**1. Introduction**

Scientific studies point out the need to act in a strategic and socially responsible way towards sustainable development [1,2]. In this sense, innovation plays a crucial role in achieving this goal [3,4]. On the other hand, the search for lasting solutions for the planet requires balancing objectives from several interest groups and strengthening relationships between institutions [5]. Therefore, countries must have a critical mass of researchers in various knowledge areas [6].

In 1987 the Brundtland Report defined sustainable development as one in which "present needs must be met without compromising the future of future generations" [7] and recognized the importance of the commitment of all to achieve this goal.

In 2015 this theme gained greater relevance with the 17 Sustainable Development Goals (SDGs) [8]. Most importantly, it invites us to create a more sustainable, secure, and prosperous planet for humanity. To achieve the SDGs, individuals, businesses, governments, and non-governmental organizations must commit to sustainable development [5]. Therefore, working together with diverse organizations allows us to remember stakeholders' importance in generating long-term value for both business and society [9].

**Citation:** Barcellos-Paula, L.; De la Vega, I.; Gil-Lafuente, A.M. The Quintuple Helix of Innovation Model and the SDGs: Latin-American Countries' Case and Its Forgotten Effects. *Mathematics* **2021**, *9*, 416. https://doi.org/10.3390/ math9040416

Academic Editor: Jorge de Andres Sanchez

Received: 22 December 2020 Accepted: 12 February 2021 Published: 20 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In this sense, the Quintuple Helix of Innovation Model (QHIM) provides an analytical framework to explain the interactions among the actors of a society that seeks, in theory, to progress [10]. The proposed model is composed of political, educational, economic, environmental, and social systems. Each helix represents a knowledge subsystem that functions as a spiral connecting with the other systems, which, in turn, have a national, regional, and global reach.

Therefore, humanity must find solutions to address significant challenges, such as harmony and cooperation among the five systems towards sustainable development. The uncertainty caused by constant and intense change, which increases decision-making, must also be considered. For these reasons, the primary motivation lies in knowing the relationships between the systems and the variables that affect sustainable development.

As a methodological alternative, the algorithms based on "Fuzzy Logic" [11] contribute to solving problems of the real world when they are dedicated to solving complex systems reducing the uncertainty in decision making [12–14].

In this context, the manuscript aims to broaden the discussion on sustainable development and propose two models to support decision making. The first one suggests 20 indicators linked to the QHIM with the SDGs in Latin American countries. The second identifies the forgotten effects through the application of a Fuzzy Logic algorithm. The main contribution of the study is in knowing these effects and supporting decision making. The main contribution of the study is in knowing these effects and supporting decision making. The results reveal the importance of correctly identifying cause-effects by seeking harmony between systems. A limitation of this research is the number of variables used.

This research can be classified as applied, with the explanatory objective and the combined approach (qualitative-quantitative), modeling and simulation, and case study methods [15]. The combination of the two methods generates an added value to the research since, on the one hand, simulation allows to inform and understand a real-world problem and propose solutions adjusted to the identified needs [16]. On the other hand, the case study method is empirical research that finds a contemporary phenomenon within its real-life context [17]. As a result, the combined research method supports the model's validation and generates interesting theoretical and practical implications.

The document is structured as follows. Section 2 presents the materials and methods. Section 3 shows the results of the simulation applying the Forgotten Effects Theory. Section 4 presents the discussions of the results. Finally, Section 5 details the conclusions followed by the references.

#### **2. Materials and Methods**

This section is organized into four parts to explain the methodology of the study. First, it explains the QHIM and SDGs' theoretical framework. Following, it discusses Latin American countries' case analysis concerning sustainable development applying the QHIM. Third, it explains the algorithm used in the simulation. Finally, it details the simulation process carried out to identify sustainable development's forgotten effects.

#### *2.1. QHIM and SDGs: Theoretical Framework*

The QHIM results from the continuous development of approaches that seek to explain the dynamic interactions of social actors at different scales, the country level being one of them. Scientific studies confirm the importance of the QHIM in integrating the five systems to achieve sustainable development [10,18]. Table A1 presents the evolution of the models related to the study, definitions, and scope.

The previous theoretical basis on which the QHIM was founded comes from several approaches, the most relevant being the Triple Helix for Development, first published by Etzkowitz and Leydesdorff in 1998 [19].

