# Decision Rules for Renewable Energy Utilization Using Rough Set Theory

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Rough Sets

- U: the set of objects
- A: the set of attributes,
- V = ${\cup}_{Va}$, Va, the set of values of attributes a $\in $ A,
- p: U × A ⟶ V, an information function, ${p}_{x}:A\to V$,
- $x\in U$ the information about x in S,

#### 2.2. Renewable Energy

## 3. Methodology and Conceptual Framework

#### 3.1. Conceptual Framework

Algorithm 1. |

1. Input t and t + 1 2. if condition changed 3. if result changed 4. if result change is significant 5. output “form 9” 6. else 7. output “form 8” 8. else 9. output “form 7” 10. else 11. if result changed 12. if condition increased 13. output “form 4” 14. elif condition decreased 15. output “form 6” 16. else 17. output “form 2” 18. else 19. if condition increased 20. output “form 3” 21. elif condition decreased 22. output “form 5” 23. else 24. output “form 1” 25. end |

#### 3.2. Methodology

- t: time interval.
- r
_{ij}: rule set. - A: condition attribute.
- O: result (decision attribute).
- v: variable of condition attribute.
- w: variable of result attribute.
- i: rule index, $i=1-{r}^{t},i\in 1,\dots ,n$.
- j: rule index, $j=1-{r}^{t+1},j\in 1,\dots ,n$.
- n: number of condition attributes
- m: number of result attributes.

