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Entropy for Machine Learning and Complex Systems Toward Regional Sustainable Development

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (15 April 2022) | Viewed by 30544

Special Issue Editors


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Guest Editor
Research Institute of Sustainable Construction, Vilnius Gediminas Technical University, LT-10223 Vilnius, Lithuania
Interests: operations research; optimization and decision analysis; multicriteria decision making; multiattribute decision making (MADM); decision support systems; civil engineering; energy; sustainable development; fuzzy sets theory; fuzzy multicriteria decision making; sustainability; management; game theory and economical computing knowledge management
Special Issues, Collections and Topics in MDPI journals

grade E-Mail Website
Guest Editor

E-Mail Website
Guest Editor
Department of Economics, University of Molise, Via De Sanctis, 86100 Campobasso, Italy
Interests: multi-criteria; fuzzy set; soft computing; renewable energy; sustainability; circular economy; technology assessment; hypersoft sets; sustainable development goals
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent decades, a need has arisen for forecasting and predictive modeling to deliver real-time solutions to sustainable development problems by integrating the models from the rapidly developing fields of machine learning, complex systems, and entropy. Machine learning is an approach for data analysis, which constructs the analytical model by giving computer systems the ability to “learn.” Machine learning is based on the idea that systems can learn from data, identify patterns, and make decisions with minimal human intervention. The concept of entropy originally developed from physics fields, but, it is clear that entropy is deeply related to machine learning and complex systems. Besides applications in machine learning, entropy is a general measure, commonly used for qualitative analysis of complex systems. In this regard, entropy is a powerful descriptive method, which presents an operational and theoretical framework to attain both qualitative and quantitative descriptions of the intrinsic properties of machine learning and complex systems theories. Therefore, to understand the importance of entropy concepts in machine learning and complex systems, in this Special Issue, we are interested in providing state‐of‐the‐art literature of entropy concepts and establishing a reliable connection between machine learning, complex systems, and the sustainable development context.

Dr. Abbas Mardani
Prof. Dr. Edmundas Kazimieras Zavadskas
Dr. Dragan Pamučar 
Prof. Dr. Fausto Cavallaro
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • entropy
  • machine learning
  • complex systems
  • predictive modeling
  • sustainable development
  • forecasting
  • decision making
  • complex systems

Published Papers (10 papers)

