mathematics
Editorial
Dynamics under Uncertainty: Modeling Simulation
and Complexity
Dragan Pamuˇcar 1,* , Dragan Marinkovi´c 2and Samarjit Kar 3
Citation: Pamuˇcar, D.; Marinkovi´c,
D.; Kar, S. Dynamics under
Uncertainty: Modeling Simulation
and Complexity. Mathematics 2021,9,
1416. https://doi.org/10.3390/
math9121416
Received: 11 June 2021
Accepted: 16 June 2021
Published: 18 June 2021
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1Department of Logistics, Military Academy, University of Defense in Belgrade, 11000 Belgrade, Serbia
2Faculty of Mechanical Engineering and Transport Systems, Technische Universitaet Berlin,
3Department of Mathematics, National Institute of Technology, Durgapur 713209, India;
*Correspondence: [email protected]; Tel.: +38-111-360-3188
This issue contains the successful invited submissions [
1
–
11
] to a Special Issue of
Mathematics on the subject area of “Dynamics under Uncertainty: Modeling Simulation
and Complexity”.
The dynamics of systems have proven to be very powerful tools in understanding
the behavior of 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 effects of different types of uncertainties. In actuality, 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, the Dempster–Shafer theory, etc.
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, has
become popular in the last few decades. The study of collective dynamics in complex
interaction networks has been proven to be useful in understanding collective dynamic
phenomena such as the emergence of cooperation between rational agents, synchroniza-
tion of signals as seen in a flashlight or fireflies, rumor spreading, or conscious forming
of a social network, etc. Different methods of statistical mechanics are also successfully
applied to the study such complex systems and to understand the emergence of different
collective behaviors. 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 aggre-
gation 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 the appro-
priate 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, such as signaling in the brain, or even in complex social interactions, such as
while forming opinions.
This Special Issue includes the most important forecasting techniques applied to the
modeling simulation and complexity in dynamic systems, such as, fuzzy multi-criteria
techniques, artificial intelligence, the Dempster–Shafer approach, and heuristics.
Response to our call had the following statistics, Figure 1.
Mathematics 2021,9, 1416. https://doi.org/10.3390/math9121416 https://www.mdpi.com/journal/mathematics
Mathematics 2021,9, 1416 2 of 3
Mathematics 2021, 9, x 2 of 3
Figure 1. Special Issue statistics.
The geographical distribution of the authors (published papers) is presented in Table
1.
Table 1. Publications by country.
Countries Countries
Serbia 7
Bosnia and Herzegovina 2
China 2
South Africa 2
Turkey 2
Vietnam 2
Chile 1
India 1
Saudi Arabia 1
Spain 1
Iran 1
UK 1
Published submissions are related to road traffic risk analysis [1], dual-rotor systems
[2], multi-criteria decision making [3,5,6,8,9], MIMO discrete-time systems [4], the classi-
fication and diagnosis of brain disease [7], data mining [10], and empathic building [11].
This Special Issue presents 11 models, which are briefly presented in the next section.
Stanković et al. [1] proposed fuzzy Measurement Alternatives and Ranking according to
the COmpromise Solution (fuzzy MARCOS) method for road traffic risk analysis. In ad-
dition, they used the fuzzy PIvot Pairwise RElative Criteria Importance Assessment—the
fuzzy PIPRECIA method— to determine the weights of the criteria on the basis of which
road network sections were evaluated. Fu et al. [2] investigated the non-probabilistic
steady-state dynamics of a dual-rotor system with parametric uncertainties under two-
frequency excitations. Žižović et al. [3] presented a new method for determining weight
coefficients by forming a non-decreasing series at criteria significance levels (the NDSL
method). Li et al. [4] investigated the problems of state feedback and the static output
feedback preview controller for uncertain discrete-time multiple-input multiple-output
Figure 1. Special Issue statistics.
The geographical distribution of the authors (published papers) is presented in
Table 1
.
Table 1. Publications by country.
Countries Countries
Serbia 7
Bosnia and Herzegovina 2
China 2
South Africa 2
Turkey 2
Vietnam 2
Chile 1
India 1
Saudi Arabia 1
Spain 1
Iran 1
UK 1
Published submissions are related to road traffic risk analysis [
1
], dual-rotor sys-
tems [
2
], multi-criteria decision making [
3
,
5
,
6
,
8
,
9
], MIMO discrete-time systems [
4
], the
classification and diagnosis of brain disease [
7
], data mining [
10
], and empathic build-
ing [11].
This Special Issue presents 11 models, which are briefly presented in the next section.
Stankovi´c et al. [
1
] proposed fuzzy Measurement Alternatives and Ranking according to the
COmpromise Solution (fuzzy MARCOS) method for road traffic risk analysis. In addition,
they used the fuzzy PIvot Pairwise RElative Criteria Importance Assessment—the fuzzy
PIPRECIA method— to determine the weights of the criteria on the basis of which road
network sections were evaluated. Fu et al. [
2
] investigated the non-probabilistic steady-
state dynamics of a dual-rotor system with parametric uncertainties under two-frequency
excitations. Žižovi´c et al. [
3
] presented a new method for determining weight coefficients
by forming a non-decreasing series at criteria significance levels (the NDSL method).
Li et al.
