Abstract:
The current study proposes a novel prediction model of sustainability classes for electricity distribution companies in Brazil, based on sustainability indicators, aiming at a more effective risk management for a certain company among their competitors. Because such indicators are based on quantitative and qualitative measures and are very likely to incur imprecisions in their measures, the model to be proposed is based on a Multicriteria Decision Support, Rough Sets Theory, which allows the mathematical treatment of those imprecisions, and Artificial Intelligence, in this case, Machine Learning by rules inference. Consequently, decision tables are generated with condition attributes, sustainability indicators, and decision attributes, sustainability classes: high, medium or low. As a result, it is possible to predict sustainability classes based in temporal series of indicators and rules inference from decision tables, using RoughSets package in R and the jMAF software, demonstrating the use of five rule generation algorithms and their respective accuracies.
Keywords:
Forecasting; Multicriteria decision; Rough sets theory; Artificial intelligence; Sustainability; Risk management
Resumo:
O presente estudo propõe um novo modelo de previsão de classes de sustentabilidade para empresas de distribuição de energia elétrica no Brasil, com base em indicadores de sustentabilidade, visando uma gestão de risco mais eficaz para uma determinada empresa frente a seus concorrentes. Como tais indicadores são baseados em medidas quantitativas e qualitativas e são muito propensos a incorrer em imprecisões em suas medidas, o modelo a ser proposto baseiase em Apoio à Decisão Multicritério, a Teoria dos Conjuntos Aproximativos, que permite o tratamento matemático destas imprecisões, e a Inteligência Artificial, neste caso, Aprendizado de Máquina, por inferência de regras. Consequentemente, são geradas tabelas de decisão com atributos de condição, indicadores de sustentabilidade, e atributos de decisão, classes de sustentabilidade: alta, média ou baixa. Como resultado, é possível prever classes de sustentabilidade com base em séries temporais de indicadores e inferência de regras a partir das tabelas de decisão, utilizandose o pacote RoughSets em R e o software jMAF, e demonstrandose a aplicação de cinco algoritmos de geração de regras e suas respectivas precisões.
Palavraschave:
Previsão; Decisão multicritério; Teoria dos conjuntos aproximativos; Inteligência artificial; Sustentabilidade; Gestão de riscos
1 Introduction
The current study is aimed at the proposition of a model for sustainability classes prediction for electricity distribution companies in Brazil, based on sustainability indicators and indexes, aiming at a more effective risk management for a certain company in relation to their competitors. The model to be proposed is based in a multicriteria approach (Gomes & Rangel, 2009aGomes, L. F. A. M., & Rangel, L. A. D. (2009a). An application of the TODIM method to the multicriteria rental evaluation of residential properties. European Journal of Operational Research, 193(1), 204211. http://dx.doi.org/10.1016/j.ejor.2007.10.046.
http://dx.doi.org/10.1016/j.ejor.2007.10...
, bGomes, L. F. A. M., & Rangel, L. A. D. (2009b). Determining the utility functions of criteria used in the evaluation of real estate. International Journal of Production Economics, 117(2), 420426. http://dx.doi.org/10.1016/j.ijpe.2008.12.006.
http://dx.doi.org/10.1016/j.ijpe.2008.12...
; Slowinski et al., 2012Slowinski, R., Greco, S., & Matarazzo, B. (2012). Rough set and rulebased multicriteria decision aiding. Pesquisa Operacional, 32(2), 213270. http://dx.doi.org/10.1590/S010174382012000200001.
http://dx.doi.org/10.1590/S010174382012...
) with the use of Rough Sets Theory (RST), a mathematical theory for treating imprecise data, and Machine Learning, an Artificial Intelligence subfield, in order to infer decision rules, if … then …, in the prediction of sustainability classes based on progress and sustainability indicators, using RoughSets package in R and the jMAF software.
According to Wu & Wu (2012)Wu, J., & Wu, T. (2012). Sustainability indicators and indices: an overview. In C. N. Madu & C. Kuei (Eds.), Handbook of sustainable management (pp. 6586). London: Imperial College Press. http://dx.doi.org/10.1142/9789814354820_0004.
http://dx.doi.org/10.1142/9789814354820_...
, Elkington (2020)Elkington, J. (2020). Green swans: the coming boom in regenerative capitalism. New York: Fast Company Press. and Pereira & Cândido (2020)Pereira, F. No., & Cândido, G. A. (2020). Sustentabilidade corporativa: definição de indicadores para organizações do setor energético. Revista de Gestão dos Países de Língua Portuguesa, 19(2), 104126. http://dx.doi.org/10.12660/rgplp.v19n2.2020.80610.
http://dx.doi.org/10.12660/rgplp.v19n2.2...
, the sustainable development and sustainability involve interdisciplinary themes and is present in discussions across many science areas, in public and private organizations, nongovernmental ones and in society as a whole. Sustainability is related not only to ecologic aspects, but it also relates to economic, political, cultural, social, temporal, and spatial aspects, deeming it essential the creation of measurement instruments, such as sustainability indicators, tools made up of one or more variables, that can be related in many ways. Consequently, establishing goals and creating instruments are fundamental steps in making possible the corporate sustainability measuring. There are many corporate sustainability indicator systems being used in Brazil, such as the Brazilian Institute of Social and Economic Analysis’ (IBASE) model; the Ethos model; the Corporate Sustainability Index (CSI); Dow Jones Sustainability Index (DJSI); and the international model Global Reporting Initiative (GRI). Paz & Kipper (2016)Paz, F. J., & Kipper, L. M. (2016). Sustentabilidade nas organizações: vantagens e desafios. Revista Gestão da Produção Operações e Sistemas, 11(2), 85102. point towards other models to measure sustainability in public and private organizations from a variety of fields: PressureStateResponse (PSR), environmental dimension; Driving ForcesStateResponse (DSR), social, environmental, institutional and economic dimensions; Genuine Progress Indicator (GPI), social and economic dimensions; World Bank, social, environmental, economic and cultural dimensions; Human Development Index (HDI), social, economic, cultural and political dimensions; Barometer of Sustainability, social and environmental dimensions; Sustainability Panel, social, environmental, institutional and economic dimensions; etc. According to Elkington (2020)Elkington, J. (2020). Green swans: the coming boom in regenerative capitalism. New York: Fast Company Press., all this effort must be aligned with the United Nations' Sustainable Development Goals: a set of 17 ambitious goals and 169 related targets. The sustainable development goals must be the “north” for the sustainability.
Furthermore, the indicators can be unique when they represent a specific dimension, or aggregated, when dimensions of the process or part of it are represented by a set of indicators that are frequently aggregated in other indicators. According to Wu & Wu (2012)Wu, J., & Wu, T. (2012). Sustainability indicators and indices: an overview. In C. N. Madu & C. Kuei (Eds.), Handbook of sustainable management (pp. 6586). London: Imperial College Press. http://dx.doi.org/10.1142/9789814354820_0004.
http://dx.doi.org/10.1142/9789814354820_...
and Franceschini et al. (2019)Franceschini, F., Galetto, M., & Maisano, D. (2019). Designing performance measurement systems: theory and practice of key performance indicators. Cham: Springer, http://dx.doi.org/10.1007/9783030011925.
http://dx.doi.org/10.1007/97830300119...
, in order to reduce the number of indicators or to reflect integrations in a system, indicators are mathematically combined to produce indexes, aggregate of two or more indicators.
Regarding Figure 1, the emphasis in identification and use of indicators in a predictive way is relatively new. Predictive indicators are suitable when the main interest is to prevent the occurrence of problems, instead of fixing them, e.g.: financial flow through time (Franceschini et al., 2019Franceschini, F., Galetto, M., & Maisano, D. (2019). Designing performance measurement systems: theory and practice of key performance indicators. Cham: Springer, http://dx.doi.org/10.1007/9783030011925.
http://dx.doi.org/10.1007/97830300119...
).
Predictive indicators for financial and operational use. Source: Franceschini et al. (2019)Franceschini, F., Galetto, M., & Maisano, D. (2019). Designing performance measurement systems: theory and practice of key performance indicators. Cham: Springer, http://dx.doi.org/10.1007/9783030011925.