#### 3.3. Case Study

## 4. Results and Discussion

#### 4.1. Result

#### 4.2. Case Study Summary

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Aksoezen, M.; Daniel, M.; Hassler, U.; Kohler, N. Building age as an indicator for energy consumption. Energy Build.
**2015**, 87, 74–86. [Google Scholar] [CrossRef] - Satyadas, A.; Harigopal, U.; Cassaigne, N.P. Knowledge management tutorial: An editorial overview. IEEE Trans. Syst. Man Cybern. Part C-Appl. Rev.
**2001**, 31, 429–437. [Google Scholar] [CrossRef] - Yen, C.E.; Huang, C.C.; Wen, D.W.; Wang, Y.P. Decision support to customer decrement detection at the early stage for theme parks. Decis. Support Syst.
**2017**, 102, 82–90. [Google Scholar] [CrossRef] - Alzahrany, A.; Kabir, G.; Al Zohbi, G. Evaluation of the barriers to and drivers of the implementation of solar energy in Saudi Arabia. Int. J. Sustain. Dev. World Ecol.
**2022**, 29, 543–558. [Google Scholar] [CrossRef] - Gung, R.R.; Huang, C.C.; Hung, W.I.; Fang, Y.J. The use of hybrid analytics to establish effective strategies for household energy conservation. Renew. Sustain. Energy Rev.
**2020**, 133, 10. [Google Scholar] [CrossRef] - Sharma, S.; Dua, A.; Singh, M.; Kumar, N.; Prakash, S. Fuzzy rough set based energy management system for self-sustainable smart city. Renew. Sustain. Energy Rev.
**2018**, 82, 3633–3644. [Google Scholar] [CrossRef] - Pawlak, Z. Rough sets. Int. J. Comput. Inf. Sci.
**1982**, 11, 341–356. [Google Scholar] [CrossRef] - Yao, Y.; Greco, S.; Słowiński, R. Probabilistic rough sets. In Springer Handbook of Computational Intelligence; Springer: Berlin/Heidelberg, Germany, 2015; pp. 387–411. [Google Scholar] [CrossRef]
- Lashin, E.F.; Kozae, A.M.; Khadra, A.A.A.; Medhat, T. Rough set theory for topological spaces. Int. J. Approx. Reason.
**2005**, 40, 35–43. [Google Scholar] [CrossRef] - Azzam, A.; Al-shami, T.M. Five Generalized Rough Approximation Spaces Produced by Maximal Rough Neighborhoods. Symmetry
**2023**, 15, 751. [Google Scholar] [CrossRef] - Al-shami, T.M. An improvement of rough sets’ accuracy measure using containment neighborhoods with a medical application. Inf. Sci.
**2021**, 569, 110–124. [Google Scholar] [CrossRef] - Al-shami, T.M.; Mhemdi, A. Approximation spaces inspired by subset rough neighborhoods with applications. Demonstr. Math.
**2023**, 56, 24. [Google Scholar] [CrossRef] - Al-shami, T.M.; Alshammari, I. Rough sets models inspired by supra-topology structures. Artif. Intell. Rev.
**2023**, 56, 6855–6883. [Google Scholar] [CrossRef] [PubMed] - Swiniarski, R.W.; Skowron, A. Rough set methods in feature selection and recognition. Pattern Recognit. Lett.
**2003**, 24, 833–849. [Google Scholar] [CrossRef] - Pawlak, Z. Rough Sets: Theoretical Aspects of Reasoning about Data; Springer Science & Business Media: Berlin/Heidelberg, Germany, 1991; Volume 9. [Google Scholar]
- Zhang, X.; Yao, Y. Tri-level attribute reduction in rough set theory. Expert Syst. Appl.
**2022**, 190, 116187. [Google Scholar] [CrossRef] - Zhang, X.; Miao, D. Three-layer granular structures and three-way informational measures of a decision table. Inf. Sci.
**2017**, 412, 67–86. [Google Scholar] [CrossRef] - Murray, L.W. Agile manufacturing: Forging new frontiers—Kidd, PT. J. Prod. Innov. Manag.
**1996**, 13, 181–182. [Google Scholar] [CrossRef] - Tseng, T.L.; Huang, C.C. Sustainable service and energy provision based on agile rule induction. Int. J. Prod. Econ.
**2016**, 181, 273–288. [Google Scholar] [CrossRef] - Wang, J.Q.; Zhang, X.H. A Novel Multi-Criteria Decision-Making Method Based on Rough Sets and Fuzzy Measures. Axioms
**2022**, 11, 15. [Google Scholar] [CrossRef] - Ayub, S.; Shabir, M.; Riaz, M.; Karaaslan, F.; Marinkovic, D.; Vranjes, D. Linear Diophantine Fuzzy Rough Sets on Paired Universes with Multi Stage Decision Analysis. Axioms
**2022**, 11, 18. [Google Scholar] [CrossRef] - Jia, Q.S.; Ho, Y.C.; Zhao, Q.C. Comparison of selection rules for ordinal optimization. Math. Comput. Model.
**2006**, 43, 1150–1171. [Google Scholar] [CrossRef] - Li, R.; Xu, M.; Chen, Z.; Gao, B.; Cai, J.; Shen, F.; He, X.; Zhuang, Y.; Chen, D. Phenology-based classification of crop species and rotation types using fused MODIS and Landsat data: The comparison of a random-forest-based model and a decision-rule-based model. Soil Tillage Res.
**2021**, 206, 12. [Google Scholar] [CrossRef] - Lim, G.G.; Kang, J.Y.; Lee, J.K.; Lee, D.C. Rule-based personalized comparison shopping including delivery cost. Electron. Commer. Res. Appl.
**2011**, 10, 637–649. [Google Scholar] [CrossRef] - Jafari, M.; Malekjamshidi, Z. Optimal energy management of a residential-based hybrid renewable energy system using rule-based real-time control and 2D dynamic programming optimization method. Renew. Energy
**2020**, 146, 254–266. [Google Scholar] [CrossRef] - Crago, C.L.; Grazier, E.; Breger, D. Income and racial disparities in financial returns from solar PV deployment. Energy Econ.
**2023**, 117, 12. [Google Scholar] [CrossRef] - Lau, L.S.; Senadjki, A.; Ching, S.L.; Choong, C.K.; Seow, A.; Choong, Y.O.; Wei, C.Y. Solar photovoltaic as a means to sustainable energy consumption in Malaysia: The role of knowledge and price value. Energy Sources Part B-Econ. Plan. Policy
**2021**, 16, 303–323. [Google Scholar] [CrossRef] - Li, Y.H.; Wang, S.Y.; Dai, W.; Wu, L.S. Prediction of the Share of Solar Power in China Based on FGM (1,1) Model. Axioms
**2022**, 11, 10. [Google Scholar] [CrossRef] - Funkhouser, E.; Blackburn, G.; Magee, C.; Rai, V. Business model innovations for deploying distributed generation: The emerging landscape of community solar in the U.S. Energy Res. Soc. Sci.
**2015**, 10, 90–101. [Google Scholar] [CrossRef] - Costa, A.; Ng, T.S.; Su, B. Long-term solar PV planning: An economic-driven robust optimization approach. Appl. Energy
**2023**, 335, 16. [Google Scholar] [CrossRef] - Barnes, J.L.; Krishen, A.S.; Chan, A. Passive and active peer effects in the spatial diffusion of residential solar panels: A case study of the Las Vegas Valley. J. Clean. Prod.
**2022**, 363, 11. [Google Scholar] [CrossRef] - Varho, V.; Rikkonen, P.; Rasi, S. Futures of distributed small-scale renewable energy in Finland—A Delphi study of the opportunities and obstacles up to 2025. Technol. Forecast. Soc. Chang.
**2016**, 104, 30–37. [Google Scholar] [CrossRef] - Namazkhan, M.; Albers, C.; Steg, L. A decision tree method for explaining household gas consumption: The role of building characteristics, socio-demographic variables, psychological factors and household behaviour. Renew. Sustain. Energy Rev.
**2020**, 119, 11. [Google Scholar] [CrossRef] - Vlek, C.; Skolnik, M.; Gatersleben, B. Sustainable development and quality of life: Expected effects of prospective changes in economic and environmental conditions. Z. Fur Exp. Psychol.
**1998**, 45, 319–333. [Google Scholar] - Rausch, T.M.; Kopplin, C.S. Bridge the gap: Consumers’ purchase intention and behavior regarding sustainable clothing. J. Clean. Prod.
**2021**, 278, 15. [Google Scholar] [CrossRef] - Gatersleben, B.; Vlek, C. Household consumption, quality of life, and environmental impacts: A psychological perspective and empirical study. In Green Households; Routledge: London, UK, 2014; pp. 141–183. [Google Scholar]
- Liu, S.-J. COVID-19 Impact Analysis and Recommendations for the Power Industry. 2020. Available online: https://km.twenergy.org.tw/Knowledge/knowledge_more?id=8407 (accessed on 1 October 2020).
- Wiedenhofer, D.; Smetschka, B.; Akenji, L.; Jalas, M.; Haberl, H. Household time use, carbon footprints, and urban form: A review of the potential contributions of everyday living to the 1.5 degrees C climate target. Curr. Opin. Environ. Sustain.
**2018**, 30, 7–17. [Google Scholar] [CrossRef] - Alrwashdeh, S.S. The effect of solar tower height on its energy output at Ma’an-Jordan. AIMS Energy
**2018**, 6, 959–966. [Google Scholar] [CrossRef] - Rai, V.; McAndrews, K. Decision-making and behavior change in residential adopters of solar PV. In Proceedings of the World Renewable Energy Forum, Denver, CO, USA, 13–17 May 2012. [Google Scholar]
- Central Bank of the Republic of China (Taiwan). Press Release on the Resolution of the Joint Conference of the Central Bank Supervisors. 2021. Available online: https://www.cbc.gov.tw/tw/cp-302-141562-49221-1.html (accessed on 23 September 2020).
- Fan, Y.N.; Tseng, T.L.; Chern, C.C.; Huang, C.C. Rule induction based on an incremental rough set. Expert Syst. Appl.
**2009**, 36, 11439–11450. [Google Scholar] [CrossRef]

