# Fuzzy Algorithm Applied to Factors Influencing Competitiveness: A Case Study of Brazil and Peru through Affinities Theory

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## Abstract

**:**

## 1. Introduction

_{1}: How are economic attractiveness factors related to the country’s competitiveness?

**H**

_{1}.## 2. Theoretical Framework

#### 2.1. Entrepreneurship and Innovation

#### 2.2. Overview of Brazil and Peru

#### 2.3. Competitiveness Ranking

#### 2.4. Global Entrepreneurship Monitor

#### 2.5. Evaluation of Innovation Policies

#### 2.6. Fuzzy Algorithms

## 3. Methodology

${C}_{1}$ | ${C}_{2}$ | ${C}_{3}$ | ${C}_{n}$ | |||

${\tilde{P}}_{j}$ | ${\mu}_{1}^{\left(j\right)}$ | ${\mu}_{2}^{\left(j\right)}$ | ${\mu}_{3}^{\left(j\right)}$ | ⋯ | ${\mu}_{n}^{\left(j\right)}$ | (1) |

${C}_{1}$ | ${C}_{2}$ | ${C}_{3}$ | ${C}_{n}$ | ||||

${P}_{1}$ | ${\mu}_{1}^{\left(1\right)}$ | ${\mu}_{2}^{\left(1\right)}$ | ${\mu}_{3}^{\left(1\right)}$ | $\cdots $ | ${\mu}_{n}^{\left(1\right)}$ | ||

${P}_{2}$ | ${\mu}_{1}^{\left(2\right)}$ | ${\mu}_{2}^{\left(2\right)}$ | ${\mu}_{3}^{\left(2\right)}$ | $\cdots $ | ${\mu}_{n}^{\left(2\right)}$ | (2) | |

$\left[\stackrel{~}{R}\right]=$ | $\cdots $ | $\cdots $ | $\cdots $ | $\cdots $ | |||

${P}_{m}$ | ${\mu}_{1}^{\left(m\right)}$ | ${\mu}_{2}^{\left(m\right)}$ | ${\mu}_{3}^{\left(m\right)}$ | $\cdots $ | ${\mu}_{n}^{\left(m\right)}$ |

_{2}a limit or threshold ${\theta}_{i}$ is determined. Therefore, the values of the ${\mu}_{i}^{\left(j\right)},i=1,2,\dots n;j=1,2,\dots m$, which satisfy ${\mu}_{i}^{\left(j\right)}\ge {\theta}_{i}$ will be assigned in a new matrix $\left[B\right]$, values for their elements ${\beta}_{i}^{\left(j\right)}$ equal to 1, while when ${\mu}_{i}^{\left(j\right)}<{\theta}_{i}$, will be made ${\beta}_{i}^{\left(j\right)}$ equal to zero. In this way, the ${\theta}_{i},i=1,2,\dots ,n$ constitute the thresholds above which the desired homogeneity exists for each element of the set E

_{2}. The same could be conducted based on set E

_{1}, if the nature of the problem is so required.

${C}_{1}$ | ${C}_{2}$ | ${C}_{3}$ | ${C}_{n}$ | ||||

${P}_{1}$ | ${\beta}_{1}^{\left(1\right)}$ | ${\beta}_{2}^{\left(1\right)}$ | ${\beta}_{3}^{\left(1\right)}$ | $\cdots $ | ${\beta}_{n}^{\left(1\right)}$ | ||

${P}_{2}$ | ${\beta}_{1}^{\left(2\right)}$ | ${\beta}_{2}^{\left(2\right)}$ | ${\beta}_{3}^{\left(2\right)}$ | $\cdots $ | ${\beta}_{n}^{\left(2\right)}$ | (3) | |

$\left[B\right]=$ | $\cdots $ | $\cdots $ | $\cdots $ | $\cdots $ | |||

${P}_{m}$ | ${\beta}_{1}^{\left(m\right)}$ | ${\beta}_{2}^{\left(m\right)}$ | ${\beta}_{3}^{\left(m\right)}$ | $\cdots $ | ${\beta}_{n}^{\left(m\right)}$ |

## 4. Algorithm’s Application and the Results

#### 4.1. Variables

#### 4.2. Data Source

#### 4.3. The Algorithm’s Application

_{1}) and the competitiveness indicators (E

_{2}). Figure 3 shows Peru’s fuzzy relationship $\left[{\stackrel{~}{R}}_{1}\right]$, and Figure 4 displays Brazil’s fuzzy relationship $\left[{\stackrel{~}{R}}_{2}\right]$.

