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Entropy
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Mathematical Modeling, Artificial Intelligence, Dynamics and Control on Complex Systems...
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Mathematical Modeling, Artificial Intelligence, Dynamics and Control on Complex Systems from Science, Engineering and Sociological Science

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

Deadline for manuscript submissions: closed (31 August 2023) | Viewed by 6266

Special Issue Editors

Prof. Dr. Miguel Ángel López Guerrero

E-Mail Website
Guest Editor
Polytechnic School of Cuenca, Department of Mathematics, University of Castilla-La Mancha, 16071 Cuenca, Spain
Interests: dynamical systems; numerical algorithms; nonlinear systems; applied mathematics; differential equations
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Juan Luis García Guirao

E-Mail Website
Guest Editor
Department of Applied Mathematics and Statistics, Technical University of Cartagena, 30203 Cartagena, Spain
Interests: dynamical systems; celestial mechanics; Hamiltonian systems; low-dimensional dynamics; differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, many complex systems have arisen in science, engineering and sociological science, described with the use of mathematical tools such as dynamical systems. Applied mathematics is currently playing an important role in scientific research.

This Special Issue aims to cover topics of high current interest falling within the scope of applied mathematics, welcoming high-quality research papers concerning mathematical modeling, applications of applied mathematics, artificial intelligence and numerical analysis methods in science, engineering and sociological science. Potential topics include, but are not limited to, the following:

  • Nonlinear differential equations and applications;
  • Stochastic dynamics;
  • Big data and parameter identification;
  • Nonlinear dynamics and engineering nonlinearity;
  • Discontinuous dynamical systems and control;
  • Synchronization and chaos control;
  • Neurodynamics and brain dynamics;
  • Social dynamics and complexity with applications to economy;
  • Switching systems with impulses in networks;
  • Discrete and continuous dynamical systems;
  • Neuronal signal analysis (e.g., EEG and BCI);
  • Mathematical modeling of diseases;
  • Fractal theories in city development;
  • Computer simulation in artificial intelligence;
  • Mathematical modeling in economy, management and engineering;
  • Nonlinear dynamics and control;
  • Fractional dynamics and control;
  • Numerical investigation and simulations of engineering problems;
  • Artificial intelligence and data science.

Prof. Dr. Miguel Ángel López Guerrero
Prof. Dr. Juan Luis García Guirao
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

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

  • nonlinear systems and applications
  • discrete and continuous systems
  • artificial intelligence
  • dynamics and control
  • algorithms
  • entropy
  • fractional calculus
  • modeling

Published Papers (5 papers)