Result Unchanged | Result Changes | |
---|---|---|

Condition attribute remains unchanged | Form 1 | Form 2 |

Addition of a condition attribute | Form 3 | Form 4 |

Removal of a condition attribute | Form 5 | Form 6 |

Change in a condition attribute value | Form 4 | Form 8 |

Special case | Form 9 |

(Announced Upper Limit, Unit: NTD/kWh) | |||||||||
---|---|---|---|---|---|---|---|---|---|

2022 | 2021 | 2020 | 2019 | ||||||

First Quarter | Second Quarter | First Quarter | Second Quarter | First Quarter | Second Quarter | First Quarter | Second Quarter | ||

Capacity ranges = x (unit: kWh) | |||||||||

1 < x < 20 | 5.8952 | 5.7848 | 5.6707 | 5.6281 | 5.7132 | 5.7132 | 5.7983 | 5.7983 | |

20 < x < 100 | NGF | 4.5549 | 4.4538 | 4.3304 | 4.2906 | 4.4366 | 4.3701 | 4.5925 | 4.5083 |

GF | 4.4861 | 4.3864 | |||||||

100 < x < 500 | 4.0970 | 3.9666 | 3.9975 | 3.9227 | 4.1372 | 4.0722 | 4.3175 | 4.2355 | |

