Special Issue "Dynamics under Uncertainty: Modeling Simulation and Complexity"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (31 December 2020).

Special Issue Editors

Prof. Dr. Dragan Marinkovic
E-Mail Website
Guest Editor
Department of Structural Analysis, Technical University of Berlin, Berlin, Germany
Interests: finite element analysis; nano materials; nano technology; materials science; modeling; mathematical modeling; experimentation; ansys; labview
Prof. Dr. Samarjit Kar
E-Mail Website
Guest Editor
Department of Mathematics, National Institute of Technology Durgapur, Durgapur, India
Interests: operations research; optimization; soft computing; uncertainty theory; financial modelling
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

The dynamics of systems have proven to be very powerful tools in understanding the behavior of the different natural phenomena throughout the last two centuries. However, the attributes of natural systems are observed to deviate from their classical state due to the effect of different types of uncertainties. Actually, randomness and impreciseness are the two major sources of uncertainties in natural systems. Randomness is modeled by different stochastic processes and impreciseness could be modeled by fuzzy sets, rough sets, Dempster–Shafer theory, etc.

Generally, symmetry, asymmetry, and antisymmetry are basic characteristics of binary relations used when modeling dynamical systems. Moreover, the notion of symmetry appeared in many articles about fuzzy sets, rough sets, Dempster–Shafer theory, etc. which are employed in the dynamical systems. Hence, the behavior of dynamical systems with uncertain variables, parameters, and functions has attracted academic attention in the recent past. Similarly, the study of the dynamics manifested in complex networks, or an interaction network of individuals became popular in the last few decades. The study of collective dynamics in complex interaction networks has been proven to be useful to understand the collective dynamic phenomenon like the emergence of cooperation between rational agents, synchronization of signal, like a flashlight or fireflies, rumor spreading, or conscious forming in a social network, etc. Different methods of statistical mechanics are also successfully applied to study such complex systems and to understand the emergence of different collective behavior. When randomness and imprecision coexist in a system the system is called a hybrid uncertain system. In such a system, the overall uncertainty is an aggregation of both types of uncertainties. However, in the context of modeling the behavior of complex natural systems, it is extremely important to analyze the effect of appropriate uncertainty to understand the predictability of different phenomena. An example of such uncertain dynamical systems could be sited in different levels of the universe ranging from the interaction of quantum particles to the complex interaction of biochemical molecules, like signaling in the brain, or even complex social interactions like forming opinions.

The Special Issue will collect high-quality papers addressing uncertain dynamics, their modeling and simulation. Submitted papers should not have been previously published or be currently under consideration for publication elsewhere.

We invite authors to submit original research articles that propose novel modeling and simulation of uncertain complex systems in various fields of natural science.

A quick query of SCOPUS on uncertain dynamics clearly demonstrates a rapid and steady growth of the area as shown in Figure 1.

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Figure 1. Publications related to Uncertain Dynamics.

Potential topics include but are not limited to the following:

  • Stochastic dynamics, SPDE
  • Random dynamical systems
  • Rough path analysis, random matrix
  • Uncertain dynamics, fuzzy dynamics, rough dynamics
  • Network analysis of complex dynamics
  • Hybrid uncertainty analysis
  • Simulation and complexity of dynamics under uncertainty

Dr. Dragan Pamučar
Prof. Dr. Dragan Marinkovic
Prof. Samarjit Kar
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 papers will be 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. Mathematics is an international peer-reviewed open access semimonthly 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 1600 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.

Published Papers (12 papers)

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Editorial

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Editorial
Dynamics under Uncertainty: Modeling Simulation and Complexity
Mathematics 2021, 9(12), 1416; https://doi.org/10.3390/math9121416 - 18 Jun 2021
Viewed by 197
Abstract
This issue contains the successful invited submissions [...] Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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Research

