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Mathematical, Statistical, and Soft Computing Methods for Uncertainty Management

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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: closed (15 December 2023) | Viewed by 10510

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Prof. Dr. José Álvarez-García

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Financial Economy and Accounting Department, Faculty of Business, Finance and Tourism, University of Extremadura, 10071 Cáceres, Spain
Interests: business; finance and tourism; resource and service management, natural resource, sustainable rural development, water resources management, financial economics; accounting and management; sustainability; entrepreneurship; innovation; quality and environmental management systems.
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Prof. Dr. Oscar V. De la Torre-Torres

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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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Prof. Dr. María de la Cruz del Río-Rama

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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 resource, sustainable rural development, water resources management, financial economics; accounting and management; sustainability; entrepreneurship; innovation; quality and environmental management systems
Special Issues, Collections and Topics in MDPI journals

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:

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

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. 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 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

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

Published Papers (7 papers)

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Research

21 pages, 1752 KiB

Open AccessArticle

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 - 02 Feb 2024

Viewed by 837

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.

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

(This article belongs to the Special Issue Mathematical, Statistical, and Soft Computing Methods for Uncertainty Management)

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20 pages, 10168 KiB

Open AccessArticle

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 1002

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 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

(This article belongs to the Special Issue Mathematical, Statistical, and Soft Computing Methods for Uncertainty Management)

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16 pages, 655 KiB

Open AccessArticle

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 1014

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 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

(This article belongs to the Special Issue Mathematical, Statistical, and Soft Computing Methods for Uncertainty Management)

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19 pages, 952 KiB

Open AccessArticle

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 - 08 Nov 2022

Cited by 4 | Viewed by 1512

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 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

(This article belongs to the Special Issue Mathematical, Statistical, and Soft Computing Methods for Uncertainty Management)

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14 pages, 2221 KiB

Open AccessArticle

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 932

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 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

(This article belongs to the Special Issue Mathematical, Statistical, and Soft Computing Methods for Uncertainty Management)

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21 pages, 1100 KiB

Open AccessArticle

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 2051

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, 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

(This article belongs to the Special Issue Mathematical, Statistical, and Soft Computing Methods for Uncertainty Management)

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13 pages, 676 KiB

Open AccessArticle

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 3 | Viewed by 1554

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 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

(This article belongs to the Special Issue Mathematical, Statistical, and Soft Computing Methods for Uncertainty Management)

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