These approaches have contributed to designing the theoretical base model used for this study, such as the Triple Helix and its evolution towards the Fourth and Fifth Helix of Innovation. This last model was finally selected to explain its relationship with the SDGs. It adds social capital and environmental capital to the Triple Helix model and was therefore considered the most appropriate for this study.

By examining the longitudinal evolution of the models related to the one used in this study, we could indicate that the Triple Helix approach operates under the construction of a socio-institutional fabric that leverages the network of interactive business-universitygovernmen<sup>t</sup> agen<sup>t</sup> relationships. This approach describes and analyzes these agents' relationships, and they were examined, considering the dynamic processes generated among the participants and materialized through initiatives that seek innovative solutions [19–23]. This model has been evolving steadily and today is related to the promotion of new modes of an action directed towards the market and also to propose solutions to problems that are fundamental of a social nature [24–26].

The Quadruple Helix model of innovation is an evolution made by a team of specialists integrating central elements of other approaches such as the Triple Helix, Mode 1 and Mode 2, and the National Innovation Systems. This process includes the attributes related to the new actor that the authors incorporate and call Social Capital.

These characteristics are related to the media and the vision of a change process towards a knowledge economy. Including this new actor as a fourth interconnected subsystem, taking into account the media to support disseminating knowledge in a given society, also integrates other aspects such as culture with its values, experience, and traditions [27]. These attributes are relevant since they can favor or condition a given country's potential development, and society has a relevant weight in decisions [28].

The QHIM has as its central purpose to include the natural environment as a new subsystem of knowledge. This approach's logic is based on generating innovation ecosystems that include nature as a central component, giving it the same weight as the other four helices [10]. The natural environment serves to preserve, survive, and vitalize humanity and create new green technologies.

The search for sustainable development of the planet as a central idea is a reality in this proposal. It speaks of social ecology, and the center of gravity of the discussion is global climate change. This aspect allows us to determine that this approach is a proposal before creating the SDGs [29]. The abuse of renewable and non-renewable natural resources is no longer conceived without global society's participation in the substantive decisions on the impact this generates on the planet. Figure 1 presents the model used in this study, and Table A1 provides the definition.

**Figure 1.** The Quintuple Helix Innovation Model (QHIM). Source: [10].

A literature review was performed on SDGs and highlights that the increasingly constant and intense changes brought about by climate change and social inequality were a warning to humanity's future in recent decades. Sustainable development became the main route to meet these challenges. In this sense, the United Nations intensified the orientations and policies towards sustainable development with various guidelines over time, such as the Brundtland Report [30], Global Compact [31], Millennium Development Goals (MDGs) [32], Paris Agreement [33], and the SDGs [34]. Consequently, sustainable development must be considered a priority and strategic in the countries' policies [2].

Currently, the focus is on Agenda 2030 through the SDGs, which in general terms, is a set of objectives, goals, and actions that aim to guide governments, academics, entrepreneurs, and society as a whole towards a fairer and better world [5,35]. Through scientific studies, the academic sector also contributes to the SDGs, seeking to explore this theme, which is complex and depends on the harmony and integration of systems to achieve effective results [3,36].

The research identified three gaps related to the SDGs that could increase uncertainty [37] and hinder the implementation of measures and problem-solving.

The first gap is in indicator assessment because countries have autonomy in the implementation of the SDGs, which will require the collection of quality, accessible, and timely data. SDG assessment results can be ambiguous and confusing due to the lack of a welldesigned conceptual framework of indicators [37]. Other authors warn that applying indicators in an inconsistent or uncoordinated manner can cause serious problems [38,39]. Therefore, consensus on the indicator framework and its use are needed.

The second gap is the lack of understanding between the MDGs and the SDGs [40]. The MDGs focused on countries, whereas the SDGs should be global. For this reason, new methods can help their implementation and systems thinking. The same study states that the danger is prioritizing individual goals without understanding the possible positive interactions between them [40].

