

**Figure 12.** Relation between Economic Capital (H3) and Climate Action (SDG13).

**Figure 13.** Relation between Ecological Capital (H4) and Zero Hunger (SDG2).

**Figure 14.** Relation between Social Capital (H5) and Peace, Justice, and Strong Institutions (SDG16).

#### **4. Discussion of the Results**

Applying the proposed QHIM model indicated that Chile was the country with the highest score, followed by Brazil, Mexico, Colombia, and Peru. In the ranking of the five helixes, social capital (H5) would rank first, followed by ecological (H4), political (H1), human (H2), and economic (H3) capital, respectively. Despite the progress made by these countries in recent years, the study identified opportunities for improvement in all helixes, which can support decision-making on strategy and prioritization of actions. In this sense, the study recommends that countries increase investment in education, incentives for research and development, fiscal balance, economic stimulus, foreign investment, and quality employment.

In response to other studies [37–39], the application of the QHIM provides a set of indicators with quality, accessible and timely data from official sources, which reduces uncertainty in decision making. In this way, the research contributes to a conceptual framework of indicators reducing the identified gap [37]. In line with another study [44], the QHIM can help implement sustainable development systems. With this model, it is possible to know each helix's result and its links with the SDGs and the country's overall performance. Also, the model makes it possible to identify the interrelationships between the systems.

However, it would be interesting in the future to compare the results with other methods, such as generations of Ordered Weighted Averaging (OWA) Operators [58] or Pythagorean Fuzzy Uncertain Environments [59]. As advantages, these methods allow to add weights to the variables, to deal with large amounts of data, and to prioritize the results. In this way, they are methods that facilitate managemen<sup>t</sup> and decision making.

On the other hand, the case study confirmed that the SDGs' scope depends on several systems [10], so it is necessary to evaluate the five helices (social, ecological, political, human, and economic) analyze them in an integrated manner. Table A3 shows the main

study results. These results reinforce the findings of other studies [3,36]. Countries should have a systemic vision since one helix will affect the others' performance and, consequently, sustainable development [8].

Nevertheless, they reinforce research [36,40] on understanding the correlation between the SDGs in decision making. Also, the application of the QHIM and the simulation conducted seek to reduce the gaps identified by other authors [8,41,42].

The research also reveals the importance of correctly identifying cause-effects by seeking harmony between systems. The application of a Fuzzy Logic algorithm identified the forgotten effects of sustainable development. It confirmed other authors' findings [37] on the uncertainty caused by the SDGs' interactions. The simulation also confirmed the results of the QHIM application from official sources.

Finally, the simulation corroborated the indications of other studies' results [14,42] by understanding this complexity, reducing uncertainty [16], and facilitating SDG-related decision making.