_{1}(Peru) and A

_{2}(Brazil):

_{1}(Peru) and F

_{2}(Brazil):

_{1}(Peru) and A

_{2}(Brazil):

_{1}(Peru) and K

_{2}(Brazil):

#### 4.4. Results of the Application of the Affinities Theory

## 5. Discussion

_{1}and confirming the hypothesis H

_{1}.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviation

Abbreviation | Nomenclature |

BON-OWAAC | Bonferroni means-Ordered Weighted Averaging Adequacy Coefficient |

BON-OWAIMAM | Bonferroni means-Ordered Weighted Averaging Index of Maximum and Minimum |

COVID-19 | Coronavirus Disease 2019 |

ECLAC | Economic Commission for Latin America and the Caribbean |

GDP | Gross Domestic Product |

GEM | Global Entrepreneurship Monitor |

GII | Global Innovation Index |

H_{1} | Hypothesis 1 |

IBGE | Brazilian Institute of Geography and Statistics |

ICT | Information and Communication Technology |

IFS | Intuitionistic Fuzzy Set |

IMD | International Institute for Management Development |

IMD WC | International Institute for Management Development World Competitiveness |

LA | Latin America |

OECD | Organization for Economic Cooperation and Development |

R&D | Research and Development |

RQ | Research Question |

SA | Sensitivity Analysis |

SMEs | Small and Medium Enterprises |

T2FS | Type-2 Fuzzy Set |

T2IFS | Type-2 Intuitionistic Fuzzy Set |

TEA | Total early-stage Entrepreneurial Activity Rate |

WEF | World Economic Forum |

WIPO | World Intellectual Property Organization |

WTO | World Trade Organization |

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**Figure 1.**Research classification. Own elaboration based on [25].

**Figure 2.**Process to obtain affinities. Own elaboration based on [18].

**Figure 3.**Peru’s Fuzzy Relationship. Source: Own elaboration based on [10].

**Figure 4.**Brazil’s Fuzzy Relationship. Source: Own elaboration based on [10].

Pillars | Indicators |
---|---|

Economic Performance | Domestic Economy; International Trade; International Investment; Employment; Prices. |

Government Efficiency | Public Finance; Tax Policy; Institutional Framework; Business Legislation; Societal Framework. |

Business Efficiency | Productivity & Efficiency; Labor Market; Finance; Management Practices; Attitudes and Values. |

Infrastructure | Basic Infrastructure; Technological Infrastructure; Scientific Infrastructure; Health and Environment; Education. |

Overall and Factors | Brazil | Peru | ||||
---|---|---|---|---|---|---|

2020 | 2021 | 2022 | 2020 | 2021 | 2022 | |

Overall | 56 | 57 | 59 | 52 | 58 | 54 |

Economic Performance | 56 | 51 | 48 | 51 | 60 | 40 |

Government Efficiency | 61 | 62 | 61 | 40 | 48 | 52 |

Business Efficiency | 47 | 49 | 52 | 50 | 53 | 53 |

Infrastructure | 53 | 52 | 53 | 60 | 60 | 59 |

Summary | Comments |
---|---|

Progress | The improvements are justified by some progress in public sector regulation and simplification of procedures, but infrastructure needs to catch up to the needs of the productive sector. |

Challenges | The challenge would be to encourage more significant incentives for investment in infrastructure and technological development. In addition, the country should focus on preserving the population’s purchasing power and creating inclusive jobs. |

Recommendations | Brazil should improve the quality of the education system and labour productivity, mitigate growing fiscal pressures, and ensure political and economic stability during an election year. |

Summary | Comments |
---|---|

Progress | The improvement in the economic area would be the rebound effect of the growth rates of the variables strongly affected by the pandemic. |