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Research

17 pages, 820 KiB  
Article
Picture Fuzzy Threshold Graphs with Application in Medicine Replenishment
by Sankar Das, Ganesh Ghorai and Qin Xin
Entropy 2022, 24(5), 658; https://doi.org/10.3390/e24050658 - 07 May 2022
Cited by 6 | Viewed by 1466
Abstract
In this study, a novel concept of picture fuzzy threshold graph (PFTG) is introduced. It has been shown that PFTGs are free from alternating 4-cycle and it can be constructed by repeatedly adding a dominating or an isolated node. Several properties about PFTGs [...] Read more.
In this study, a novel concept of picture fuzzy threshold graph (PFTG) is introduced. It has been shown that PFTGs are free from alternating 4-cycle and it can be constructed by repeatedly adding a dominating or an isolated node. Several properties about PFTGs are discussed and obtained the results that every picture fuzzy graph (PFG) is equivalent to a PFTG under certain conditions. Also, the underlying crisp graph (UCG) of PFTG is a split graph (SG), and conversely, a given SG can be applied to constitute a PFTG. A PFTG can be decomposed in a unique way and it generates three distinct fuzzy threshold graphs (FTGs). Furthermore, two important parameters i.e., picture fuzzy (PF) threshold dimension (TD) and PF partition number (PN) of PFGs are defined. Several properties on TD and PN have also been discussed. Lastly, an application of these developed results are presented in controlling medicine resources. Full article
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18 pages, 14408 KiB  
Article
Dissolved Oxygen Concentration Prediction Model Based on WT-MIC-GRU—A Case Study in Dish-Shaped Lakes of Poyang Lake
by Dianwei Chi, Qi Huang and Lizhen Liu
Entropy 2022, 24(4), 457; https://doi.org/10.3390/e24040457 - 25 Mar 2022
Cited by 4 | Viewed by 1980
Abstract
Dissolved oxygen concentration has the characteristics of nonlinearity, time series and instability, which increase the difficulty of accurate prediction. In order to accurately predict the dissolved oxygen concentration in the dish-shaped lakes in Poyang Lake of Jiangxi Province, China, a dissolved oxygen concentration [...] Read more.
Dissolved oxygen concentration has the characteristics of nonlinearity, time series and instability, which increase the difficulty of accurate prediction. In order to accurately predict the dissolved oxygen concentration in the dish-shaped lakes in Poyang Lake of Jiangxi Province, China, a dissolved oxygen concentration prediction model, based on wavelet transform (WT)-based denoising, maximal information coefficient (MIC)-based feature selection, and the gated recurrent unit (GRU), was proposed for this study. In experiments, the proposed model showed good prediction performance, achieving a root-mean-square error (RMSE) of 0.087 mg/L, a mean absolute percentage error (MAPE) of 0.723%, and a coefficient of determination (R2) as high as 0.998. It shows that the prediction model based on the combination of the wavelet transform and the GRU has a relatively high prediction accuracy and a better fitting effect. The model proposed in this study can provide a reference for protecting this type of lake-water body and the restoration of missing values in lake water quality monitoring data. Full article
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23 pages, 3006 KiB  
Article
Prediction Method of Soft Fault and Service Life of DC-DC-Converter Circuit Based on Improved Support Vector Machine
by Yuntao Hou, Zequan Wu, Xiaohua Cai and Zhongge Dong
Entropy 2022, 24(3), 402; https://doi.org/10.3390/e24030402 - 13 Mar 2022
Cited by 2 | Viewed by 2628
Abstract
A data-driven prediction method is proposed to predict the soft fault and estimate the service life of a DC–DC-converter circuit. First, based on adaptive online non-bias least-square support-vector machine (AONBLSSVM) and the double-population particle-swarm optimization (DP-PSO), the prediction model of the soft fault [...] Read more.
A data-driven prediction method is proposed to predict the soft fault and estimate the service life of a DC–DC-converter circuit. First, based on adaptive online non-bias least-square support-vector machine (AONBLSSVM) and the double-population particle-swarm optimization (DP-PSO), the prediction model of the soft fault is established. After analyzing the degradation-failure mechanisms of multiple key components and considering the influence of the co-degradation of these components over time on the performance of the circuit, the output ripple voltage is chosen as the fault-characteristic parameter. Finally, relying on historical output ripple voltages, the prediction model is utilized to gradually deduce the predicted values of the fault-characteristic parameter; further, in conjunction with the circuit-failure threshold, the soft fault and the service life of the circuit can be predicted. In the simulation experiment, (1) a time-series prediction is made for the output ripple voltage using the model proposed herein and the online least-square support-vector machine (OLS-SVM). Comparative analyses of fitting-assessment indicators of the predicted and experimental curves confirm that our model is superior to OLS-SVM in both modeling efficiency and prediction accuracy. (2) The effectiveness of the service life prediction method of the circuit is verified. Full article
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23 pages, 511 KiB  
Article
A New Group Decision-Making Technique under Picture Fuzzy Soft Expert Information
by Fairouz Tchier, Ghous Ali, Muhammad Gulzar, Dragan Pamučar and Ganesh Ghorai
Entropy 2021, 23(9), 1176; https://doi.org/10.3390/e23091176 - 07 Sep 2021
Cited by 17 | Viewed by 2366
Abstract
As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals with the degrees of rejection and acceptance but also considers the degree of refusal during a decision-making process; therefore, by incorporating this competency of picture fuzzy sets, [...] Read more.