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Article
Synthetic Emotions for Empathic Building
Mathematics 2021, 9(7), 701; https://doi.org/10.3390/math9070701 - 24 Mar 2021
Cited by 1 | Viewed by 401
Abstract
Empathic buildings are intelligent ones that aim to measure and execute the best user experience. A smoother and intuitive environment leads to a better mood. The system gathers data from sensors that measure things like air quality, occupancy, noise and analyse it for [...] Read more.
Empathic buildings are intelligent ones that aim to measure and execute the best user experience. A smoother and intuitive environment leads to a better mood. The system gathers data from sensors that measure things like air quality, occupancy, noise and analyse it for the better experience of the users. This research proposes an artificial intelligence-based approach to detect synthetic emotions based on Thayer’s emotional model and Fuzzy Cognitive Maps. This emotional model is based on a biopsychological approach to the analysis of the humans’ emotional state. In this research, Fuzzy Grey Cognitive Maps are used, which are an extension of the fuzzy cognitive maps using the grey systems theory to model uncertainty. Fuzzy Cognitive Grey Maps (FGCMs) have become a very valuable theory for modeling high-uncertainty systems when small and incomplete discrete data sets are available. This research includes experiments with a couple of synthetic case studies for testing this proposal. This proposal provides an innovative way for simulating synthetic emotions and designing an empathic building. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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Article
Prediction of Important Factors for Bleeding in Liver Cirrhosis Disease Using Ensemble Data Mining Approach
Mathematics 2020, 8(11), 1887; https://doi.org/10.3390/math8111887 - 30 Oct 2020
Cited by 1 | Viewed by 473
Abstract
The main motivation to conduct the study presented in this paper was the fact that due to the development of improved solutions for prediction risk of bleeding and thus a faster and more accurate diagnosis of complications in cirrhotic patients, mortality of cirrhosis [...] Read more.
The main motivation to conduct the study presented in this paper was the fact that due to the development of improved solutions for prediction risk of bleeding and thus a faster and more accurate diagnosis of complications in cirrhotic patients, mortality of cirrhosis patients caused by bleeding of varices fell at the turn in the 21th century. Due to this fact, an additional research in this field is needed. The objective of this paper is to develop one prediction model that determines most important factors for bleeding in liver cirrhosis, which is useful for diagnosis and future treatment of patients. To achieve this goal, authors proposed one ensemble data mining methodology, as the most modern in the field of prediction, for integrating on one new way the two most commonly used techniques in prediction, classification with precede attribute number reduction and multiple logistic regression for calibration. Method was evaluated in the study, which analyzed the occurrence of variceal bleeding for 96 patients from the Clinical Center of Nis, Serbia, using 29 data from clinical to the color Doppler. Obtained results showed that proposed method with such big number and different types of data demonstrates better characteristics than individual technique integrated into it. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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Article
Development of a Novel Integrated CCSD-ITARA-MARCOS Decision-Making Approach for Stackers Selection in a Logistics System
Mathematics 2020, 8(10), 1672; https://doi.org/10.3390/math8101672 - 01 Oct 2020
Cited by 8 | Viewed by 757
Abstract
The main goal of this paper is to propose a Multiple-Criteria Decision-Making (MCDM) approach that will facilitate decision-making in the field of logistics—i.e., in the selection of the optimal equipment for performing a logistics activity. For defining the objective weights of the criteria, [...] Read more.
The main goal of this paper is to propose a Multiple-Criteria Decision-Making (MCDM) approach that will facilitate decision-making in the field of logistics—i.e., in the selection of the optimal equipment for performing a logistics activity. For defining the objective weights of the criteria, the correlation coefficient and the standard deviation (CCSD method) are applied. Furthermore, for determining the semi-objective weights of the considered criteria, the indifference threshold-based attribute ratio analysis method (ITARA) is used. In this way, by combining these two methods, the weights of the criteria are determined with a higher degree of reliability. For the final ranking of the alternatives, the measurement of alternatives and ranking according to the compromise solution method (MARCOS) is utilized. For demonstrating the applicability of the proposed approach, an illustrative case study pointing to the selection of the best manual stacker for a small warehouse is performed. The final results are compared with the ones obtained using the other proved MCDM methods that confirmed the reliability and stability of the proposed approach. The proposed integrated approach shows itself as a suitable technique for applying in the process of logistics equipment selection, because it defines the most influential criteria and the optimal choice with regard to all of them in a relatively easy and comprehensive way. Additionally, conceiving the determination of the criteria with the combination of objective and semi-objective methods enables defining the objective weights concerning the attitudes of the involved decision-makers, which finally leads to more reliable results. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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Article