http://dx.doi.org/10.1007/97830300119... .
Furthermore, ISO 26000, Social Responsibility Guidance Standard (ABNT, 2010Associação Brasileira de Normas Técnicas  ABNT. (2010). NBR ISO 26000diretrizes sobre responsabilidade social. São Paulo: ABNT.), established that “An organization can exert influence over others to strengthen the positive impacts on sustainable development or to minimize the negative impact, or both cases”. Among the proposed methods to exert influence, there is promoting best practices. In September of 2015, the United Nations General Assembly, through the 2030 Agenda, established a collection of 17 global goals (Global Goals for a Sustainable Development) (ONU, 2015Organização das Nações Unidas  ONU. (2015). Transformando nosso mundo: a agenda 2030 para o desenvolvimento sustentável. Retrieved in 2020, March 5, https://www.mds.gov.br/webarquivos/publicacao/Brasil_Amigo_Pesso_Idosa/Agenda2030.pdf.
https://www.mds.gov.br/webarquivos/publi...
). In that Agenda, regarding Goal “12”, Ensure sustainable consumption and production patterns, you can read: Encourage companies, especially large and transnational companies, to adopt sustainable practices and to integrate sustainability information into their reporting cycle.
In Brazil, the National Electric Energy Agency (ANEEL), through Normative Resolution n. 605, from 03/11/2014, approved the Electricity Sector Accounting Manual (ESAM), where it was established, among other goals, contributing to the optimization of social environmental performance through explicitly showing costs originated from compliance with the National Environment Policy, necessary to the environmental conformity and the sustainability of concessions attributed by the Federal Union, aiming at the elaboration of the Report on SocioEnvironmental and EconomicFinancial e (RSA) (Brasil, 2014Brasil. Agência Nacional de Energia Elétrica  ANEEL. (2014). Resolução normativa nº 605, de 11/03/2014 (seção 1, nº 53, p. 43). Brasília, DF: Diário Oficial da República Federativa do Brasil.; ANEEL, 2015Agência Nacional de Energia Elétrica  ANEEL. (2015). Manual de contabilidade do setor elétrico. Brasília: ANEEL.). The ESAM relates more than two hundred quantitative indicators related to the general, corporate governance, economicfinancial, social and sectorial, and environmental dimensions for granted companies, generation, transmission and distribution of electricity, demanded and/or suggested by ANEEL, beyond environmental performance indicators that are specific to generation and transmission and/or distribution companies (ANEEL, 2015Agência Nacional de Energia Elétrica  ANEEL. (2015). Manual de contabilidade do setor elétrico. Brasília: ANEEL.). The ESAM still mentions qualitative indicators, e.g.: aspects of corporate governance.
The contributions of this study are in the model proposition that: a) uses Rough Sets Theory/Dominance principle and Machine Learning to extract decision rules and infer sustainability classes from historical series of indicators and simulated values, aiming to obtain better risk management in the economic, social, environmental and corporate governance dimensions of a company against competitors; b) establishes sustainability classes for companies in order to identify possible links on aspects of sustainability and performance between companies belonging to the same class, as opposed to simple ranking; c) allows to relate condition and decision criteria in decision rules, for example, by coverage factor, and consequently, obtain patterns in data, without referring to a priori and posterior probabilities, as in Bayesian analysis (Pawlak, 2002Pawlak, Z. (2002). Rough sets, decision algorithms and Bayes’ theorem. European Journal of Operational Research, 136(1), 181189. http://dx.doi.org/10.1016/S03772217(01)000297.
http://dx.doi.org/10.1016/S03772217(01)...
).
This study is currently divided into the following additional sections: 2, Literature review; 3, Methodology, composed of 3.1, Rough Sets Theory and Dominance principle, and 3.2, Machine Learning; 4, Results and discussions; and 5, Conclusion and future studies.
2 Literature review
A systematic literature review was carried out in May/2022, in the databases Scopus, Web of Science, Compendex, IEEE Xplore, Emerald Insight, Scielo, ACM Digital Library, EBSCO and Wiley Online, for the period 20002022, using the ProKnowC methodology, Knowledge Development Process  Constructivist (Afonso et al., 2011Afonso, M. H. F., Souza, J. V., Ensslin, S. R., & Ensslin, L. (2011). Como construir conhecimento sobre o tema de pesquisa? Aplicação do processo ProKnowC na busca de literatura sobre avaliação do desenvolvimento sustentável. Revista de Gestão Social e Ambiental, 5(2), 4762. http://dx.doi.org/10.24857/rgsa.v5i2.424.
http://dx.doi.org/10.24857/rgsa.v5i2.424...
; Ensslin et al., 2014Ensslin, S. R., Ensslin, L., Yamakawa, E. K., Nagaoka, M. P. T., Aoki, A. R., & Siebert, L. C. (2014). Processo estruturado de revisão da literatura e análise bibliométrica sobre avaliação de desempenho de processos de implementação de eficiência energética. Revista Brasileira de Energia, 20(1), 2150.). Table 1 illustrates the sequence of procedures in eight phases adapted from the ProKnowC methodology, which was used to build the systematic literature review. The following search string (1) was used for the abstract field: (“sustainability” OR “sustainable”) AND “performance” AND (“indicator” OR “indice” OR “index” OR “measurement” OR “assessment” OR “evaluation” OR “appraisal” OR “metric” OR “model” OR “framework” OR “template” OR “example”) AND (“energy companies” OR “electricity companies” OR “energy firms” OR “electricity firms” OR “energy industry” OR “power industry” OR “energy sector” OR “electricity sector” OR “electric sector” OR “energy enterprises”). There was a return of 689 articles (bibliographic portfolio BP0, Phase 4, according to Table 1) which, after excluding repeated publications, reading the titles and abstracts, using a “cut line” (above, at least 85% of the total citations on Google Scholar; below, most recent articles, published in the last 3 years), full reading of the remainder and verification of adherence to the research, resulted in 53 studies. To this set of 53 studies, the following search string (2) was applied to the abstract field: ((“multicriteria” OR “multicriteria” OR “multiobjective” OR “multiobjective”) OR “machine learning”). From this set, 14 studies resulted. Complementarily, for the period JanuaryMay 2022, the junction “and” of the previous strings 1 and 2 was applied to search for new studies. It resulted in 7 studies. Thus, there are 14 + 7 studies. Table 2 summarizes the results of the systematic literature review.
Systematic literature review, ProKnowC methodology. Source: Authors, adapted from Ensslin et al. (2014)Ensslin, S. R., Ensslin, L., Yamakawa, E. K., Nagaoka, M. P. T., Aoki, A. R., & Siebert, L. C. (2014). Processo estruturado de revisão da literatura e análise bibliométrica sobre avaliação de desempenho de processos de implementação de eficiência energética. Revista Brasileira de Energia, 20(1), 2150..
The Table 1 shows the sequence of procedures divided into eight phases adapted from the ProKnowC methodology, aiming to simplify its use in systematic literature review works.
There are studies with the application of several multicriteria decision support methods, in individual or hybrid form, as well as proposals for specific models aimed at solving electrical energy problems. This reveals trends to use models with Machine Learning and Neural Networks, for example, to infer results on production, efficiency and consumption of electricity (Ahmad et al., 2021Ahmad, T., Zhang, D., Huang, C., Zhang, H., Dai, N., Song, Y., & Chen, H. (2021). Artificial intelligence in sustainable energy industry: status quo, challenges and opportunities. Journal of Cleaner Production, 289, 125834. http://dx.doi.org/10.1016/j.jclepro.2021.125834.
http://dx.doi.org/10.1016/j.jclepro.2021...
; Ahmadi et al., 2022Ahmadi, M., Soofiabadi, M., Nikpour, M., Naderi, H., Abdullah, L., & Arandian, B. (2022). Developing a deep neural network with fuzzy wavelets and integrating an inline PSO to predict energy consumption patterns in urban buildings. Mathematics, 10(8), 1270. http://dx.doi.org/10.3390/math10081270.
http://dx.doi.org/10.3390/math10081270...
; Buțurache & Stancu, 2022Buțurache, A.N., & Stancu, S. (2022). Building energy consumption prediction using neuralbased models. International Journal of Energy Economics and Policy, 12(2), 3038. http://dx.doi.org/10.32479/ijeep.12739.
http://dx.doi.org/10.32479/ijeep.12739...