As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals with the degrees of rejection and acceptance but also considers the degree of refusal during a decision-making process; therefore, by incorporating this competency of picture fuzzy sets, the goal of this study is to propose a novel hybrid model called picture fuzzy soft expert sets by combining picture fuzzy sets with soft expert sets for dealing with uncertainties in different real-world group decision-making problems. The proposed hybrid model is a more generalized form of intuitionistic fuzzy soft expert sets. Some novel desirable properties of the proposed model, namely, subset, equality, complement, union and intersection, are investigated together with their corresponding examples. Two well-known operations AND and OR are also studied for the developed model. Further, a decision-making method supporting by an algorithmic format under the proposed approach is presented. Moreover, an illustrative application is provided for its better demonstration, which is subjected to the selection of a suitable company of virtual reality devices. Finally, a comparison of the initiated method is explored with some existing models, including intuitionistic fuzzy soft expert sets. Full article
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16 pages, 321 KiB  
Article
A Novel Algebraic Structure of (α,β)-Complex Fuzzy Subgroups
by Hanan Alolaiyan, Halimah A. Alshehri, Muhammad Haris Mateen, Dragan Pamucar and Muhammad Gulzar
Entropy 2021, 23(8), 992; https://doi.org/10.3390/e23080992 - 30 Jul 2021
Cited by 21 | Viewed by 2136
Abstract
A complex fuzzy set is a vigorous framework to characterize novel machine learning algorithms. This set is more suitable and flexible compared to fuzzy sets, intuitionistic fuzzy sets, and bipolar fuzzy sets. On the aspects of complex fuzzy sets, we initiate the abstraction [...] Read more.
A complex fuzzy set is a vigorous framework to characterize novel machine learning algorithms. This set is more suitable and flexible compared to fuzzy sets, intuitionistic fuzzy sets, and bipolar fuzzy sets. On the aspects of complex fuzzy sets, we initiate the abstraction of (α,β)-complex fuzzy sets and then define α,β-complex fuzzy subgroups. Furthermore, we prove that every complex fuzzy subgroup is an (α,β)-complex fuzzy subgroup and define (α,β)-complex fuzzy normal subgroups of given group. We extend this ideology to define (α,β)-complex fuzzy cosets and analyze some of their algebraic characteristics. Furthermore, we prove that (α,β)-complex fuzzy normal subgroup is constant in the conjugate classes of group. We present an alternative conceptualization of (α,β)-complex fuzzy normal subgroup in the sense of the commutator of groups. We establish the (α,β)-complex fuzzy subgroup of the classical quotient group and show that the set of all (α,β)-complex fuzzy cosets of this specific complex fuzzy normal subgroup form a group. Additionally, we expound the index of α,β-complex fuzzy subgroups and investigate the (α,β)-complex fuzzification of Lagrange’s theorem analog to Lagrange’ theorem of classical group theory. Full article
15 pages, 991 KiB  
Article
Entropy as an Objective Function of Optimization Multimodal Transportations
by Oleg Bazaluk, Sergiy Kotenko and Vitalii Nitsenko
Entropy 2021, 23(8), 946; https://doi.org/10.3390/e23080946 - 24 Jul 2021
Cited by 22 | Viewed by 2070
Abstract
This article considers the use of the entropy method in the optimization and forecasting of multimodal transport under conditions of risks that can be determined simultaneously by deterministic, stochastic and fuzzy quantities. This will allow to change the route of transportation in real [...] Read more.
This article considers the use of the entropy method in the optimization and forecasting of multimodal transport under conditions of risks that can be determined simultaneously by deterministic, stochastic and fuzzy quantities. This will allow to change the route of transportation in real time in an optimal way with an unacceptable increase in the risk at one of its next stages and predict the redistribution of the load of transport nodes. The aim of this study is to develop a mathematical model for the optimal choice of an alternative route, the best for one or more objective functions in real time. In addition, it is proposed to use this mathematical model to estimate the dynamic change in turnover through intermediate transport nodes, forecasting their loading over time under different conditions that also include long-term risks which are significant in magnitude. To substantiate the feasibility of the proposed mathematical model, the analysis and forecast of cargo turnover through the seaports of Ukraine are presented, taking into account and analysing the existing risks. Full article
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26 pages, 2749 KiB  
Article
Assessment and Prediction of Water Resources Vulnerability Based on a NRS-RF Model: A Case Study of the Song-Liao River Basin, China
by Weizhong Chen, Yan Chen and Yazhong Feng
Entropy 2021, 23(7), 882; https://doi.org/10.3390/e23070882 - 11 Jul 2021
Cited by 7 | Viewed by 2192
Abstract
The vulnerability of water resources is an important criterion for evaluating the carrying capacity of water resources systems under the influence of climate change and human activities. Moreover, assessment and prediction of river basins’ water resources vulnerability are important means to assess the [...] Read more.
The vulnerability of water resources is an important criterion for evaluating the carrying capacity of water resources systems under the influence of climate change and human activities. Moreover, assessment and prediction of river basins’ water resources vulnerability are important means to assess the water resources security state of river basins and identify possible problems in future water resources systems. Based on the constructed indicator system of water resources vulnerability assessment in Song-Liao River Basin, this paper uses the neighborhood rough set (abbreviated as NRS) method to reduce the dimensionality of the original indicator system to remove redundant attributes. Then, assessment indicators’ standard values after dimensionality reduction are taken as the evaluation sample, and the random forest regression (abbreviated as RF) model is used to assess the water resources vulnerability of the river basin. Finally, based on data under three different future climate and socio-economic scenarios, scenario predictions are made on the vulnerability of future water resources. The results show that the overall water resources vulnerability of the Song-Liao River Basin has not improved significantly in the past 18 years, and the overall vulnerability of the Song-Liao River Basin is in the level V of moderate to high vulnerability. In the future scenario 1, the overall water resources vulnerability of the river basin will improve, and it is expected to achieve an improvement to the level III of moderate to low vulnerability. At the same time, the natural vulnerability and vulnerability of carrying capacity will increase significantly in the future, and the man-made vulnerability will increase slowly, which will deteriorate to the level V of moderate to high vulnerability under Scenario 3. Therefore, taking active measures can significantly reduce the vulnerability of nature and carrying capacity, but man-made vulnerability will become a bottleneck restricting the fragility of the overall water resources of the river basin in the future. Full article