Application of Improved Best Worst Method (BWM) in Real-World Problems
Mathematics 2020, 8(8), 1342; https://doi.org/10.3390/math8081342 - 11 Aug 2020
Cited by 6 | Viewed by 853
Abstract
The Best Worst Method (BWM) represents a powerful tool for multi-criteria decision-making and defining criteria weight coefficients. However, while solving real-world problems, there are specific multi-criteria problems where several criteria exert the same influence on decision-making. In such situations, the traditional postulates of [...] Read more.
The Best Worst Method (BWM) represents a powerful tool for multi-criteria decision-making and defining criteria weight coefficients. However, while solving real-world problems, there are specific multi-criteria problems where several criteria exert the same influence on decision-making. In such situations, the traditional postulates of the BWM imply the defining of one best criterion and one worst criterion from within a set of observed criteria. In this paper, an improvement of the traditional BWM that eliminates this problem is presented. The improved BWM (BWM-I) offers the possibility for decision-makers to express their preferences even in cases where there is more than one best and worst criterion. The development enables the following: (1) the BWM-I enables us to express experts’ preferences irrespective of the number of the best/worst criteria in a set of evaluation criteria; (2) the application of the BWM-I reduces the possibility of making a mistake while comparing pairs of criteria, which increases the reliability of the results; and (3) the BWM-I is characterized by its flexibility, which is expressed through the possibility of the realistic processing of experts’ preferences irrespective of the number of the criteria that have the same significance and the possibility of the transformation of the BWM-I into the traditional BWM (should there be a unique best/worst criterion). To present the applicability of the BWM-I, it was applied to defining the weight coefficients of the criteria in the field of renewable energy and their ranking. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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Article
A Robust Algorithm for Classification and Diagnosis of Brain Disease Using Local Linear Approximation and Generalized Autoregressive Conditional Heteroscedasticity Model
Mathematics 2020, 8(8), 1268; https://doi.org/10.3390/math8081268 - 02 Aug 2020
Cited by 6 | Viewed by 697
Abstract
Regions detection has an influence on the better treatment of brain tumors. Existing algorithms in the early detection of tumors are difficult to diagnose reliably. In this paper, we introduced a new robust algorithm using three methods for the classification of brain disease. [...] Read more.
Regions detection has an influence on the better treatment of brain tumors. Existing algorithms in the early detection of tumors are difficult to diagnose reliably. In this paper, we introduced a new robust algorithm using three methods for the classification of brain disease. The first method is Wavelet-Generalized Autoregressive Conditional Heteroscedasticity-K-Nearest Neighbor (W-GARCH-KNN). The Two-Dimensional Discrete Wavelet (2D-DWT) is utilized as the input images. The sub-banded wavelet coefficients are modeled using the GARCH model. The features of the GARCH model are considered as the main property vector. The second method is the Developed Wavelet-GARCH-KNN (D-WGK), which solves the incompatibility of the WGK method for the use of a low pass sub-band. The third method is the Wavelet Local Linear Approximation (LLA)-KNN, which we used for modeling the wavelet sub-bands. The extracted features were applied separately to determine the normal image or brain tumor based on classification methods. The classification was performed for the diagnosis of tumor types. The empirical results showed that the proposed algorithm obtained a high rate of classification and better practices than recently introduced algorithms while requiring a smaller number of classification features. According to the results, the Low-Low sub-bands are not adopted with the GARCH model; therefore, with the use of homomorphic filtering, this limitation is overcome. The results showed that the presented Local Linear (LL) method was better than the GARCH model for modeling wavelet sub-bands. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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Article
Eliminating Rank Reversal Problem Using a New Multi-Attribute Model—The RAFSI Method
Mathematics 2020, 8(6), 1015; https://doi.org/10.3390/math8061015 - 21 Jun 2020
Cited by 4 | Viewed by 852
Abstract
Multi-attribute decision-making (MADM) methods represent reliable ways to solve real-world problems for various applications by providing rational and logical solutions. In reaching such a goal, it is expected that MADM methods would eliminate inconsistencies like rank reversal issues in a given solution. In [...] Read more.