The third gap is to understand the correlation between the SDGs in decision making [36,40]. For example, the decision-maker must understand that responding to the threat of climate change (SDG13) influences natural resource managemen<sup>t</sup> (SDGs 14 and 15) and food production (SDG2). Conversely, climate stability (SDG13) and preventing ocean acidification (SDG14) will support sustainable food production and fisheries (SDG2) [41]. Other examples would be gender equality (SDG10) or improving health (SDG3), which help eradicate poverty (SDG1), and fostering peace and inclusive societies (SDG16), which will reduce inequalities (SDG10) and help economies thrive (SDG8) [8]. However, decisionmakers cannot correctly identify interacting variables, which can harm the environment and compromise the SDGs' scope [42]. It is essential to understand sustainable development from a broad and systemic approach, which considers each stakeholder's importance to achieving a more socially just, inclusive, economically viable, and environmentally friendly development.

Along these lines, other studies sought to understand this complexity, reduce uncertainty and facilitate SDG-related decision making through modeling and simulation. For example, in a case study on sustainable tourism in Brazil [14], photovoltaic energy investments in Tanzania [42], and different models, including both scenario analysis and quantitative modeling [43]. However, there is no scientific research on the application of QHIM with the 20 indicators proposed in this study. Also, there are no studies on the Forgotten Effects Theory considering the QHIM and SDGs. In this sense, the study seeks to reduce the identified gaps and contribute to sustainable development with the proposed models. Consequently, the manuscript is novel and useful to various stakeholders, such as governments, society, and academia.

In this context, the present research intends to advance the frontier of knowledge on sustainable development, relating the QHIM with the SDGs through a case study in Latin America and contributing an algorithm in decision making. The next subsection is dedicated to case analysis.

#### *2.2. QHIM: The Latin-American Countries' Case*

This subsection is dedicated to five Latin American countries' case analysis concerning sustainable development applying the QHIM. The countries analyzed were Brazil, Chile, Colombia, Peru, and Mexico. The QHIM was the model chosen to carry out the case study because it is scientifically based on the importance of integrating the five systems to achieve sustainable development [10,18].

However, the model has some drawbacks associated with the choice of indicators and data homogenization. Useful tips to overcome the drawbacks are: (i) use official databases, (ii) the indicators must present transversal characteristics. In this way, it will be possible to compare each helix, and according country's real situation, (iii) use the same period, (iv) create a single value scale, and (v) validate the indicators with experts.

The study focused on this region of the world, but the model presented is generic, which means that it can compare any country. Brazil and Mexico were selected for this case study because they are the two countries with the largest Latin American populations. Colombia and Peru have an intermediate population concerning the first two and Chile, the latter being the least densely populated of the five.

Also, this region of the world presents, in general terms, short-term policies, low investment in Research and Development (R&D), and a low number of scientists per million inhabitants. These countries also have low scientific and technological production, economies with high percentages of informality and unemployment, and inefficient use of renewable and non-renewable resources. Finally, society's low participation as an "auditor" of the activities carried out in the political, educational, business, and environmental spheres is evident [6,44]. This selection shows that the indicators applied are useful, regardless of the size of the country analyzed.

The data from official sources correspond to the period between 2000 and 2017. It should be noted that only some indicators had data until 2019, so a period was chosen in which all the information was available. The study uses 20 indicators that represent the QHIM as criteria for analysis. Each helix was assigned four indicators that are associated with the SDGs. Ten experts in the field of sustainability validated the indicators. The 20 indicators present transversal characteristics that allow a generic comparison of each helix and close the relationship with each country's real functioning. For this purpose, the proximity and remoteness method and ten initial indicators were used for each helix until a consensus was reached. Subsequently, the SDGs were assigned to each helix.

Official sources use different measurement scales when presenting data, which could make analysis difficult. For this reason, the study will use the same scale to homogenize the data. In this case, the endecadary scale with 11 values of [0, 1] will be used. Thus, the value closest to 1 expresses an approach to sustainable development, and the value closest to 0 shows a move away from development. Table A2 shows the five helixes' analysis criteria, the 20 indicators, the concepts, and the SDGs' links. The results of the case study are presented below. Also, Table A3 details the results of QHIM indicators.

Firstly, Figure 2 presents the four indicators of political capital (PC). The results indicated that Chile leads in all indicators of helix 1. On the other hand, there was an alternation in second place between Peru (PC1), Brazil (PC2 and PC3), and Mexico (PC4). In general terms, Brazil, Colombia, Peru, and Mexico presented results below 0.50, which shows these countries' fragility in political capital. Consequently, low governmen<sup>t</sup> regulatory capacity, corruption, political instability, and inadequate public services can be barriers to achieving the SDGs (3, 10, 11, 16, and 17).