[
4
] investigated the problems of state feedback and the static output feedback
preview controller for uncertain discrete-time multiple-input multiple-output systems
based on the parameter-dependent Lyapunov function and the linear matrix inequality
Mathematics 2021,9, 1416 3 of 3
technique. Pribi´cevi´c et al. [
5
] developed a new multi-criteria methodology that enables the
objective processing of fuzzy linguistic information in the pairwise comparison of criteria,
and they called it the fuzzy DEMATEL-D method. Žižovi´c et al. [
6
] presented a new
MADM method in their research called RAFSI (Ranking of Alternatives through Functional
mapping of criterion sub-intervals into a Single Interval), which successfully eliminates the
rank reversal problem. Hamzenejad et al. [
7
] introduced a new robust algorithm using three
methods for the classification of brain disease: (1) the Wavelet-Generalized Autoregressive
Conditional Heteroscedasticity-K-Nearest Neighbor method; (2) the Wavelet-GARCH-
KNN method; and (3) the Wavelet Local Linear Approximation. Pamuˇcar et al. [
8
] presented
an improved Best Worst Method for determining criteria weights in multi-criteria decision
making. Uluta¸s et al. [
9
] proposed a multiple-criteria decision-making approach for the
selection of the optimal equipment for performing logistics activity. For defining the
objective weights of the criteria, they applied the correlation coefficient and the standard
deviation, and for the final ranking of the alternatives, they utilized the MARCOS method.
Aleksi´c et al. [
10
] developed a prediction model that determines the most important
factors for bleeding in liver cirrhosis. Salmeron and Ruiz-Celma [
11
] proposed an artificial
intelligence-based approach to detect synthetic emotions based on Thayer’s emotional
model and Fuzzy Cognitive Maps.
We found the submissions and selections of papers for this issue very inspiring and
rewarding. We also thank the editorial staff and reviewers for their efforts and help during
the process.
Author Contributions:
Conceptualization, D.P., D.M. and S.K.; methodology, D.P. and D.M.; formal
analysis, S.K.; investigation, D.P.; supervision, D.M. and D.P. All authors have read and agreed to the
published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Stankovi´c, M.; Stevi´c, Ž.; Das, D.; Suboti´c, M.; Pamuˇcar, D. A New Fuzzy MARCOS Method for Road Traffic Risk Analysis.
Mathematics 2020,8, 457. [CrossRef]
2.
Fu, C.; Feng, G.; Ma, J.; Lu, K.; Yang, Y.; Gu, F. Predicting the Dynamic Response of Dual-Rotor System Subject to Interval
Parametric Uncertainties Based on the Non-Intrusive Metamodel. Mathematics 2020,8, 736. [CrossRef]
3.
Žižovi´c, M.; Pamuˇcar, D.; ´
Cirovi´c, G.; Žižovi´c, M.; Miljkovi´c, B. A Model for Determining Weight Coefficients by Forming a
Non-Decreasing Series at Criteria Significance Levels (NDSL). Mathematics 2020,8, 745. [CrossRef]
4.
Li, L.; Liao, F. Preview Control for MIMO Discrete-Time System with Parameter Uncertainty. Mathematics
2020
,8, 756. [CrossRef]
5.
Pribi´cevi´c, I.; Doljanica, S.; Momˇcilovi´c, O.; Das, D.; Pamuˇcar, D.; Stevi´c, Ž. Novel Extension of DEMATEL Method by Trapezoidal
Fuzzy Numbers and D Numbers for Management of Decision-Making Processes. Mathematics 2020,8, 812. [CrossRef]
6.
Žižovi´c, M.; Pamuˇcar, D.; Albijani´c, M.; Chatterjee, P.; Pribi´cevi´c, I. Eliminating Rank Reversal Problem Using a New Multi-
Attribute Model—The RAFSI Method. Mathematics 2020,8, 1015. [CrossRef]
7.
Hamzenejad, A.; Jafarzadeh Ghoushchi, S.; Baradaran, V.; Mardani, A. A Robust Algorithm for Classification and Diagnosis
of Brain Disease Using Local Linear Approximation and Generalized Autoregressive Conditional Heteroscedasticity Model.
Mathematics 2020,8, 1268. [CrossRef]
8.
Pamuˇcar, D.; Ecer, F.; Cirovic, G.; Arlasheedi, M. Application of Improved Best Worst Method (BWM) in Real-World Problems.
Mathematics 2020,8, 1342. [CrossRef]
9.
Uluta¸s, A.; Karabasevic, D.; Popovic, G.; Stanujkic, D.; Nguyen, P.; Karaköy, Ç. Development of a Novel Integrated CCSD-ITARA-
MARCOS Decision-Making Approach for Stackers Selection in a Logistics System. Mathematics 2020,8, 1672. [CrossRef]
10.
Aleksi´c, A.; Nedeljkovi´c, S.; Jovanovi´c, M.; Ran ¯
delovi´c, M.; Vukovi´c, M.; Stojanovi´c, V.; Radovanovi´c, R.; Ran ¯
delovi´c, M.;
Ran ¯
delovi´c, D. Prediction of Important Factors for Bleeding in Liver Cirrhosis Disease Using Ensemble Data Mining Approach.
Mathematics 2020,8, 1887. [CrossRef]
11. Salmeron, J.; Ruiz-Celma, A. Synthetic Emotions for Empathic Building. Mathematics 2021,9, 701. [CrossRef]