Multi-attribute decision-making (MADM) methods represent reliable ways to solve real-world problems for various applications by providing rational and logical solutions. In reaching such a goal, it is expected that MADM methods would eliminate inconsistencies like rank reversal issues in a given solution. In this paper, an endeavor is taken to put forward a new MADM method, called RAFSI (Ranking of Alternatives through Functional mapping of criterion sub-intervals into a Single Interval), which successfully eliminates the rank reversal problem. The developed RAFSI method has three major advantages that recommend it for further use: (i) its simple algorithm helps in solving complex real-world problems, (ii) RAFSI method has a new approach for data normalization, which transfers data from the starting decision-making matrix into any interval, suitable for making rational decisions, (iii) mathematical formulation of RAFSI method eliminates the rank reversal problem, which is one of the most significant shortcomings of existing MADM methods. A real-time case study that shows the advantages of RAFSI method is presented. Additional comprehensive analysis, including a comparison with other three traditional MADM methods that use different ways for data normalization and testing the resistance of RAFSI method and other MADM methods to rank the reversal problem, is also carried out. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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Article
Novel Extension of DEMATEL Method by Trapezoidal Fuzzy Numbers and D Numbers for Management of Decision-Making Processes
Mathematics 2020, 8(5), 812; https://doi.org/10.3390/math8050812 - 17 May 2020
Cited by 3 | Viewed by 694
Abstract
The decision-making trial and evaluation laboratory (DEMATEL) method is one of the most significant multi-criteria techniques for defining the relationships among criteria and for defining the weight coefficients of criteria. Since multi-criteria models are very often used in management and decision-making under conditions [...] Read more.
The decision-making trial and evaluation laboratory (DEMATEL) method is one of the most significant multi-criteria techniques for defining the relationships among criteria and for defining the weight coefficients of criteria. Since multi-criteria models are very often used in management and decision-making under conditions of uncertainty, the fuzzy DEMATEL model has been extended in this paper by D numbers (fuzzy DEMATEL-D). The aim of this research was to develop a multi-criteria methodology that enables the objective processing of fuzzy linguistic information in the pairwise comparison of criteria. This aim was achieved through the development of the fuzzy DEMATEL-D method. Combining D numbers with trapezoidal fuzzy linguistic variables (LVs) allows for the additional processing of uncertainties and ambiguities that exist in experts’ preferences when comparing criteria with each other. In addition, the fuzzy DEMATEL-D methodology has a unique reasoning algorithm that allows for the rational processing of uncertainties when using fuzzy linguistic expressions for pairwise comparisons of criteria. The fuzzy DEMATEL-D methodology provides an original uncertainty management framework that is rational and concise. In order to illustrate the effectiveness of the proposed methodology, a case study with the application of the proposed multi-criteria methodology is presented. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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Article
Preview Control for MIMO Discrete-Time System with Parameter Uncertainty
Mathematics 2020, 8(5), 756; https://doi.org/10.3390/math8050756 - 09 May 2020
Cited by 2 | Viewed by 548
Abstract
We consider the problems of state feedback and static output feedback preview controller (PC) for uncertain discrete-time multiple-input multiple output (MIMO) systems based on the parameter-dependent Lyapunov function and the linear matrix inequality (LMI) technique in this paper. First, for each component of [...] Read more.
We consider the problems of state feedback and static output feedback preview controller (PC) for uncertain discrete-time multiple-input multiple output (MIMO) systems based on the parameter-dependent Lyapunov function and the linear matrix inequality (LMI) technique in this paper. First, for each component of a reference signal, an augmented error system (AES) containing previewed information is constructed via the difference operator and state augmentation technique. Then, for the AES, the state feedback and static output feedback are introduced, and when considering the output feedback, a previewable reference signal is utilized by modifying the output equation. The preview controllers’ parameter matrices can be achieved from the solution of LMI problems. The superiority of the PC is illustrated via two numerical examples. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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Article
A Model for Determining Weight Coefficients by Forming a Non-Decreasing Series at Criteria Significance Levels (NDSL)
Mathematics 2020, 8(5), 745; https://doi.org/10.3390/math8050745 - 08 May 2020
Cited by 1 | Viewed by 497
Abstract
In this paper, a new method for determining weight coefficients by forming a non-decreasing series at criteria significance levels (the NDSL method) is presented. The NDLS method includes the identification of the best criterion (i.e., the most significant and most influential criterion) and [...] Read more.