; Kwakkel & Pruyt, 2013Kwakkel, J. H., & Pruyt, E. (2013). Exploratory modeling and analysis, an approach for modelbased foresight under deep uncertainty. Technological Forecasting and Social Change, 80(3), 419431. http://dx.doi.org/10.1016/j.techfore.2012.10.005.
http://dx.doi.org/10.1016/j.techfore.201...
; Rolnick et al., 2022Rolnick, D., Donti, P. L., Kaack, L. H., Kochanski, K., Lacoste, A., Sankaran, K., Ross, A. S., MilojevicDupont, N., Jaques, N., WaldmanBrown, A., Luccioni, A. S., Maharaj, T., Sherwin, E. D., Mukkavilli, S. K., Kording, K. P., Gomes, C. P., Ng, A. Y., Hassabis, D., Platt, J. C., Creutzig, F., Chayes, J., & Bengio, Y. (2022). Tackling climate change with machine learning. ACM Computing Surveys, 55(2), 42. http://dx.doi.org/10.1145/3485128.
http://dx.doi.org/10.1145/3485128...
; VargasSolar et al., 2022VargasSolar, G., Khalil, M., EspinosaOviedo, J. A., & ZechinelliMartini, J.L. (2022). GREENHOME: a household energy consumption and CO2 footprint metering environment. ACM Transactions on Internet Technology, 22(3), 72. http://dx.doi.org/10.1145/3505264.
http://dx.doi.org/10.1145/3505264...
). In addition, there are proposals for models for analyzing problems using Fuzzy logic, a theory for the mathematical treatment of data imprecision (AlBarakati et al., 2022AlBarakati, A., Mishra, A. R., Mardani, A., & Rani, P. (2022). An extended intervalvalued Pythagorean fuzzy WASPAS method based on new similarity measures to evaluate the renewable energy sources. Applied Soft Computing, 120, 108689. http://dx.doi.org/10.1016/j.asoc.2022.108689.
http://dx.doi.org/10.1016/j.asoc.2022.10...
; Ervural et al., 2018aErvural, B. C., Evren, R., & Delen, D. (2018a). A multiobjective decisionmaking approach for sustainable energy investment planning. Renewable Energy, 126, 387402. http://dx.doi.org/10.1016/j.renene.2018.03.051.
http://dx.doi.org/10.1016/j.renene.2018....
, bErvural, B. C., Zaim, S., Demireld, O. F., Aydin, Z., & Delen, D. (2018b). An ANP and fuzzy TOPSISbased SWOT analysis for Turkey’s energy planning. Renewable & Sustainable Energy Reviews, 82, 15381550. http://dx.doi.org/10.1016/j.rser.2017.06.095.
http://dx.doi.org/10.1016/j.rser.2017.06...
; Panchal et al., 2022Panchal, D., Chatterjee, P., Pamucar, D., & Yazdani, M. (2022). A novel fuzzy‐based structured framework for sustainable operation and environmental friendly production in coal‐fired power industry. International Journal of Intelligent Systems, 37(4), 27062738. http://dx.doi.org/10.1002/int.22507.
http://dx.doi.org/10.1002/int.22507...
; Qi et al., 2020Qi, W., Huang, Z., Dinçer, H., Korsakiene, R., & Yuksel, S. (2020). Corporate governancebased strategic approach to sustainability in energy industry of emerging economies with a novel intervalvalued intuitionistic fuzzy hybrid decision making model. Sustainability, 12(8), 3307. http://dx.doi.org/10.3390/su12083307.
http://dx.doi.org/10.3390/su12083307...
; Zhou et al., 2019Zhou, P., Zhou, P., Yüksel, S., Dinçer, H., & Uluer, G. S. (2019). Balanced scorecardbased evaluation of sustainable energy investment projects with IT2 fuzzy hybrid decision making approach. Energies, 13(1), 82. http://dx.doi.org/10.3390/en13010082.
http://dx.doi.org/10.3390/en13010082...
).
Furthermore, there was an extension of the systematic literature review in the Web of Science and Scopus bases, in the period 20202022, using the following search string: “TITLEABSKEY ((“multicriteria” OR “multicriteria” OR “multiobjective” OR “multiobjective”) AND “decision making” AND (“predicting” OR “forecasting”))”, “decision” and “artificial intelligence” subareas. There was a return of 36 (thirtysix) articles. However, of these studies, only 12 are related to energy, classification or machine learning. There are studies with the joint application of the Promethee multicriteria method and Machine Learning prediction in financial decision making (Mousavi & Lin, 2020Mousavi, M. M., & Lin, J. (2020). The application of PROMETHEE multicriteria decision aid in financial decision making: case of distress prediction models evaluation. Expert Systems with Applications, 159, 113438. http://dx.doi.org/10.1016/j.eswa.2020.113438.
http://dx.doi.org/10.1016/j.eswa.2020.11...
); and a new hybrid fuzzy prediction method is introduced by combining the Fuzzy Analytic Hierarchy Process (FAHP) and machine learning model (Ozdemir et al., 2021Ozdemir, C., Onar, S. C., Bagriyanik, S., Kahraman, C., Akalin, B. Z., & Öztayşi, B. (2021). Estimating shopping center visitor numbers based on a new hybrid fuzzy prediction method. Journal of Intelligent & Fuzzy Systems, 42(1), 6376. http://dx.doi.org/10.3233/JIFS219175.
http://dx.doi.org/10.3233/JIFS219175...
). For applications to energy or classification problems: fuzzy interval time series energy and financial forecasting model (Liu et al., 2020Liu, G., Xiao, F., Lin, C.T., & Cao, Z. (2020). A fuzzy interval time series energy and financial forecasting model using networkbased multiple timefrequency spaces and the induced ordered weighted averaging aggregation operation. IEEE Transactions on Fuzzy Systems, 28(11), 26772690. http://dx.doi.org/10.1109/TFUZZ.2020.2972823.
http://dx.doi.org/10.1109/TFUZZ.2020.297...
); flood hazards susceptibility mapping using statistical, fuzzy logic and MCDM methods (Akay, 2021Akay, H. (2021). Flood hazards susceptibility mapping using statistical, fuzzy logic, and MCDM methods. Soft Computing, 25(14), 93259346. http://dx.doi.org/10.1007/s00500021059031.
http://dx.doi.org/10.1007/s00500021059...
); assessment of a failure prediction model in the energy sector with multicriteria discrimination approach, Promethee based classification (Angilella & Pappalardo, 2021Angilella, S., & Pappalardo, M. R. (2021). Assessment of a failure prediction model in the European energy sector: a multicriteria discrimination approach with a PROMETHEE based classification. Expert Systems with Applications, 184, 115513. http://dx.doi.org/10.1016/j.eswa.2021.115513.
http://dx.doi.org/10.1016/j.eswa.2021.11...
); hybrid neurofuzzy investigation of shortterm variability of wind resource (Adedeji et al., 2021Adedeji, P. A., Akinlabi, S. A., Madushele, N., & Olatunji, O. O. (2021). Hybrid neurofuzzy investigation of shortterm variability of wind resource in site suitability analysis: a case study in South Africa. Neural Computing & Applications, 33(19), 1304913074. http://dx.doi.org/10.1007/s0052102106001x.
http://dx.doi.org/10.1007/s00521021060...
); TOPSISELM framework for stock index price movement prediction (Samal & Dash, 2021Samal, S., & Dash, R. (2021). A TOPSISELM framework for stock index price movement prediction. Intelligent Decision Technologies, 15(2), 201220. http://dx.doi.org/10.3233/IDT200013.
http://dx.doi.org/10.3233/IDT200013...
); costsensitive business failure prediction when misclassification costs are uncertain (Bock et al., 2020Bock, K. W., Coussement, K., & Lessmann, S. (2020). Costsensitive business failure prediction when misclassification costs are uncertain: a heterogeneous ensemble selection approach. European Journal of Operational Research, 285(2), 612630. http://dx.doi.org/10.1016/j.ejor.2020.01.052.
http://dx.doi.org/10.1016/j.ejor.2020.01...
); multi objective optimization of crude oil supply portfolio based on interval prediction data (Sun et al., 2022Sun, X., Hao, J., & Li, J. (2022). Multiobjective optimization of crude oilsupply portfolio based on interval prediction data. Annals of Operations Research, 309(2), 611639. http://dx.doi.org/10.1007/s1047902003701w.
http://dx.doi.org/10.1007/s10479020037...
); optimization of integrated fuzzy decision tree and regression models for selection of oil spill response (Mohammadiun et al., 2021Mohammadiun, S., Hu, G., Gharahbagh, A. A., Mirshahi, R., Li, J., Hewage, K., & Sadiq, R. (2021). Optimization of integrated fuzzy decision tree and regression models for selection of oil spill response method in the Arctic. KnowledgeBased Systems, 213, 106676. http://dx.doi.org/10.1016/j.knosys.2020.106676.
http://dx.doi.org/10.1016/j.knosys.2020....
); use of PairCode algorithm for ordinal classification based on pairwise comparison (Yang et al., 2020Yang, Y., Chen, B., & Yang, Z. (2020). An algorithm for ordinal classification based on pairwise comparison. Journal of Classification, 37(1), 158179. http://dx.doi.org/10.1007/s0035701993114.
http://dx.doi.org/10.1007/s00357019931...
); and client profile prediction using convolutional neural networks (Nedjah et al., 2022Nedjah, N., Azevedo, V. R., & Mourelle, L. D. M. (2022). Client profile prediction using convolutional neural networks for efficient recommendation systems in the context of smart factories. Enterprise Information Systems, 16(1011), 16531693. http://dx.doi.org/10.1080/17517575.2020.1856423.
http://dx.doi.org/10.1080/17517575.2020....