Challenges | The challenges would be eliminating corruption, strengthening public institutions, increasing regional productivity and competitiveness, and achieving a more efficient and effective health system. |

Recommendations | Peru should focus on reducing poverty, increasing formal employment, and promoting an efficient and decentralized education system. |

Group | World Economic Forum Classification |
---|---|

G1 | Factor-driven countries. That are predominantly dependent on labour factors and natural resources |

G2 | Efficiency-driven countries. They are classified by the advance of industrialisation and gains in scale, predominantly capital-intensive organisations |

G3 | Innovation-driven countries. Knowledge-intensive enterprises and the expansion and modernisation of the service sector categorise them. |

Countries | GII 2022 Rank | Output Rank | Input Rank | Latin America and the Caribbean |
---|---|---|---|---|

Brazil | 54th | 53rd | 58th | 2nd |

Peru | 65th | 81st | 52nd | 6th |

Variables | Indicators |
---|---|

a | Strong R&D culture |

b | Competency of government |

c | Reliable infrastructure |

d | Business-friendly environment |

e | Dynamism of the economy |

f | High educational level |

g | Access to financing |

Variables | Indicators |
---|---|

A | Economic Performance |

B | Government Efficiency |

C | Business Efficiency |

D | Infrastructure |

Peru | Brazil |
---|---|

${A}_{A}\cap {A}_{B}\cap {A}_{C}\cap {A}_{D}=\varnothing $ | ${A}_{A}\cap {A}_{B}\cap {A}_{C}\cap {A}_{D}=\varnothing $ |

${A}_{A}\cap {A}_{B}\cap {A}_{C}\cap {\overline{A}}_{D}=\varnothing $ | ${A}_{A}\cap {A}_{B}\cap {A}_{C}\cap {\overline{A}}_{D}=\varnothing $ |

${A}_{A}\cap {A}_{B}\cap {\overline{A}}_{C}\cap {A}_{D}=\varnothing $ | ${A}_{A}\cap {A}_{B}\cap {\overline{A}}_{C}\cap {A}_{D}=\varnothing $ |

${A}_{A}\cap {\overline{A}}_{B}\cap {A}_{C}\cap {A}_{D}=\varnothing $ | ${A}_{A}\cap {\overline{A}}_{B}\cap {A}_{C}\cap {A}_{D}=\varnothing $ |

${\overline{A}}_{A}\cap {A}_{B}\cap {A}_{C}\cap {A}_{D}=\varnothing $ | ${\overline{A}}_{A}\cap {A}_{B}\cap {A}_{C}\cap {A}_{D}=\varnothing $ |

${A}_{A}\cap {A}_{B}\cap {\overline{A}}_{C}\cap {\overline{A}}_{D}=\left\{b,e\right\}$ | ${A}_{A}\cap {A}_{B}\cap {\overline{A}}_{C}\cap {\overline{A}}_{D}=\left\{e\right\}$ |

${A}_{A}\cap {\overline{A}}_{B}\cap {A}_{C}\cap {\overline{A}}_{D}=\left\{g\right\}$ | ${A}_{A}\cap {\overline{A}}_{B}\cap {A}_{C}\cap {\overline{A}}_{D}=\left\{g\right\}$ |

${\overline{A}}_{A}\cap {A}_{B}\cap {A}_{C}\cap {\overline{A}}_{D}=\left\{d\right\}$ | ${\overline{A}}_{A}\cap {A}_{B}\cap {A}_{C}\cap {\overline{A}}_{D}=\left\{d\right\}$ |

${A}_{A}\cap {\overline{A}}_{B}\cap {\overline{A}}_{C}\cap {A}_{D}=\varnothing $ | ${A}_{A}\cap {\overline{A}}_{B}\cap {\overline{A}}_{C}\cap {A}_{D}=\varnothing $ |

${\overline{A}}_{A}\cap {A}_{B}\cap {\overline{A}}_{C}\cap {A}_{D}=\varnothing $ | ${\overline{A}}_{A}\cap {A}_{B}\cap {\overline{A}}_{C}\cap {A}_{D}=\varnothing $ |