In this paper, a new method for determining weight coefficients by forming a non-decreasing series at criteria significance levels (the NDSL method) is presented. The NDLS method includes the identification of the best criterion (i.e., the most significant and most influential criterion) and the ranking of criteria in a decreasing series from the most significant to the least significant criterion. Criteria are then grouped as per the levels of significance within the framework of which experts express their preferences in compliance with the significance of such criteria. By employing this procedure, fully consistent results are obtained. In this paper, the advantages of the NDSL model are singled out through a comparison with the Best Worst Method (BWM) and Analytic Hierarchy Process (AHP) models. The advantages include the following: (1) the NDSL model requires a significantly smaller number of pairwise comparisons of criteria, only involving an n − 1 comparison, whereas the AHP requires an n(n − 1)/2 comparison and the BWM a 2n − 3 comparison; (2) it enables us to obtain reliable (consistent) results, even in the case of a larger number of criteria (more than nine criteria); (3) the NDSL model applies an original algorithm for grouping criteria according to the levels of significance, through which the deficiencies of the 9-degree scale applied in the BWM and AHP models are eliminated. By doing so, the small range and inconsistency of the 9-degree scale are eliminated; (4) while the BWM includes the defining of one unique best/worst criterion, the NDSL model eliminates this limitation and gives decision-makers the freedom to express the relationships between criteria in accordance with their preferences. In order to demonstrate the performance of the developed model, it was tested on a real-world problem and the results were validated through a comparison with the BWM and AHP models. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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Article
Predicting the Dynamic Response of Dual-Rotor System Subject to Interval Parametric Uncertainties Based on the Non-Intrusive Metamodel
Mathematics 2020, 8(5), 736; https://doi.org/10.3390/math8050736 - 07 May 2020
Cited by 4 | Viewed by 896
Abstract
In this paper, the non-probabilistic steady-state dynamics of a dual-rotor system with parametric uncertainties under two-frequency excitations are investigated using the non-intrusive simplex form mathematical metamodel. The Lagrangian formulation is employed to derive the equations of motion (EOM) of the system. The simplex [...] Read more.
In this paper, the non-probabilistic steady-state dynamics of a dual-rotor system with parametric uncertainties under two-frequency excitations are investigated using the non-intrusive simplex form mathematical metamodel. The Lagrangian formulation is employed to derive the equations of motion (EOM) of the system. The simplex form metamodel without the distribution functions of the interval uncertainties is formulated in a non-intrusive way. In the multi-uncertain cases, strategies aimed at reducing the computational cost are incorporated. In numerical simulations for different interval parametric uncertainties, the special propagation mechanism is observed, which cannot be found in single rotor systems. Validations of the metamodel in terms of efficiency and accuracy are also carried out by comparisons with the scanning method. The results will be helpful to understand the dynamic behaviors of dual-rotor systems subject to uncertainties and provide guidance for robust design and analysis. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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Article
A New Fuzzy MARCOS Method for Road Traffic Risk Analysis
Mathematics 2020, 8(3), 457; https://doi.org/10.3390/math8030457 - 24 Mar 2020
Cited by 31 | Viewed by 1833
Abstract
In this paper, a new fuzzy multi-criteria decision-making model for traffic risk assessment was developed. A part of a main road network of 7.4 km with a total of 38 Sections was analyzed with the aim of determining the degree of risk on [...] Read more.
In this paper, a new fuzzy multi-criteria decision-making model for traffic risk assessment was developed. A part of a main road network of 7.4 km with a total of 38 Sections was analyzed with the aim of determining the degree of risk on them. For that purpose, a fuzzy Measurement Alternatives and Ranking according to the COmpromise Solution (fuzzy MARCOS) method was developed. In addition, a new fuzzy linguistic scale quantified into triangular fuzzy numbers (TFNs) was developed. The fuzzy PIvot Pairwise RElative Criteria Importance Assessment—fuzzy PIPRECIA method—was used to determine the criteria weights on the basis of which the road network sections were evaluated. The results clearly show that there is a dominant section with the highest risk for all road participants, which requires corrective actions. In order to validate the results, a comprehensive validity test was created consisting of variations in the significance of model input parameters, testing the influence of dynamic factors—of reverse rank, and applying the fuzzy Simple Additive Weighing (fuzzy SAW) method and the fuzzy Technique for Order of Preference by Similarity to Ideal Solution (fuzzy TOPSIS). The validation test show the stability of the results obtained and the justification for the development of the proposed model. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
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