). In addition, there are studies that show the application of the PROMETHEESAPEVOM1 multicriteria method to the analysis of OECD countries (Pereira et al., 2022Pereira, D. A. M., Santos, M., Costa, I. P. A., Moreira, M. A. L., Terra, A. V., Rocha, C. S. Jr., & Gomes, C. F. S. (2022). Multicriteria and statistical approach to support the outranking analysis of the OECD countries. IEEE Access: Practical Innovations, Open Solutions, 10, 6971469726. http://dx.doi.org/10.1109/ACCESS.2022.3187001.
http://dx.doi.org/10.1109/ACCESS.2022.31...
) and multicriteria analysis applied to aircraft selection, case in Brazilian Navy (Maêda et al., 2021Maêda, S. M. N., Costa, I. P. A., Castro, M. A. P. Jr., Fávero, L. P., Costa, A. P. A., Corriça, J. V. P., Gomes, C. F. S., & Santos, M. (2021). Multicriteria analysis applied to aircraft selection by Brazilian Navy. Production, 31, e20210011. http://dx.doi.org/10.1590/01036513.20210011.
http://dx.doi.org/10.1590/01036513.2021...
).
Consequently, a gap is identified in the literature regarding the proposition of a model with the use of Rough Sets Theory/Dominance principle, theory for mathematical treatment of data imprecision and generation of decision rules, and Machine Learning for the inference of sustainability classes for electric power companies.
3 Methodology
3.1 Rough sets theory and dominance principle
According to Pawlak (1982Pawlak, Z. (1982). Rough sets. IInternational Journal of Computer & Information Sciences, 11(5), 341356. http://dx.doi.org/10.1007/BF01001956.
http://dx.doi.org/10.1007/BF01001956...
, 1991Pawlak, Z. (1991). Rough sets, theoretical aspects of reasoning about data. Dordrecht: Kluwer Academic Publishers.), Pawlak & So̵winski (1994)Pawlak, Z., & So̵winski, R. (1994). Rough set approach to multiattribute decision analysis. European Journal of Operational Research, 72(3), 443459. http://dx.doi.org/10.1016/03772217(94)904154.
http://dx.doi.org/10.1016/03772217(94)9...
, Pawlak et al. (1995)Pawlak, Z., GrzymalaBusse, J., Slowinski, R., & Ziarko, W. (1995). Rough sets. Communications of the ACM, 38(11), 8895. http://dx.doi.org/10.1145/219717.219791.
http://dx.doi.org/10.1145/219717.219791...
and Slowinski et al. (2012)Slowinski, R., Greco, S., & Matarazzo, B. (2012). Rough set and rulebased multicriteria decision aiding. Pesquisa Operacional, 32(2), 213270. http://dx.doi.org/10.1590/S010174382012000200001.
http://dx.doi.org/10.1590/S010174382012...
, the Rough Sets Theory (RST) was originated with Zdzislaw Pawlak, at the beginning of the 1980s, as a mathematical tool to treat imprecision and uncertainty of data. The approach made possible with RST is of fundamental importance for Artificial Intelligence (AI) and the cognitive sciences, especially in the Machine Learning areas, knowledge acquisition, decision analysis, knowledge discovery in databases, specialist systems, decision making support systems, inductive reasoning and pattern recognition. RST does not compete with Fuzzy Logic, with which it is frequently compared, but it complements it.
In any case, these theories are independent approaches of imperfect knowledge. One of the main advantages RST offers is that it doesn’t need preliminary or additional information about data, the way probability distribution or pertinence level need in the fuzzy sets theory. There is a concept of Information Systems with: K = (U, A), where U is a finite and nonempty set of objects; A is a finite and nonempty set of attributes, such that a: U → V_{a} for every a ϵ A, where V_{a} is a set of values that can be attributed to attribute a.
There is also the concept about indiscernibility relation: given an information system (U,A) and for any B ⊆ A, an equivalence relation (or classification, indistinctively) R_{B} is defined as (Riza et al., 2014Riza, L. S., Janusz, A., Bergmeir, C., Cornelis, C., Herrera, F., Slezak, D., & Benitez, J. M. (2014). Implemeting algorithms of rough set theory and fuzzy rough set theory in the R package “roughsets”. Information Sciences, 287, 6889. http://dx.doi.org/10.1016/j.ins.2014.07.029.
http://dx.doi.org/10.1016/j.ins.2014.07....
), Equation 1:
If (x,y) ϵ R_{B}(x,y), then x and y have exactly the same values for attributes in B. According to Pawlak (1991)Pawlak, Z. (1991). Rough sets, theoretical aspects of reasoning about data. Dordrecht: Kluwer Academic Publishers., it is not always possible to express exactly a certain set of objects with the available knowledge. Consequently, it is possible to express a set of objects by other two subsets: lower (R) and upper ($\stackrel{}{\mathrm{R}}$) approximations, given that X ⊆ U and an equivalence relation R, Equation 2:
where RX is the subset of U elements, that can certainly be classified as X elements; RX is the subset of U elements, that can possibly be classified as X elements. A set is rough with relation to R, if and only if, RX ≠ $\stackrel{}{\mathrm{R}}\mathrm{X}$.
From the Information System concept, K = (U, A), it can be obtained the concept of decision table: when A is formed by two subsets: C and D, attributes of condition and decision, respectively, (C, D ⊂ A); or, T = (U, A, C, D). The equivalence classes of R_{B} and R_{C} relations are known as condition and decision classes, respectively. For each x ϵ U, a function d_{x}: A → V is associated, such that d_{x}(a) = a(x), for every a ϵ C ∪ D; the d_{x} function is known as decision rule in T (Pawlak, 1991Pawlak, Z. (1991). Rough sets, theoretical aspects of reasoning about data. Dordrecht: Kluwer Academic Publishers.). According to Riza et al. (2014), aRiza, L. S., Janusz, A., Bergmeir, C., Cornelis, C., Herrera, F., Slezak, D., & Benitez, J. M. (2014). Implemeting algorithms of rough set theory and fuzzy rough set theory in the R package “roughsets”. Information Sciences, 287, 6889. http://dx.doi.org/10.1016/j.ins.2014.07.029.
http://dx.doi.org/10.1016/j.ins.2014.07....
superreduct is a set of attributes B ⊂ A such that R_{B} = R_{A}, where R_{B} and R_{A} are indiscernibility relations defined by B and A, respectively. If this relation is also minimum, it is a reduct. The intersection of all reducts is a core of an information system. In Pawlak (2000)Pawlak, Z. (2000). Rough sets and decision analysis. Information Systems & Operational Research, 38(3), 132144. http://dx.doi.org/10.1080/03155986.2000.11732405.
http://dx.doi.org/10.1080/03155986.2000....
, it is found an example of a Decision Table ‒ Table 3. This table is composed of six stores and four attributes (quantitative or qualitative aspects): E, sellers’ autonomy; Q, merchandise quality; L, location with intense traffic; P, result profit or loss. E, Q and L represent condition attributes; P represents a decision attribute.
Example table. Source: Pawlak (2000)Pawlak, Z. (2000). Rough sets and decision analysis. Information Systems & Operational Research, 38(3), 132144. http://dx.doi.org/10.1080/03155986.2000.11732405.
http://dx.doi.org/10.1080/03155986.2000.... .
The attributes E, Q and L, it is possible to affirm the following: stores 1 and 6 achieved profit, stores 4 and 5 had losses and stores 2 and 3 cannot be classified (in profit or loss), because they are indiscernible to these attributes. Being so, employing attributes E, Q and L, it can deduce that: stores 1 and 6 certainly made profit, that is, possibly belong to the set {1,3,6}; while stores 1, 2, 3 and 6 possibly had profit, that is, possibly belong to set {1,3,6}. The sets {1,6} and {1,2,3,6} represent, respectively, the lower and upper approximations. Possible rules extracted from Decision Table (Equations 35):
Being so, a decision rule in S is an expression Φ → Ψ, reading if Φ then Ψ, where Φ ∈ For(C), Ψ ∈ For(D), C and D are attributes of condition and decision, respectively.
Consequently, the RST ignores not only the order of preference in the set of attribute values, but also the “monotonic” relationship of object evaluations regarding the values of condition attributes and the order of preference of the values of decision attributes (classification or degree of preference). Slowinski et al. (2012)Slowinski, R., Greco, S., & Matarazzo, B. (2012). Rough set and rulebased multicriteria decision aiding. Pesquisa Operacional, 32(2), 213270. http://dx.doi.org/10.1590/S010174382012000200001.
http://dx.doi.org/10.1590/S010174382012...
presents the Dominance principle ‒ Dominance Rough Sets Approach, DRSA: “objects that possess a better evaluation or that possess at the minimum the same evaluation (decision class), cannot be associated to a worse decision class, all decision criteria considered”. The indiscernibility relations are replaced by dominance relations in the decision class approximations. By DRSA, due to the order of preference between the decision classes, the sets become approximations and are known as unions of decision classes: upward and downward classes. The decision rules can be considered under 5 types:

1 certain decision rulesD_{≥}:
if f(x,q_{1}) ≥ r_{q1} and f(x,q_{2}) ≥ r_{q2} and ... f(x,q_{p}) ≥ r_{qp}, then x Cl${}_{t}^{\ge}$;

2 possible decision rulesD_{≥}:
if f(x,q_{1}) ≥ r_{q1} and f(x,q_{2}) ≥ r_{q2} and ... f(x,q_{p}) ≥ r_{qp}, then x possibly belongs to Cl${}_{t}^{\ge}$;

3 certain decision rulesD_{≤}:
if f(x,q_{1})≤ r_{q1} and f(x,q_{2}) ≤ r_{q2} and ... f(x,q_{p}) ≤ r_{qp}, then x$\in $ Cl${}_{t}^{\le}$;

4 possible decision rulesD_{≤}:
if f(x,q_{1})≤ r_{q1} and f(x,q_{2}) ≤ r_{q2} and ... f(x,q_{p}) ≤ r_{qp}, then x possibly belongs to Cl${}_{t}^{\le}$
where P = {q_{1}, ..., q_{p}} $\subseteq $C, (r_{q1}, ..., r_{qp}) $\in $V_{q1} x V_{q2} x ... x V_{qp} and t $\in $T;

5 approximate decision rulesD_{≤ ≥}:
if f(x,q_{1}) ≥ r_{q1} and f(x,q_{2}) ≥ r_{q2} and ... f(x,q_{k}) ≥ r_{qk} and f(x,q_{k+1}) ≤ r_{qk+1} and f(x,q_{p}) ≤ r_{qp}, then
x$\in $Cl_{s} ∪ Cl_{s+1} ∪ ... ∪ Cl_{t}.
The rules of type 1) and 3) represent certain knowledge extracted from data (ordinal classification, for example); the rules of type 2) and 4) represent possible knowledge; and the rules of type 5) represent doubtful knowledge (are supported by inconsistent objects only).
3.2 Machine learning
Machine Learning refers to the subfield of Artificial Intelligence that aims to project algorithms and allow computers to elaborate behaviours based on empirical data. And, as an instrument, for example, it can find the induction of rules: conditionaction rules, decision trees or similar knowledge structures (Langley & Simon, 1995Langley, P., & Simon, H. A. (1995). Applications of machine learning and rule induction. Communications of the ACM, 38(11), 5464. http://dx.doi.org/10.1145/219717.219768.
http://dx.doi.org/10.1145/219717.219768...
; Pawlak et al., 1995Pawlak, Z., GrzymalaBusse, J., Slowinski, R., & Ziarko, W. (1995). Rough sets. Communications of the ACM, 38(11), 8895. http://dx.doi.org/10.1145/219717.219791.
http://dx.doi.org/10.1145/219717.219791...
). Softwares learn automatically to recognize complex patterns and to take intelligent decisions based in data. The Machine Learning methods are divided in: supervised (classification cases; training data has a label), nonsupervised (clustering case; training data has no label) and semisupervised (a combination of both previous methods) (Russell & Norvig, 2010Russell, S. J., & Norvig, P. (2010). Artificial intelligence: a modern approach. Hoboken: Prentice Hall.; Han et al., 2012Han, J., Kamber, M., & Pei, J. (2012). Data mining: concepts and techniques (3rd ed.). Waltham: Morgan Kaufmann Publishers/Elsevier.).
4 Results and discussion
Initially, there was a collection and treatment of information related to constant indicators in the Reports of Socio Environmental and EconomicFinancial Responsibility (RSA), according to the Electricity Sector Accounting Manual (ESAM) (ANEEL, 2015Agência Nacional de Energia Elétrica  ANEEL. (2015). Manual de contabilidade do setor elétrico. Brasília: ANEEL.). The ESAM distinguishes indicators regarding sustainability in: directly related (filled column, with reference to the GRI pattern, Global Reporting Initiative/Sustainability Reporting Guidelines & Electric Unity Sector Supplement), in this study identified by the initials “Su”. In March 2021, from a total of 63 (sixtythree) electricity distribution companies, there were 26 (twentysix) RSA reports regarding the fiscal year of 2019 (ANEEL, 2021Agência Nacional de Energia Elétrica  ANEEL. (2021). Distribuição. Retrieved in 2021, March 30, from https://www.gov.br/aneel/ptbr/centraisdeconteudos/relatorioseindicadores/distribuicao.
https://www.gov.br/aneel/ptbr/centrais...
). The RSA reports are annual, with demonstrations from the past three fiscal years. For the current study, the 10 biggest electricity distribution companies were considered (EPE, 2020Empresa de Pesquisa Energética  EPE. Ministério de Minas e Energia. (2020). Anuário Estatístico de Energia Elétrica 2020, ano base 2019. Brasília: EPE. Retrieved in 2021, March 30, from https://www.epe.gov.br/sitespt/publicacoesdadosabertos/publicacoes/PublicacoesArquivos/publicacao160/topico168/Anu%C3%A1rio%20Estat%C3%ADstico%20de%20Energia%20El%C3%A9trica%202020.pdf.
https://www.epe.gov.br/sitespt/publicac...
). However, in case of lack of information, the function RANDOM()*(MAXIMUM(interval)MINIMUM(interval))+MINIMUM(interval)” was used, in Microsoft Excel, to simulate the values of the absent indicators. The indicators were then distributed by environmental, economic, social and corporate governance dimensions, according to the classification established on ESAM. For this study, 5 (five) indicators of each environmental, economic and social dimensions were used, except for corporate governance, where twenty indicators were used. Following, there was an identification as to the type of indicator: if it is “G”, gain (the bigger the value, the best); or if it is “C”; cost or loss (the smaller the value, the best), as shown in the Tables 45.
Indicators directly related to sustainability  part 1. Sources: GRI (2000)Global Reporting Initiative  GRI. (2000). Sustainability reporting guidelines & electric utility sector supplement, RG version 3.0/EUSS. Amsterdam: GRI., ANEEL (2015)Agência Nacional de Energia Elétrica  ANEEL. (2015). Manual de contabilidade do setor elétrico. Brasília: ANEEL., authors.
Indicators directly related to sustainability, dimension Governance  part 2. Sources: GRI (2000)Global Reporting Initiative  GRI. (2000). Sustainability reporting guidelines & electric utility sector supplement, RG version 3.0/EUSS. Amsterdam: GRI., Pereira & Cândido (2020)Pereira, F. No., & Cândido, G. A. (2020). Sustentabilidade corporativa: definição de indicadores para organizações do setor energético. Revista de Gestão dos Países de Língua Portuguesa, 19(2), 104126. http://dx.doi.org/10.12660/rgplp.v19n2.2020.80610.
http://dx.doi.org/10.12660/rgplp.v19n2.2... , authors.
The Table 4 shows the indicators directly related to sustainability in the environmental, economic and social dimensions, considering five indicators of each dimension.
Specifically, for governance (corporate) dimension indicators, the RSA reports’ contents were analysed (read) according to the text mining technique, researched the frequency of words, according to contents from the columns Keyword, Table 6. The reading of these reports was aided with the use of mining text software, KH Coder, version 3.Beta.01a (Higuchi, 2001Higuchi, K. (2001). KH coder. Retrieved in 2019, October 9, from http://khcoder.net/en/#
http://khcoder.net/en/#...
), through the use of options (Word) Frequency list, searched words and its respective frequency of occurrence, Word association, words strongly associated with other words, KWIC (Key Words in Context) concordance, how the searched words are used in the text, and Cooccurrence network, a net with syntagmatic relations between words (Higuchi, 2001Higuchi, K. (2001). KH coder. Retrieved in 2019, October 9, from http://khcoder.net/en/#