<500 | NGF | 4.1122 | 3.9727 | 3.9449 | 3.8980 | 4.0571 | 3.9917 | 4.2313 | 4.1579 |

GF | 4.4191 | 4.3722 | 4.5245 | 4.4591 | 4.6902 | 4.6168 | |||

Rate increase items and percentages: | |||||||||

Green Energy Roofs Project | 3% | 3% | 3% | 3% | |||||

Indigenous or remote areas | none | 1% | none | 1% | 1% | none | none | ||

Northern Taiwan | 15% | 15% | 15% | 15% | |||||

OT1 | 15% | 15% | 15% | 15% | |||||

OT2 | 4% | 4% | 4% | 4% |

Type | Attribute | Definition | Intervention |
---|---|---|---|

Basic information factors | Region | Offshore islands, northern region, others | Yes |

Remote area | Remote area: no, yes | Yes | |

Background factors | Family type | Single family, childless family, single-parent family, grandparent family, extended family, others | No |

Gender | Gender of the head of household: F = female, M = male | No | |

Age | Age of the head of household (years, adults over 20 years old): 20~29, 30~39, 40~49, 50~59, 60~69, >69 | No | |

Education | Head of household education level: 0 = elementary and under, 1 = junior, 2 = senior, 3 = college, 4 = graduate and above | No | |

Population (pop.) | Number of persons: ≤1, 2~3, 4~5, >5 | Yes | |

Income | Household annual net income (USD): 0~18,000; 18,001~40,000; 40,001~80,000; 80,001~150,000; >150,001 | Yes | |

Age of house | Age of house (years): ≤5, 6~20, >20 | Yes | |

Number of stories | Number of stories: 1~2, 3~4, >5 | Yes | |

Capacity (cap) | Device capacity (kilowatts): <20, 20~100, 100~500, >500 | Yes | |

Perceived value (PV) | Perceived value/benefit or no benefit: no, yes | Yes | |

Reward factors | Reward | Incentive bonus for household installation of rooftop solar panels: 3%, 4%, 7%, 8%, 18%, 19% | Yes |

Basic Attributes | Background Attributes | Outcome Attribute | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

No | A1 | A2 | B1 | B2 | B3 | B4 | B5 | B6 | O1 | O2 |

Region | Remote | pop. | Income | House | Stories | cap | PV | Ratio | Accept | |

0 | Offshore islands | No | ≤1 | 0~18,000 | ≤5 | 1~2 | <20 | No | 3% | Low |

1 | Northern region | Yes | 2~3 | 18,001 ~40,000 | 6~20 | 3~4 | 20~100 | Yes | 4% | Sustain |

2 | Others | 4~5 | 40,001 ~80,000 | >20 | >5 | 100~500 | 7% | High | ||

3 | >5 | 80,001 ~150,000 | >500 | 8% | ||||||

4 | >150,001 | 18% | ||||||||

5 | 19% |

Condition Attributes | Outcome | Type | Evolutionary Implications |
---|---|---|---|

Maintenance | Result does not change | 1 | Maintain original attitude |

Result changes | 2 | No longer feel policy relevance or have higher expectations | |

Increasing restrictions | Result does not change | 3 | Attributes are not noticed by the target households or have little impact on participation conditions |

Result changes | 4 | Attributes are more valued by the target households, and the program’s original goals may need to be reassessed | |

Reducing conditions | Result does not change | 5 | Deleted attributes are less necessary |

Result changes | 6 | Attributes have a significant impact on target households | |

Adjusting conditions | Result does not change | 7 | Low changes before and after adjustment, with little impact on willingness to participate |

Result changes | 8 | Changes in attributes have a significant impact on target households, and subtle adjustments may have a significant impact | |

Special circumstances | 9 | New decision rules are generated |

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## Share and Cite

**MDPI and ACS Style**

Huang, C.; Huang, C.-C.; Chen, D.-N.; Wang, Y.
Decision Rules for Renewable Energy Utilization Using Rough Set Theory. *Axioms* **2023**, *12*, 811.
https://doi.org/10.3390/axioms12090811

**AMA Style**

Huang C, Huang C-C, Chen D-N, Wang Y.
Decision Rules for Renewable Energy Utilization Using Rough Set Theory. *Axioms*. 2023; 12(9):811.
https://doi.org/10.3390/axioms12090811

**Chicago/Turabian Style**

Huang, Chuying, Chun-Che Huang, Din-Nan Chen, and Yuju Wang.
2023. "Decision Rules for Renewable Energy Utilization Using Rough Set Theory" *Axioms* 12, no. 9: 811.
https://doi.org/10.3390/axioms12090811