Secondly, Figure 3 shows the human capital (HC) indicators. The results revealed that Brazil led in three indicators (HC1, HC2, and HC3) and Mexico in one indicator (HC4). Overall, all five countries had the best result in HC1, which refers to total R&D expenditure. However, the total score for helix 2 would be below 0.30 (except for Brazil with 0.32), which shows a weakness in the education helix. At the same time, a concern, since low investment in education will compromise the reach of SDGs 4 and 9.

**Figure 2.** Political Capital (PC). Source: Own elaboration based on [45].

**Figure 3.** Human Capital (HC). Source: Own elaboration based on [45–48].

Thirdly, Figure 4 shows the indicators of helix 3, economic capital (EC). The results indicated that Colombia led in EC4, Mexico in EC2, Brazil in EC1, and Chile in EC3. In general, economic capital presented the worst result among all the helices. In general terms, the region has low foreign direct investment, high unemployment, a weak current account balance, and low purchasing power. As a consequence, it will negatively affect the fight against poverty (SDG1), hunger (SDG2), decent work (SDG8), industry, innovation and infrastructure (SDG9), and partnerships (SDG17).

Fourthly, Figure 5 presents the indicators of ecological capital (EN). Peru led in EN1, EN2, and EN4, and Brazil in EN3. Except for Mexico, the other four countries achieved a score above 0.60. In Mexico's case, the lowest ratings were in renewable energy (EN3) and population density (EN4), which impacted the final result. In helix 4, the countries analyzed show a small advance towards achieving the objectives (SDG 1, 2, 6, 7, 13, 14, and 15).

Fifthly, Figure 6 shows the social capital indicators (SC). Chile led in SC1, SC2, and SC4, and Mexico in SC3. All five countries presented total scores above 0.50, indicating some progress in gender development, human development, and poverty reduction, contributing to the SDGs (SDG 1, 2, 5, 10, 11, 12, and 15). However, the results point to the existence of gaps in the social sphere.

**Figure 4.** Economic Capital (EC). Source: Own elaboration based on [45].

**Figure 5.** Ecological Capital (EN). Source: Own elaboration based on [45,49,50].

**Figure 6.** Social Capital (SC). Source: Own elaboration based on [45,51,52].

Figure 7 reveals the overall result of the five helices. Also, Table A4 shows the results of QHIM per each helix and country. The result of each helix is the average value of the four indicators per block. Social capital led the ranking (0.63), followed by ecological capital (0.55). Political capital would be in third position (0.51), followed by human capital (0.22)

and economic capital (0.20). Chile led in H1, Brazil in H2, Colombia in H3, Peru in H4, and Mexico in H5.

**Figure 7.** The Five Helix (H1–5) from QHIM: Latin-American countries' case. Source: Own elaboration based on [8,45–53].

> Finally, Figure 8 shows the result of applying the QHIM through the case study in Latin America. The total value represents the average of the five helices for each country. Chile led the ranking with an overall score of 0.46. The second position would be Brazil (0.45), followed by Mexico (0.43), Peru (0.39), and Colombia (0.38).

**Figure 8.** QHIM: Latin-American countries' case. Source: Own elaboration based on [8,45–53].

It should be remembered that the rating scale used was 11 values [0, 1]. Thus, the value closest to 1 expresses an approach to sustainable development, and the value closest to 0 shows a distance to sustainable development. Therefore, results show that there is still a long way to go for the countries analyzed towards sustainable development according to the indicators proposed by the QHIM. The main reason for this would be the low performance in the human and economic capital indicators.

Therefore, the study recommends that countries increase investment in education, incentives for research and development, fiscal balance, economic stimuli, foreign investment, and quality employment. The next subsection explains the use of the Forgotten Effects Theory.

## *2.3. Forgotten Effects Theory*

This subsection explains the simulation algorithm and presents the process carried out to identify sustainable development's forgotten effects.

The "Forgotten Effects Theory" [54] is the mathematical model chosen to simulate this research. This algorithm was applied in several knowledge areas based on previous studies and presented reliable decision-making results [14,55]. However, the model has drawbacks associated with the selection of variables and the choice of experts. Useful tips for solving these problems are: first, it is necessary to know the research topic well and support the use of the variables scientifically. Secondly, it is essential to invite experts on the subject under investigation with time available to collaborate.