http://khcoder.net/en/#...
; Zhai & Massung, 2016Zhai, C., & Massung, S. (2016). Text data management and analysis: a practical introduction to information retrieval and text mining. New York: Association for Computing Machinery/Morgan & Claypool Publishers/University of Waterloo.). This way, in case it found a keyword associated to the indicator in a certain paragraph of the RSA report, and if this paragraph was associated to the description of the indicator, “1” was computed to the indicator (Andreopoulou & Koliouska, 2018Andreopoulou, Z., & Koliouska, C. (2018). Benchmarking internet promotion of renewable energy enterprises: is sustainability present? Sustainability, 10(11), 4187. http://dx.doi.org/10.3390/su10114187.
http://dx.doi.org/10.3390/su10114187...
). At the end, it obtained a general corporate governance indicator through adding the values 0 or 1 of the respective indicators.
Each value of the indicator (v_{i}) was then normalized (v_{in}), that is, it is found in the interval [0; 1], and aims to obtain a percentage in relation to the maximum found value (v_{max}), if gain or profit indicator, or minimum (v_{min}), if cost or loss indicator: v_{in} = v_{i} / v_{max} or v_{in} = 1 / (v_{i} / v_{min}), respectively. This way, for each company and for each indicator, it is obtained a relative position (%) to the company that can be considered a paradigm in that indicator, that obtained the maximum or minimum values, according to the type of indicator  gain or cost, respectively. For each company and for each set of indicators of the same dimension (example, social), it was computed an index by simple arithmetic average of the normalized values. At the end. It was obtained indexes in the environmental InA, economic InE, social InS and corporate governance InG dimensions; the simple arithmetic average of these 4 (four) indexes results in the final index InSu, for ten companies, E01 to E10. Class “L”, low, “M”, medium or “H”, high, is obtained considering the index value in the intervals: (0; 0.3333], (0.3333; 0.6666] and (0.6666; 1], respectively, Table 7. There is a crescent order of preference for classes: low, medium and high.
The collected and simulated values of the indicators for each company, and its respective final classes, Su Class, are found on Table 8, and represents a Decision Table, considering the indicators as attributes or condition criteria and Su class as an attribute or decision criteria.
However, when it is desired to simulate a sustainability class for a certain company, for a future situation and/or when there is not yet all the sustainability indicators set for all the companies taken into account, by means Rough Sets and Machine Learning (ML), it becomes doable the use of past absolute values of those indicators for sustainability class prediction ‒ Figure 2.
Prediction model for sustainability class by means Rough Sets and Machine Learning. Source: authors.
Once it is had a temporal series of indicators and its respective sustainability classes for each company, the class can be obtained through prediction for a certain company “X”. The values for X_{1}, X_{2}, ..., X_{n} can be obtained by regression, for example, or can be directly informed or suggested.
For this research proposal, it was used the RoughSets package in R and it is available on CRAN at http://cran.rproject.org/package=RoughSets. This package makes available four algorithms for inference or generation of decision rules using a script in R: AQRules, CN2Rules, indiscernibilityBasedRules and LEM2Rules (Clark & Niblett, 1989Clark, P., & Niblett, T. (1989). The CN2 induction algorithm. Machine Learning, 3(4), 261283. http://dx.doi.org/10.1007/BF00116835.
http://dx.doi.org/10.1007/BF00116835...
; Michalski et al., 1991Michalski, R. S., Kaufman, K., & Wnek, J. (1991). The AQ family of learning programs: a review of recent developments and an exemplary application. Fairfax: George Mason University. Reports of Machine Learning and Inference Laboratory.; GrzymalaBusse, 1997GrzymalaBusse, J. W. (1997). A new version of the rule induction system LERS. Fundamenta Informaticae, 31(1), 2739. http://dx.doi.org/10.3233/FI19973113.
http://dx.doi.org/10.3233/FI19973113...
; Riza et al., 2014Riza, L. S., Janusz, A., Bergmeir, C., Cornelis, C., Herrera, F., Slezak, D., & Benitez, J. M. (2014). Implemeting algorithms of rough set theory and fuzzy rough set theory in the R package “roughsets”. Information Sciences, 287, 6889. http://dx.doi.org/10.1016/j.ins.2014.07.029.
http://dx.doi.org/10.1016/j.ins.2014.07....
, 2019Riza, L. S., Janusz, A., Slezak, D., Cornelis, C., Herrera, F., Benitez, J. M., Bergmeir, C., & Stawicki, S. (2019). Data analysis using rough set and fuzzy rough set theories. Retrieved in 2021, December 3, from https://cran.rproject.org/web/packages/RoughSets/RoughSets.pdf
https://cran.rproject.org/web/packages/...
).
In order to calculate the accuracy, correct results / total of instances, of the inference of decision rules algorithms, it was used the information in Table 8 and the method Holdout: randomly, 1/3 of the thirty existing records were chosen as test records (column “#”, Table 9); and the rest 2/3 were used as training records (Han et al., 2012Han, J., Kamber, M., & Pei, J. (2012). Data mining: concepts and techniques (3rd ed.). Waltham: Morgan Kaufmann Publishers/Elsevier.). The algorithms in highlight use these training records to infer or generate the decision rules. These rules are then used to predict sustainability classes based on absolute values of indicators (test records) (Riza et al., 2014Riza, L. S., Janusz, A., Bergmeir, C., Cornelis, C., Herrera, F., Slezak, D., & Benitez, J. M. (2014). Implemeting algorithms of rough set theory and fuzzy rough set theory in the R package “roughsets”. Information Sciences, 287, 6889. http://dx.doi.org/10.1016/j.ins.2014.07.029.
http://dx.doi.org/10.1016/j.ins.2014.07....
, 2019Riza, L. S., Janusz, A., Slezak, D., Cornelis, C., Herrera, F., Benitez, J. M., Bergmeir, C., & Stawicki, S. (2019). Data analysis using rough set and fuzzy rough set theories. Retrieved in 2021, December 3, from https://cran.rproject.org/web/packages/RoughSets/RoughSets.pdf
https://cran.rproject.org/web/packages/...
). The estimated values for accuracy are found on Table 9. The lowest accuracy 0.6 is a result of indiscernibilityBasedRules and LEM2Rules algorithms, 0.7 of AQRules and the highest 0.9, of CN2Rules algorithm.
Use of the Holdout method to determine the accuracy of rule inference algorithms. Source: authors.
And, following, some examples of multicriteria rules that were inferred by the CN2Rules algorithm and its respective rules quality indexes.

