Mathematical, Statistical, and Soft Computing Methods for Uncertainty Management

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: 15 November 2024 | Viewed by 13716

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Departamento de Economía Financiera y Contabilidad, Instituto Universitario de Investigación para el Desarrollo Territorial Sostenible (INTERRA), Universidad de Extremadura, 10071 Cáceres, Spain
Interests: business; finance and tourism; resource and service management; natural resources; sustainable rural development; water resources management; agricultural resources management; land resources management; financial economics; accounting and management; sustainability; entrepreneurship; innovation; quality and environmental management systems
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Faculty of Accounting and Management, Saint Nicholas and Hidalgo Michoacán State University (UMSNH), Morelia 58030, Mexico
Interests: portfolio management; Markov-switching models; financial market distress prediction; commodity futures’ trading; active future trading; socially responsible investment
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Business Management and Marketing Department, Faculty of Business Sciences and Tourism, University of Vigo, 32004 Ourense, Spain
Interests: business; finance and tourism; resource and service management; natural resources; sustainable rural development; water resources management; agricultural resources management; land resources management; financial economics; accounting and management; sustainability; entrepreneurship; innovation; quality and environmental management systems
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Special Issue Information

Dear Colleagues,

One of the critical areas of quantitative analysis is the behavior of the statistical parameters of a random event. The statistical parameters are random, or the probability function is not fixed or homogeneous in specific scenarios or periods. A fundamental assumption in this type of analysis is either fixed statistical parameters or a fixed probability function in their values. Relaxing this assumption implies that the model is subject to uncertainty. This issue applies in the study of phenomena in several knowledge areas such as natural sciences, social sciences, data science, or physics (among others).

Even if this assumption led to improvements, several phenomena, such as the COVID-19 pandemic and its natural or social impact, showed that the fixed-parameter or probability function assumption does not hold. This conclusion suggests that using or developing more advanced mathematical, statistical, or soft computing methods is a necessity. The proper use of such techniques could lead to better quantitative results and, if applied, to better decisions.

For the particular case of social and natural sciences, not incorporating the presence of uncertainty in the model or the decision process leads to skewed estimation, and the use of a model that does not describe the actual phenomena of interest.

The purpose of this Special Issue is the development and discussion of methods that lead with uncertainty either in the statistical parameters, the probability function, or even the debate of applied soft computing methods that allow for incorporating latent or unknown information in the model of interest.

With this focus in mind, this Special Issue will accept papers in the following (not exclusive) list of topics of interest:

  1. Bayesian statistics methods with application in robust parameter estimation in physics, computational, natural, and social sciences;
  2. Fuzzy logic methods to deal with the uncertainty of parameter or probability function in physics, computational, natural and social sciences;
  3. Development of soft computing methods in Bayesian, fuzzy logic, or other quantitative areas that deal with model uncertainty;
  4. Developments of theoretical Bayesian statistics methods and related philosophical discussions;
  5. Development of theoretical fuzzy logic and related philosophical discussions;
  6. Development of soft computing models to deal with uncertainty, such as, Markov-chain Monte Carlo, artificial intelligence, data science algorithms, or computational uncertainty modeling;
  7. Statistical uncertainty models applied in economics, econometrics, finance, management, biology, chemistry, health sciences, sociology, psychology or any social or natural science;
  8. Optimization or optimal control methods that incorporate uncertainty in their estimation;
  9. Other related topics.

Prof. Dr. José Álvarez-García
Prof. Dr. Oscar V. De la Torre-Torres
Prof. Dr. María de la Cruz del Río-Rama
Guest Editors

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Keywords

  • Bayesian statistics methods
  • fuzzy logic methods
  • Markov-chain Monte Carlo
  • optimization or optimal control methods
  • soft computing methods
  • statistical uncertainty models

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Published Papers (7 papers)