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Research

15 pages, 7273 KiB  
Article
Sustainable Optimal Control for Switched Pollution-Control Problem with Random Duration
by Yilun Wu, Anna Tur and Hongbo Wang
Entropy 2023, 25(10), 1426; https://doi.org/10.3390/e25101426 - 08 Oct 2023
Viewed by 820
Abstract
Considering the uncertainty of game duration and periodic seasonal fluctuation, an n-player switched pollution-control differential game is modeled to investigate a sustainable and adaptive strategy for players. Based on the randomness of game duration, two scenarios are considered in this study. In [...] Read more.
Considering the uncertainty of game duration and periodic seasonal fluctuation, an n-player switched pollution-control differential game is modeled to investigate a sustainable and adaptive strategy for players. Based on the randomness of game duration, two scenarios are considered in this study. In the first case, the game duration is a random variable, Tf, described by the shifted exponential distribution. In the second case, we assumed that players’ equipment is heterogeneous, and the i-th player’s equipment failure time, Tfi, is described according to the shifted exponential distribution. The game continues until a player’s equipment breaks down. Thus, the game duration is defined as Tf=min{Tf1,…,Tfn}. To achieve the goal of sustainable development, an environmentally sustainable strategy and its corresponding condition are defined. By using Pontryagin’s maximum principle, a unique control solution is obtained in the form of a hybrid limit cycle, the state variable converges to a stable hybrid limit cycle, and the total payoff of all players increases and then converges. The results indicate that the environmentally sustainable strategy in the n-player pollution-control cooperative differential game with switches and random duration is a unique strategy that not only ensures profit growth but also considers environmental protection. Full article
(This article belongs to the Special Issue Mathematical Modeling, Artificial Intelligence, Dynamics and Control on Complex Systems from Science, Engineering and Sociological Science)
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21 pages, 384 KiB  
Article
Application of the Esscher Transform to Pricing Forward Contracts on Energy Markets in a Fuzzy Environment
by Piotr Nowak and Michał Pawłowski
Entropy 2023, 25(3), 527; https://doi.org/10.3390/e25030527 - 18 Mar 2023
Cited by 2 | Viewed by 1050
Abstract
The paper is dedicated to modeling electricity spot prices and pricing forward contracts on energy markets. The underlying dynamics of electricity spot prices is governed by a stochastic mean reverting diffusion with jumps having mixed-exponential distribution. Application of financial mathematics and stochastic methods [...] Read more.
The paper is dedicated to modeling electricity spot prices and pricing forward contracts on energy markets. The underlying dynamics of electricity spot prices is governed by a stochastic mean reverting diffusion with jumps having mixed-exponential distribution. Application of financial mathematics and stochastic methods enabled the derivation of the analytical formula for the forward contract’s price in a crisp case. Since the model parameters’ incertitude is considered, their fuzzy counterparts are introduced. Utilization of fuzzy arithmetic enabled deriving an analytical expression for the futures price and proposing a modified method for decision-making under uncertainty. Finally, numerical examples are analyzed to illustrate our pricing approach and the proposed financial decision-making method. Full article
(This article belongs to the Special Issue Mathematical Modeling, Artificial Intelligence, Dynamics and Control on Complex Systems from Science, Engineering and Sociological Science)
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16 pages, 1581 KiB  
Article
Kernel Partial Least Squares Feature Selection Based on Maximum Weight Minimum Redundancy
by Xiling Liu and Shuisheng Zhou
Entropy 2023, 25(2), 325; https://doi.org/10.3390/e25020325 - 10 Feb 2023
Viewed by 1055
Abstract
Feature selection refers to a vital function in machine learning and data mining. The maximum weight minimum redundancy feature selection method not only considers the importance of features but also reduces the redundancy among features. However, the characteristics of various datasets are not [...] Read more.
Feature selection refers to a vital function in machine learning and data mining. The maximum weight minimum redundancy feature selection method not only considers the importance of features but also reduces the redundancy among features. However, the characteristics of various datasets are not identical, and thus the feature selection method should have different feature evaluation criteria for all datasets. Additionally, high-dimensional data analysis poses a challenge to enhancing the classification performance of the different feature selection methods. This study presents a kernel partial least squares feature selection method on the basis of the enhanced maximum weight minimum redundancy algorithm to simplify the calculation and improve the classification accuracy of high-dimensional datasets. By introducing a weight factor, the correlation between the maximum weight and the minimum redundancy in the evaluation criterion can be adjusted to develop an improved maximum weight minimum redundancy method. In this study, the proposed KPLS feature selection method considers the redundancy between the features and the feature weighting between any feature and a class label in different datasets. Moreover, the feature selection method proposed in this study has been tested regarding its classification accuracy on data containing noise and several datasets. The experimental findings achieved using different datasets explore the feasibility and effectiveness of the proposed method which can select an optimal feature subset and obtain great classification performance based on three different metrics when compared with other feature selection methods. Full article
(This article belongs to the Special Issue Mathematical Modeling, Artificial Intelligence, Dynamics and Control on Complex Systems from Science, Engineering and Sociological Science)
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21 pages, 1694 KiB  
Article
Relative Density-Based Intuitionistic Fuzzy SVM for Class Imbalance Learning
by Cui Fu, Shuisheng Zhou, Dan Zhang and Li Chen
Entropy 2023, 25(1), 34; https://doi.org/10.3390/e25010034 - 24 Dec 2022
Cited by 5 | Viewed by 1537
Abstract
The support vector machine (SVM) has been combined with the intuitionistic fuzzy set to suppress the negative impact of noises and outliers in classification. However, it has some inherent defects, resulting in the inaccurate prior distribution estimation for datasets, especially the imbalanced datasets [...] Read more.
The support vector machine (SVM) has been combined with the intuitionistic fuzzy set to suppress the negative impact of noises and outliers in classification. However, it has some inherent defects, resulting in the inaccurate prior distribution estimation for datasets, especially the imbalanced datasets with non-normally distributed data, further reducing the performance of the classification model for imbalance learning. To solve these problems, we propose a novel relative density-based intuitionistic fuzzy support vector machine (RIFSVM) algorithm for imbalanced learning in the presence of noise and outliers. In our proposed algorithm, the relative density, which is estimated by adopting the k-nearest-neighbor distances, is used to calculate the intuitionistic fuzzy numbers. The fuzzy values of the majority class instances are designed by multiplying the score function of the intuitionistic fuzzy number by the imbalance ratio, and the fuzzy values of minority class instances are assigned the intuitionistic fuzzy membership degree. With the help of the strong capture ability of the relative density to prior information and the strong recognition ability of the intuitionistic fuzzy score function to noises and outliers, the proposed RIFSVM not only reduces the influence of class imbalance but also suppresses the impact of noises and outliers, and further improves the classification performance. Experiments on the synthetic and public imbalanced datasets show that our approach has better performance in terms of G-Means, F-Measures, and AUC than the other class imbalance classification algorithms. Full article
(This article belongs to the Special Issue Mathematical Modeling, Artificial Intelligence, Dynamics and Control on Complex Systems from Science, Engineering and Sociological Science)
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12 pages, 304 KiB  
Article
The Determination Method of Satisfactory Consistency of the Interval Number Pairwise Comparisons Matrix Based on Submatrix
by Fengxia Jin, Zhonghua Wu, Kun Zhao, Juan L. G. Guirao and Huatao Chen
Entropy 2022, 24(12), 1795; https://doi.org/10.3390/e24121795 - 08 Dec 2022
Viewed by 859
Abstract
The decision-maker obtains the pairwise comparisons matrix by comparing two entities. In the process of comparing the two entities, the relationship between the two entities and other entities is not considered. In this way, the judgment may be illogical. This paper mainly studies [...] Read more.
The decision-maker obtains the pairwise comparisons matrix by comparing two entities. In the process of comparing the two entities, the relationship between the two entities and other entities is not considered. In this way, the judgment may be illogical. This paper mainly studies the satisfactory consistency of the interval number pairwise comparisons matrix based on cyclic matrix. Firstly, the illogical judgment entity in the process of the decision-maker’s judgment is expressed by the cyclic matrix. There are three entities and four entities to form the cyclic matrix. The relationship and various forms of the cyclic cycle formed by the four entities and the three entities are discussed; then, the satisfactory consistency of the interval number pairwise comparisons matrix is determined by judging whether there is a cyclic matrix in the submatrix of the interval number pairwise comparisons matrix. Finally, two examples are given to verify the rationality and effectiveness of the method. Full article
(This article belongs to the Special Issue Mathematical Modeling, Artificial Intelligence, Dynamics and Control on Complex Systems from Science, Engineering and Sociological Science)
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