1: IF IG is [0.833, Inf] THEN class is H; (supportSize=8; laplace=0.9);

2: IF IA3 is [8.02e+05, Inf] THEN class is M; (supportSize=5; laplace=0.8571);

3: IF IA4 is [Inf,7.97e+04) and IS3 is [7.4, Inf] THEN class is M; (supportSize=5; laplace=0.8571);

4: IF IA2 is [Inf,8.25e+04) THEN class is H; (supportSize=2; laplace=0.75).
> RI.laplace(rules2)
Rule_1 Rule_2 Rule_3 Rule_4
0.9000000 0.8571429 0.8571429 0.7500000
> RI.support(rules2)
Rule_1 Rule_2 Rule_3 Rule_4
0.40 0.25 0.25 0.10
> RI.confidence(rules2)
Rule_1 Rule_2 Rule_3 Rule_4
1 1 1 1
> RI.lift(rules2)
Rule_1 Rule_2 Rule_3 Rule_4
1.800000 1.714286 1.714286 1.500000
By the previous rule “1”, for example, and exclusively considering the training instances set, 2/3 of a total of 30, or 20 instances, there are the following quality indexes on this rule: a) supportSize = 8, which means there are 8 or 8/20 instances or companies that satisfy this rule; b) laplace = 0.9, which means this rule has an adjusted accuracy of 90%; c) confidence = 1, which means there is a probability of 100% of the instances that the class is an “H”, given that the governance index IG is within the interval [0.833;1]; d) lift = 1.8, which means a company classed as “H” bumps up in almost twice (1.8) the chance of the governance index IG being in the interval [0.833;1] (Dzeroski et al., 1993Dzeroski, S., Cestnik, B., & Petrovski, I. (1993). Using the mestimate in rule induction. Journal of Computing and Information Technology, 1, 3746.; Słowiński et al., 2008Słowiński, R., Greco, S., & Matarazzo, B. (2008). Dominancebased rough set approach to multiple criteria decision support. Troina, 2, 956.; Han et al., 2012Han, J., Kamber, M., & Pei, J. (2012). Data mining: concepts and techniques (3rd ed.). Waltham: Morgan Kaufmann Publishers/Elsevier.; Provost & Fawcett, 2013Provost, F., & Fawcett, T. (2013). Data science for business: what you need to know about data mining and dataanalytic thinking. Sebastopol: O'Reilly Media, Inc..). There was also, reduct suggestion: a feature subset consisting of 3 attributes: IA2, IE2 e IG.
Based on the proposed model for predicting sustainability classes, Figure 2, there are two cases to analyze, as examples.

a
Case 1
In this first situation, company E05 was used as reference. According to Figure 3, with relation to the year 2019, it was estimated a situation: for cost indicators, it was simulated an increase of 40% and 50% and, for gain indicators, a reduction of similar percentages. Following, the script in R was executed and it was obtained the inference of the following sustainability classes:
Inference of sustainability class for company E05, with variations of 40% and 50% in the gain and cost indicators. Source: authors.
Considering it was simulated an increase of 40% and 50% for cost indicators and a reduction for gain indicators with both percentages, the CN2Rules algorithm with higher accuracy shows that the class will probably remain “M”.