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Research

21 pages, 1752 KiB  
Article
An EM/MCMC Markov-Switching GARCH Behavioral Algorithm for Random-Length Lumber Futures Trading
by Oscar V. De la Torre-Torres, José Álvarez-García and María de la Cruz del Río-Rama
Mathematics 2024, 12(3), 485; https://doi.org/10.3390/math12030485 - 2 Feb 2024
Cited by 1 | Viewed by 1409
Abstract
This paper tests using two-regime Markov-switching models with asymmetric, time-varying exponential generalized autoregressive conditional heteroskedasticity (MS-EGARCH) variances in random-length lumber futures trading. By assuming a two-regime context (a low s=1 and high s=2 volatility), a trading algorithm was simulated [...] Read more.
This paper tests using two-regime Markov-switching models with asymmetric, time-varying exponential generalized autoregressive conditional heteroskedasticity (MS-EGARCH) variances in random-length lumber futures trading. By assuming a two-regime context (a low s=1 and high s=2 volatility), a trading algorithm was simulated with the following trading rule: invest in lumber futures if the probability of being in the high-volatility regime s=2 is lower or equal to 50%, or invest in the 3-month U.S. Treasury bills (TBills) otherwise. The rationale tested in this paper was that using a two-regime Markov-switching (MS) algorithm leads to an overperformance against a buy-and-hold strategy in lumber futures. To extend the current literature in MS trading algorithms, two location parameter scenarios were simulated. The first uses an unconditional mean or expected value (no factors), and the second incorporates market and behavioral factors. With weekly simulations form 2 January 1994 to 28 July 2023, the results suggest that using MS-EGARCH models in a no-factors scenario is appropriate for active lumber futures trading with an accumulated return of 158.33%. Also, the results suggest that it is not useful to add market and behavioral factors in the MS-GARCH estimation because it leads to a lower performance. Full article
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20 pages, 10168 KiB  
Article
Risk Premium of Bitcoin and Ethereum during the COVID-19 and Non-COVID-19 Periods: A High-Frequency Approach
by José Antonio Núñez-Mora, Mario Iván Contreras-Valdez and Roberto Joaquín Santillán-Salgado
Mathematics 2023, 11(20), 4395; https://doi.org/10.3390/math11204395 - 23 Oct 2023
Viewed by 1389
Abstract
This paper reports our findings on the return dynamics of Bitcoin and Ethereum using high-frequency data (minute-by-minute observations) from 2015 to 2022 for Bitcoin and from 2016 to 2022 for Ethereum. The main objective of modeling these two series was to obtain a [...] Read more.
This paper reports our findings on the return dynamics of Bitcoin and Ethereum using high-frequency data (minute-by-minute observations) from 2015 to 2022 for Bitcoin and from 2016 to 2022 for Ethereum. The main objective of modeling these two series was to obtain a dynamic estimation of risk premium with the intention of characterizing its behavior. To this end, we estimated the Generalized Autoregressive Conditional Heteroskedasticity in Mean with Normal-Inverse Gaussian distribution (GARCH-M-NIG) model for the residuals. We also estimated the other parameters of the model and discussed their evolution over time, including the skewness and kurtosis of the Normal-Inverse Gaussian distribution. Similarly, we determined the parameters that define the evolution of the estimated variance, i.e., the parameters related to the fitted past variance, square error and long-term average value. We found that, despite the market uncertainty during the COVID-19 emergency period (2020 and 2021), the selected cryptocurrencies’ return volatility and kurtosis were even greater for several other subperiods within our sample’s time frame. Our model represents an analytical tool that estimates the risk premium that should be delivered by Bitcoin and Ethereum and is therefore of interest to risk managers, traders and investors. Full article
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16 pages, 655 KiB  
Article
Bayesian Estimations of Shannon Entropy and Rényi Entropy of Inverse Weibull Distribution
by Haiping Ren and Xue Hu
Mathematics 2023, 11(11), 2483; https://doi.org/10.3390/math11112483 - 28 May 2023
Cited by 1 | Viewed by 1317
Abstract
In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy [...] Read more.
In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve the likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real dataset are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation. Full article
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19 pages, 952 KiB  
Article
Quality Performance Indicators Evaluation and Ranking by Using TOPSIS with the Interval-Intuitionistic Fuzzy Sets in Project-Oriented Manufacturing Companies
by Snežana Nestić, Ranka Gojković, Tijana Petrović, Danijela Tadić and Predrag Mimović
Mathematics 2022, 10(22), 4174; https://doi.org/10.3390/math10224174 - 8 Nov 2022
Cited by 5 | Viewed by 2017
Abstract
Project-oriented manufacturing companies aim to produce high-quality products according to customer requirements and a minimum rate of complaints. In order to achieve this, performance indicators, especially those related to product quality, must be measured and monitored by managers. This research proposes a fuzzy [...] Read more.
Project-oriented manufacturing companies aim to produce high-quality products according to customer requirements and a minimum rate of complaints. In order to achieve this, performance indicators, especially those related to product quality, must be measured and monitored by managers. This research proposes a fuzzy multi-criteria model for the selection of key performance indicators that are critical to product quality. The uncertainties in the relative importance of decision-makers, performance indicators, and their values are described by sets of natural language words that are modeled by the interval-valued intuitionistic fuzzy numbers. The assessment of the relative importance of the decision-makers and the determination of their weights are based on the inclusion comparison probability between the closeness intuitionistic fuzzy sets. The determination of the weights vector of performance indicators is based on the integration of an interval-value fuzzy weighted geometric operator and the inclusion comparison probability between the closeness intuitionistic fuzzy sets. TOPSIS expanded with interval-valued intuitionistic fuzzy numbers for ranking performance indicators is proposed. The developed model was tested on the real data collected from three manufacturing companies in the Republic of Serbia. Based on the obtained results, the top-ranked performance indicators were marked as critical for product quality and selected as quality key performance indicators. Full article