The process begins with the presence of a direct incidence relationship, defined by a cause-and-effect matrix defined by two sets of elements: *C* = {*ci*/*<sup>i</sup>* = 1, 2, . . . , *n*} which act as causes; *E* = {*e*/*j* = 1, 2, . . . , *m*} which act as effects and a causality relationship *G* - defined by the *n* × *m* dimension matrix: G- = *<sup>μ</sup>ciej* ∈ [0, 1]/*i* = 1, 2, . . . , *n*; *j* = 1, 2, . . . , *m* being *<sup>μ</sup> ci*,*ej* of the values the characteristic function of belonging of each one of the elements of the matrix *G*- (formed by the rows corresponding to the set's elements-causes-and the columns corresponding to the elements of the set-effects). The matrix *G* - , also named first-generation, is the result of cause-effect estimates. 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.

The second step is to calculate the relationships between the causes, and the relationships between the effects, through two square auxiliary matrices. These two matrices include the possible effects derived from relating causes and effects to each other: *C*- = *<sup>μ</sup>cicj* ∈ [0, <sup>1</sup>]/*i*, *j* = 1, 2, . . . , *n* and *E*- = *<sup>μ</sup>eiej* ∈ [0, <sup>1</sup>]/*i*, *j* = 1, 2, . . . , *m*. 

The Matrix *C*-shows the incidence relationships that can occur between causes, and the matrix *E*- presents the incidence relationships that can occur between effects. Both matrices are reflexive: *μcicj* = 1 ∀*i*=1,2,...,*<sup>n</sup>* and *μeiebj* = 1 <sup>∀</sup>*j*=1,2,...,*<sup>m</sup>*. Therefore, an element, either cause or effect, affects itself with the greatest presumption. Neither *C*- nor *E*- are symmetrical matrices, there is at least some pair of subscripts *i*, *j* so: *μcicj* = *μcjci and μeiej* = *μejei* .

The third step is to establish the direct and indirect incidences, through the maximumminimum composition of the three matrices (1): *C*- ◦ *G*- ◦ *E*- = *G*-∗. The result is the matrix *G*-∗ that collects the incidences between causes and effects of second generation.

$$
\begin{bmatrix}
\ ^\* & \varepsilon\_1 & \varepsilon\_2 & \cdots & \varepsilon\_m \\
\varepsilon\_1 & \mu^\* & \mu^\* & \mu^\* & \cdots & \mu^\* \\
\varepsilon\_2 & \mu^\* & \varepsilon\_{2\varepsilon\_1} & \mu^\* & \varepsilon\_{2\varepsilon\_2} & \cdots & \mu^\* \\
\vdots & \vdots & \vdots & \vdots & \vdots \\
\varepsilon\_n & \mu^\* & \mu^\* & \mu^\* & \cdots & \mu^\* \\
\end{bmatrix} \tag{1}
$$

The fourth step is to calculate the degree to which some causal relationships were forgotten or overlooked (2): *F*- = *G*-∗ − *G*-.

*F*- = - *e*1 ··· *em c*1 *<sup>μ</sup>*<sup>∗</sup>*c*1*e*1 − *μ<sup>c</sup>*1*e*1 ··· *<sup>μ</sup>*<sup>∗</sup>*c*1*em* − *μ<sup>c</sup>*1*em c*2 *<sup>μ</sup>*<sup>∗</sup>*c*2*e*1 − *μ<sup>c</sup>*1*e*1 ··· *<sup>μ</sup>*<sup>∗</sup>*c*2*em* − *μ<sup>c</sup>*2*em* . . . . . . . . . . . . *cn <sup>μ</sup>*<sup>∗</sup>*cne*1 − *μcne*1 ··· *<sup>μ</sup>*<sup>∗</sup>*cnem* − *μcnem* (2)

With the result, it is possible to know the element that has been interposed between cause and effect. Figure 9 indicates the steps to follow.

**Figure 9.** The max-min composition of the matrices.

Finally, the forgotten effects matrix shows that values closer to number 1 have a more significant forgotten effect. Therefore, some effects were not considered initially, and that can generate negative impacts.

The algorithm identifies an interposed element that enhances and accumulates the causal relationship's effects from its application. Therefore, the results allow predicting and acting more effectively on the causes, thus minimizing the effects.