b
Case 2
In this second case, for company E07 and in relation to the year 2019, it was simulated a favourable situation: ascending the sustainability class from “M” to “H”, however, establishing a variation for indicators sets, environmental, economic, social and governance, with the goal of identifying the set that could influence the most the class change ‒ Figure 4. The indicators of a cost nature had a reduction and the ones of gain nature had a raise. Both of 50%.
Inference of sustainability class for company E07, with variation of 50% by indicators set and for the best case, from “M” to “H”. Source: authors.
In this case, it was identified that the environmental indicators set, IA1 to IA5, presents the biggest influence over a positive change of sustainability class, probably, from “M” to “H”, according to the indiscernibilityBasedRules algorithm, accuracy = 0.6.
Furthermore, the data from Tables 89, 2/3 or 20 training records were submitted to the jMAF software, DominanceBased Rough Set Data Analysis Framework, it was used in order to support the multicriteria analysis, provided by the Institute of Computing Science, Poznan University of Technology (Błaszczyński et al., 2013Błaszczyński, J., Greco, S., Matarazzo, B., Słowinski, R., & Szelag, M. (2013). jMAFdominancebased rough set data analysis framework. In A. Skowron & Z. Suraj (Eds.), Rough sets and intelligent systems  Professor Zdzisław Pawlak in memoriam (vol. 1, pp. 185209, Intelligent Systems Reference Library, no. 42). Berlin: Springer. http://dx.doi.org/10.1007/9783642303449_5.
http://dx.doi.org/10.1007/97836423034...
). There was a suggestion of 250 reducts, Cross validation (DRSA; 10 folds; standard) for training records with 85% or 17/20 accuracy and the confusion matrix  Figure 5. The following sequence was followed in the jMAF software, option Calculate: PDominance sets, ${D}_{P}^{+}\mathrm{}$Calculate dominating set, ${D}_{P}^{}\mathrm{}$Calculate dominated set; Unions of classes, standard, consistency level, 1.0; Reducts, all reducts; Rules, VCDOMLEM algorithm, consistency level, 1.0, type of rules, certain, type of unions, standard.
jMAF software, Cross validation with 2/3 training records. Source: authors, adapted from Błaszczyński et al. (2013)Błaszczyński, J., Greco, S., Matarazzo, B., Słowinski, R., & Szelag, M. (2013). jMAFdominancebased rough set data analysis framework. In A. Skowron & Z. Suraj (Eds.), Rough sets and intelligent systems  Professor Zdzisław Pawlak in memoriam (vol. 1, pp. 185209, Intelligent Systems Reference Library, no. 42). Berlin: Springer. http://dx.doi.org/10.1007/9783642303449_5.
http://dx.doi.org/10.1007/97836423034... .
And the multicriteria rules generated with VCDomLEM algorithm (Błaszczyński et al., 2009Błaszczyński, J., Słowinski, R., & Szelag, M. (2009). VCDomLEM: rule induction algorithm for variable consistency rough set approaches. Poznań: University of Technology. Technical Report RA07/09., 2011Błaszczyński, J., Słowinski, R., & Szelag, M. (2011). Sequential covering rule induction algorithm for variable consistency rough set approaches. Information Sciences, 181(5), 9871002. http://dx.doi.org/10.1016/j.ins.2010.10.030.
http://dx.doi.org/10.1016/j.ins.2010.10....
):
#Certain at least rules

1: (IG >= 0.8333) => (class >= H) CERTAIN, AT_LEAST, H (Support:8; CoverageFactor: 0.8)

2: (IA5 <= 17.0) => (class >= H) CERTAIN, AT_LEAST, H (Support:1; CoverageFactor: 0.1)

3: (IA3 <= 133286.0) & (IE1 >= 8337594.0) => (class >= H) CERTAIN, AT_LEAST, H (Support:1; CoverageFactor: 0.1)
#Certain at most rules

4: (IS3 >= 7.77) => (class <= M) CERTAIN, AT_MOST, M (Support:6; CoverageFactor: 0.6)

5: (IA2 >= 121715.0) => (class <= M) CERTAIN, AT_MOST, M (Support:4; CoverageFactor: 0.4)

6: (IE1 <= 255045.0) => (class <= M) CERTAIN, AT_MOST, M (Support:3; CoverageFactor: 0.3)
As a way of interpreting the previous decision rules, according to rule 1, the CoverageFactor of 0.8 indicates that, given that the class is H, there is a conditional probability of 80% that the companies have a governance index (IG) greater than or equal to 0.8333; and, by rule 4, given that the class is at most M, there is a conditional probability of 60% or CoverageFactor 0.6 that, the social indicator 3 (IS3) of the companies is greater than or equal to 7.77 (Pawlak, 2002Pawlak, Z. (2002). Rough sets, decision algorithms and Bayes’ theorem. European Journal of Operational Research, 136(1), 181189. http://dx.doi.org/10.1016/S03772217(01)000297.
http://dx.doi.org/10.1016/S03772217(01)...
).
The set of 1/3 or 10 test records was submitted to classification using the previous rules, as shown in Figure 6.
jMAF software, classifying 1/3 test records. Source: authors, adapted from Błaszczyński et al. (2013)Błaszczyński, J., Greco, S., Matarazzo, B., Słowinski, R., & Szelag, M. (2013). jMAFdominancebased rough set data analysis framework. In A. Skowron & Z. Suraj (Eds.), Rough sets and intelligent systems  Professor Zdzisław Pawlak in memoriam (vol. 1, pp. 185209, Intelligent Systems Reference Library, no. 42). Berlin: Springer. http://dx.doi.org/10.1007/9783642303449_5.
http://dx.doi.org/10.1007/97836423034... .
There was a 90% or 9/10 accuracy in classifying these records by VCDRSA method, Variable Consistency Dominancebased Rough Set Approaches (Greco et al., 2005Greco, S., Matarazzo, B., Slowinsk, R., & Stefanowski, J. (2005). Variable consistency model of dominancebased rough sets approach. In W. Ziarko & Y. Yao (Eds.), Rough sets and current trends in computing: second international conference, RSCTC 2000 Banff, Canada, October 1619, 2000 revised papers (pp. 170181, Lecture Notes in Artificial Intelligence). Berlin: Springer.): example 4, the original decision was “H” and the classification result was “M”. For the others, there was agreement in the classification of records.
5 Conclusion and future studies
The sustainability indicators continue to still be the best way of monitoring and controlling economic, social, environmental, corporate governance impacts etc. accrued from development in its broadest form. As an example of indicators and indexes use, there is the HDI (Human Development Index) to measure the progresses of a population regarding its life expectancy, level of schooling and per capita income; the Covid19 transmission rate, from Imperial College of London, to evaluate if it is appropriate or not to adopt restrictive measures of mobility in a certain region; index Riskcountry; stock exchange index etc. In other words, we use indicators and indexes to guide our decision making in the most diverse circumstances and needs.
In the context of company management and, specifically in this research proposal, electricity distribution companies in Brazil, from a certain universe of indicators, it was presented a proposal for sustainability classes prediction based on past values of indicators directly related to sustainability for a certain company, before a situation in which it is not available the whole indicators set of the other electricity distribution companies.
The two cases that were addressed in the study show that sustainability class prediction based on indicators can collaborate in the anticipation of conditions and/or situations of risk, as well as the opportunity of improvements in a future moment and/or when it is not yet available the entire sustainability indicators set for all the companies considered. Beyond that, the study shows the use of the AQRules, CN2Rules, indiscernibility BasedRules, LEM2Rules and VCDomLEM algorithms for generation of decision rules in the sustainability classes prediction, based on historical absolute values of the indicators.
Consequently, the contributions of this study are in the model proposition that: a) uses Rough Sets Theory/Dominance principle and Machine Learning to extract decision rules and infer sustainability classes from historical series of indicators and simulated values, aiming to obtain better risk management in the economic, social, environmental and corporate governance dimensions of a company against competitors; b) establishes sustainability classes for companies in order to identify possible links on aspects of sustainability and performance between companies belonging to the same class, as opposed to simple ranking; c) allows to relate condition and decision criteria in decision rules, for example, by coverage factor, and consequently, obtain patterns in data, without referring to a priori and posterior probabilities, as in Bayesian analysis.
As future study, there is a possibility of broadening this set of indicators, visàvis with the existence of other quantitative and qualitative indicators on the electric sector.
Acknowledgements
The authors are grateful to the Institute of Computing Science of Poznan University of Technology, Poland, for permission of using the jMAF software.

Financial support: None.Model proposition for predicting sustainability classes using multicriteria decision support and artificial intelligence

How to cite: Couto, A. B. G., & Rangel, L. A. D. (2022). Model proposition for predicting sustainability classes using multicriteria decision support and artificial intelligence. Gestão & Produção, 29, e6922. https://doi.org/10.1590/180696492022v29e6922
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» http://dx.doi.org/10.3390/en13010082
Publication Dates

Publication in this collection
07 Nov 2022 
Date of issue
2022
History

Received
25 Aug 2022 
Accepted
10 Oct 2022