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14 pages, 2221 KiB  
Article
Simulating Portfolio Decisions under Uncertainty When the Risky Asset and Short Rate Are Modulated by an Inhomogeneous and Asset-Dependent Markov Chain
by Benjamín Vallejo-Jiménez, Francisco Venegas-Martínez, Oscar V. De la Torre-Torres and José Álvarez-García
Mathematics 2022, 10(16), 2926; https://doi.org/10.3390/math10162926 - 14 Aug 2022
Cited by 1 | Viewed by 1210
Abstract
This paper aims to simulate portfolio decisions under uncertainty when the diffusion parameters of the risky asset and short rate paid for a bond are both modulated by a time-inhomogeneous Markov chain, with transition probabilities dependent on states, time, and asset prices. To [...] Read more.
This paper aims to simulate portfolio decisions under uncertainty when the diffusion parameters of the risky asset and short rate paid for a bond are both modulated by a time-inhomogeneous Markov chain, with transition probabilities dependent on states, time, and asset prices. To do this, we first found closed-form solutions of the corresponding utility-maximization problem, which solves a rational consumer that makes portfolio and consumption decisions by using the corresponding infinitesimal generator associated with the Markov chain. Subsequently, as an illustration of the theoretical results obtained, several scenarios were simulated for the Mexican case. The expected economic policy was inferred from announced monetary policy decisions regarding the reference rate and possible changes in trend due to the lack of fiscal stimuli. Under this framework, states were defined from the current and expected economic policies, and transition probabilities were expressed in terms of the ratio between the prices of the risky asset and the bond. It should be noted, as far as the authors know, that no analytical solutions are known in the literature for the case of Markov-modulated time-inhomogeneous chains with transition probabilities that, themselves, are stochastic processes. Full article
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21 pages, 1100 KiB  
Article
A Novel IBA-DE Hybrid Approach for Modeling Sovereign Credit Ratings
by Srđan Jelinek, Pavle Milošević, Aleksandar Rakićević, Ana Poledica and Bratislav Petrović
Mathematics 2022, 10(15), 2679; https://doi.org/10.3390/math10152679 - 29 Jul 2022
Cited by 3 | Viewed by 2638
Abstract
Nowadays, the sovereign credit rating is not only an index of a country’s economic performance and political stability but also an overall indicator of development and growth, as well as the trust factor that is associated with the country. Due to its importance, [...] Read more.
Nowadays, the sovereign credit rating is not only an index of a country’s economic performance and political stability but also an overall indicator of development and growth, as well as the trust factor that is associated with the country. Due to its importance, the vast amount of available information, and the lack of a closed-form solution, prediction models based on machine learning (ML) and computation intelligence (CI) techniques are being increasingly used to complement traditional financial approaches. In this paper, we aim to introduce a novel ML-CI approach for sovereign credit rating prediction based on a differential evolution (DE) algorithm and interpolative Boolean algebra (IBA). In fact, the proposed approach is based on a pseudo-logical function in the IBA framework derived from the historical data of publicly available indicators using the DE algorithm. Such functions are easily interpreted and enable a subtle gradation among countries. It is shown that the IBA-DE approach outperforms back-propagation neural networks on the observed problem while also providing a deeper insight into each of the indicators used for prediction and its respective influence on the prediction rating on the other. Full article
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13 pages, 676 KiB  
Article
Bonferroni Weighted Logarithmic Averaging Distance Operator Applied to Investment Selection Decision Making
by Victor G. Alfaro-Garcia, Fabio Blanco-Mesa, Ernesto León-Castro and Jose M. Merigo
Mathematics 2022, 10(12), 2100; https://doi.org/10.3390/math10122100 - 16 Jun 2022
Cited by 4 | Viewed by 1873
Abstract
Distance measures in ordered weighted averaging (OWA) operators allow the modelling of complex decision making problems where a set of ideal values or characteristics are required to be met. The objective of this paper is to introduce extended distance measures and logarithmic OWA-based [...] Read more.
Distance measures in ordered weighted averaging (OWA) operators allow the modelling of complex decision making problems where a set of ideal values or characteristics are required to be met. The objective of this paper is to introduce extended distance measures and logarithmic OWA-based decision making operators especially designed for the analysis of financial investment options. Based on the immediate weights, Bonferroni means and logarithmic averaging operators, in this paper we introduce the immediate weights logarithmic distance (IWLD), the immediate weights ordered weighted logarithmic averaging distance (IWOWLAD), the hybrid weighted logarithmic distance (HWLD), the Bonferroni ordered weighted logarithmic averaging distance (B-OWLAD) operator, the Bonferroni immediate weights ordered weighted logarithmic averaging distance (B-IWOWLAD) operator and the Bonferroni hybrid weighted logarithmic distance (HWLD). A financial decision making illustrative example is proposed, and the main benefits of the characteristic design of the introduced operators is shown, which include the analysis of the interrelation between the modelled arguments required from the decision makers and the stakeholders, and the comparison to an ideal set of characteristics that the possible companies in the example must portray. Moreover, some families, particular cases and brief examples of the proposed operators, are studied and presented. Finally, among the main advantages are the modeling of diverse perspectives, attitudinal characteristics and complex scenarios, through the interrelation and comparison between the elements with an ideal set of characteristics given by the decision makers and a set of options. Full article
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