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16 pages, 5730 KiB  
Article
Global Sensitivity Analysis Based on Entropy: From Differential Entropy to Alternative Measures
by Zdeněk Kala
Entropy 2021, 23(6), 778; https://doi.org/10.3390/e23060778 - 19 Jun 2021
Cited by 11 | Viewed by 6100
Abstract
Differential entropy can be negative, while discrete entropy is always non-negative. This article shows that negative entropy is a significant flaw when entropy is used as a sensitivity measure in global sensitivity analysis. Global sensitivity analysis based on differential entropy cannot have negative [...] Read more.
Differential entropy can be negative, while discrete entropy is always non-negative. This article shows that negative entropy is a significant flaw when entropy is used as a sensitivity measure in global sensitivity analysis. Global sensitivity analysis based on differential entropy cannot have negative entropy, just as Sobol sensitivity analysis does not have negative variance. Entropy is similar to variance but does not have the same properties. An alternative sensitivity measure based on the approximation of the differential entropy using dome-shaped functionals with non-negative values is proposed in the article. Case studies have shown that new sensitivity measures lead to a rational structure of sensitivity indices with a significantly lower proportion of higher-order sensitivity indices compared to other types of distributional sensitivity analysis. In terms of the concept of sensitivity analysis, a decrease in variance to zero means a transition from the differential to discrete entropy. The form of this transition is an open question, which can be studied using other scientific disciplines. The search for new functionals for distributional sensitivity analysis is not closed, and other suitable sensitivity measures may be found. Full article
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26 pages, 2359 KiB  
Article
Assessing the Europe 2020 Strategy Implementation Using Interval Entropy and Cluster Analysis for Interrelation between Two Groups of Headline Indicators
by Natalja Kosareva and Aleksandras Krylovas
Entropy 2021, 23(3), 345; https://doi.org/10.3390/e23030345 - 15 Mar 2021
Cited by 2 | Viewed by 1526
Abstract
The research analyzes the progress of Member States in the implementation of Europe 2020 strategy targets and goals in 2016–2018. Multiple criteria decision-making approaches applied for this task. The set of headline indicators was divided into two logically explained groups. Interval entropy is [...] Read more.
The research analyzes the progress of Member States in the implementation of Europe 2020 strategy targets and goals in 2016–2018. Multiple criteria decision-making approaches applied for this task. The set of headline indicators was divided into two logically explained groups. Interval entropy is proposed as an effective tool to make prioritization of headline indicators in separate groups. The sensitivity of the interval entropy is its advantage over classical entropy. Indicator weights were calculated by applying the WEBIRA (weight-balancing indicator ranks accordance) method. The WEBIRA method allows the best harmonization of ranking results according to different criteria groups—this is its advantage over other multiple-criteria methods. Final assessing and ranking of the 28 European Union countries (EU-28) was implemented through the α-cut approach. A k-means clustering procedure was applied to the EU-28 countries by summarizing the ranking results in 2016–2018. Investigation revealed the countries–leaders and countries–outsiders of the Europe 2020 strategy implementation process. It turned out that Sweden, Finland, Denmark, and Austria during the three-year period were the countries that exhibited the greatest progress according to two headline indicator groups’ interrelation. Cluster analysis results are mainly consistent with the EU-28 countries’ categorizations set by other authors. Full article
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16 pages, 3958 KiB  
Article
A New Algorithm for Digital Image Encryption Based on Chaos Theory
by Yaghoub Pourasad, Ramin Ranjbarzadeh and Abbas Mardani
Entropy 2021, 23(3), 341; https://doi.org/10.3390/e23030341 - 13 Mar 2021
Cited by 103 | Viewed by 6229
Abstract
In recent decades, image encryption, as one of the significant information security fields, has attracted many researchers and scientists. However, several studies have been performed with different methods, and novel and useful algorithms have been suggested to improve secure image encryption schemes. Nowadays, [...] Read more.
In recent decades, image encryption, as one of the significant information security fields, has attracted many researchers and scientists. However, several studies have been performed with different methods, and novel and useful algorithms have been suggested to improve secure image encryption schemes. Nowadays, chaotic methods have been found in diverse fields, such as the design of cryptosystems and image encryption. Chaotic methods-based digital image encryptions are a novel image encryption method. This technique uses random chaos sequences for encrypting images, and it is a highly-secured and fast method for image encryption. Limited accuracy is one of the disadvantages of this technique. This paper researches the chaos sequence and wavelet transform value to find gaps. Thus, a novel technique was proposed for digital image encryption and improved previous algorithms. The technique is run in MATLAB, and a comparison is made in terms of various performance metrics such as the Number of Pixels Change Rate (NPCR), Peak Signal to Noise Ratio (PSNR), Correlation coefficient, and Unified Average Changing Intensity (UACI). The simulation and theoretical analysis indicate the proposed scheme’s effectiveness and show that this technique is a suitable choice for actual image encryption. Full article
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