${\overline{A}}_{A}\cap {\overline{A}}_{B}\cap {A}_{C}\cap {A}_{D}=\left\{a,c,f\right\}$ | ${\overline{A}}_{A}\cap {\overline{A}}_{B}\cap {A}_{C}\cap {A}_{D}=\left\{a,c\right\}$ |

${A}_{A}\cap {\overline{A}}_{B}\cap {\overline{A}}_{C}\cap {\overline{A}}_{D}=\varnothing $ | ${A}_{A}\cap {\overline{A}}_{B}\cap {\overline{A}}_{C}\cap {\overline{A}}_{D}=\varnothing $ |

${\overline{A}}_{A}\cap {A}_{B}\cap {\overline{A}}_{C}\cap {\overline{A}}_{D}=\varnothing $ | ${\overline{A}}_{A}\cap {A}_{B}\cap {\overline{A}}_{C}\cap {\overline{A}}_{D}=\varnothing $ |

${\overline{A}}_{A}\cap {\overline{A}}_{B}\cap {A}_{C}\cap {\overline{A}}_{D}=\varnothing $ | ${\overline{A}}_{A}\cap {\overline{A}}_{B}\cap {A}_{C}\cap {\overline{A}}_{D}=\varnothing $ |

${\overline{A}}_{A}\cap {\overline{A}}_{B}\cap {\overline{A}}_{C}\cap {A}_{D}=\varnothing $ | ${\overline{A}}_{A}\cap {\overline{A}}_{B}\cap {\overline{A}}_{C}\cap {A}_{D}=\varnothing $ |

${\overline{A}}_{A}\cap {\overline{A}}_{B}\cap {\overline{A}}_{C}\cap {\overline{A}}_{D}=\varnothing $ | ${\overline{A}}_{A}\cap {\overline{A}}_{B}\cap {\overline{A}}_{C}\cap {\overline{A}}_{D}=\varnothing $ |

Peru | Brazil |
---|---|

${E}_{2}\to \varnothing $ | ${E}_{2}\to \varnothing $ |

$\left\{A,C\right\}\to \left\{g\right\}$ $\left\{B,C\right\}\to \left\{d\right\}$ | $\left\{A,C\right\}\to \left\{g\right\}$ $\left\{B,C\right\}\to \left\{d\right\}$ |

$\left\{A,B\right\}\to \left\{b,e\right\}$ $\left\{C,D\right\}\to \left\{a,c,f\right\}$ | $\left\{A,B\right\}\to \left\{e\right\}$ $\left\{C,D\right\}\to \left\{a,c\right\}$ |

$\left\{A\right\}\to \left\{b,e,g\right\}$ | $\left\{A\right\}\to \left\{e,g\right\}$ |

$\left\{B\right\}\to \left\{b,d,e\right\}$ | $\left\{B\right\}\to \left\{d,e\right\}$ |

$\left\{C\right\}\to \left\{a,c,d,f,g\right\}$ | $\left\{C\right\}\to \left\{a,c,d,g\right\}$ |

$\varnothing \to {E}_{1}$ | $\varnothing \to {E}_{1}$ |

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## Share and Cite

**MDPI and ACS Style**

Barcellos-Paula, L.; Castro-Rezende, A.; Alvares, D.F.
Fuzzy Algorithm Applied to Factors Influencing Competitiveness: A Case Study of Brazil and Peru through Affinities Theory. *Axioms* **2023**, *12*, 1038.
https://doi.org/10.3390/axioms12111038

**AMA Style**

Barcellos-Paula L, Castro-Rezende A, Alvares DF.
Fuzzy Algorithm Applied to Factors Influencing Competitiveness: A Case Study of Brazil and Peru through Affinities Theory. *Axioms*. 2023; 12(11):1038.
https://doi.org/10.3390/axioms12111038

**Chicago/Turabian Style**

Barcellos-Paula, Luciano, Aline Castro-Rezende, and Daniela Fantoni Alvares.
2023. "Fuzzy Algorithm Applied to Factors Influencing Competitiveness: A Case Study of Brazil and Peru through Affinities Theory" *Axioms* 12, no. 11: 1038.
https://doi.org/10.3390/axioms12111038