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- Estimation problems in two types of uncertain varying coefficient models
with imprecise observations-
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Abstract: The varying coefficient model mitigates the curse of dimensionality in nonparametric regression as the number of explanatory variables increases. To address high-dimensional uncertain phenomena characterized by imprecise observations, this paper introduces two uncertain varying coefficient models, employing uncertain variables for robust modeling. Based on the least squares method, we use local linear and B-spline estimations for the two models with crisp and uncertain explanatory variables. To account for potential differences in smoothness among various coefficient functions, we propose two-step estimation procedures based on the two approaches to improve the fitting accuracy. In addition, residual analysis and uncertain hypothesis testing are performed to evaluate the suitability of the fitted model. Two numerical examples and an application involving weather data demonstrate the effectiveness of these methods.
PubDate: 2025-04-12
- Computing weighted overall equipment effectiveness based on a fuzzy
approach: a comparative study with an application-
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Abstract: This paper introduces a new method for calculating weighted Overall Equipment Effectiveness (OEE) by using fuzzy logic. Traditional crisp methods for computing weighted OEE have limitations due to the multiplicative nature of the OEE equation, leading to questionable outcomes. OEE is computed as the product of three key factors -Availability, Performance and Quality- that means that even a small reduction in any one factor results in a disproportionately lower OEE value. This multiplicative structure also makes it difficult to incorporate weighting mechanisms fairly. Previous literature has explored fuzzy logic-based approaches, particularly fuzzy rule-based methods, which do not necessitate the multiplication of OEE variables (Availability, Performance, and Quality). These fuzzy logic approaches can also handle system uncertainties and yield satisfactory results. However, there is currently no study in the literature for calculating weighted OEE by utilizing fuzzy rule-based techniques. The current paper outlines an approach to address this issue, accompanied by a case study conducted in an actual manufacturing company. Additionally, alternative weighted OEE computation methods are also evaluated for demonstrating suitability of the proposed approach.
PubDate: 2025-04-10
- Convergence criteria of fuzzy bilinear systems subject to bounded
uncertainties-
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Abstract: An effective method for examining stability and resolving different fuzzy controller design issues for Takagi–Sugeno (T–S) fuzzy systems, which encompass a broad category of nonlinear systems, is the linear matrix inequality approach. Moreover, the Lyapunov method is a very effective tool for studying the stability of this class of fuzzy systems. This paper explores the potential applications of these approaches for a class of perturbed fuzzy systems where the stability is considered for the nominal system, which is assumed to be bilinear with specific constraints on the uncertainties. We construct a fuzzy controller that guarantees the ultimate boundedness of the solutions of the uncertain bilinear Takagi–Sugeno fuzzy systems in order to study the convergence of solutions of the closed-loop system even in cases where the origin is not the equilibrium point of the system. One of the advantages of the method used in this work is the possibility of studying the convergence of trajectories towards a particular neighborhood of the origin which characterizes the asymptotic behavior of the system where a rate of convergence can be estimated. Furthermore, we show that the Van de Vusse reactor model illustrates the validity of the main result.
PubDate: 2025-04-02
- Fuzzy robust optimization for a dual-channel supply chain with blockchain
adoption under consumer perception and demand uncertainties-
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Abstract: A dual-channel supply chain with a supplier and a retailer is considered under customer product information perception uncertainty in the online channel and market demand uncertainty. The supplier may adopt blockchain in the online channel to ensure information transparency and enhance product traceability. Fuzzy robust optimization is used to deal with market demand uncertainty. The demand functions of the online and offline channels are set up. Stackelberg game models are formulated to analyze the problem, and backward induction is used to obtain robust equilibrium solutions. The impacts of the parameters on the equilibrium prices, demands, and profits of the supply chain and its members are analyzed. The theoretical results are verified through numerical experiments and corresponding managerial insights and suggestions are provided. The results show that blockchain adoption generally benefits the supplier, but not necessarily the retailer, by increasing product information transparency. Blockchain adoption may increase the supplier’s profit under strict conditions but may negatively impact the supply chain and its members under improper conditions. The prevalent supply chain contracts are explored to coordinate the dual-channel supply chain with blockchain adoption. The results show that the profit-sharing contract can, but the two-part tariff and the revenue-sharing contracts cannot, coordinate the dual-channel supply chain with blockchain adoption in the online channel.
PubDate: 2025-03-14
- A flexible soft nonlinear quantile-based regression model
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Abstract: There are several models for soft regression analysis in the literature, but relatively few are based on quantiles, and these models are limited to the linear case. As quantile-based regression models offer a series of benefits (like robustness and handling of asymmetric distributions) but have not been considered in the nonlinear case, we present the first soft nonlinear quantile-based regression model in this paper. Considering nonlinearity instead of limiting to linearity in the modeling brings numerous advantages such as a higher flexibility, more accurate predictions, a better model fit and an improved explainability/interpretability of the model. In particular, we embed fuzzy quantiles into nonlinear regression analysis with crisp predictor variables and fuzzy responses. We propose a new method for parameter estimation by implementing a three-stage technique on the basis of the center and the spreads. In the framework of this procedure, we utilize kernel-fitting, a least quantile loss function, least absolute errors, and generalized cross-validation criteria to estimate the model parameters. We perform comprehensive comparative analysis with other soft nonlinear regression models that have demonstrated superiority in previous studies. The results reveal that the proposed nonlinear quantile-based regression technique leads to better outcomes compared to the competitors.
PubDate: 2025-03-06
- Numerical solution of uncertain partial differential equations and its
applications-
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Abstract: Uncertain partial differential equations are widely used in practice, such as demography, traffic flows and so on. This paper proves an existence and uniqueness theorem for a class of uncertain partial differential equations. Then the properties of $$\alpha$$-path are given based on linear growth, Lipschitz and regular conditions. Since uncertain partial differential equations are difficult to get analytical solutions, this paper presents a formula which combines an uncertain partial differential equation with a class of classical partial differential equations. Based on the formula, an algorithm for calculating the inverse uncertainty distribution of solution of an uncertain partial differential equation is also deduced. Finally, expected value, extreme value, first hitting time, time and spatial integrals of the solution of uncertain partial differential equation are also discussed.
PubDate: 2025-02-18
- A highly accurate Mamdani fuzzy inference system for tennis match
predictions-
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Abstract: This paper presents a Mamdani fuzzy inference system (FIS) designed for predicting tennis match outcomes with greater accuracy compared to existing models such as the Weighted Elo (WElo) ranking system. By integrating factors like historical performance, surface-specific proficiency, and recent form trends, the Mamdani FIS provides a nuanced approach to forecasting match results. Central to this method is the optimization of membership functions using a Bacterial Evolutionary Algorithm (BEA), which fine-tunes parameters to better model uncertainties inherent in sports analytics. This is the further development of Nawa and Furuhashi’s original approach of fuzzy system parameter discovery, which operates on the stricter conditions concerning the membership function shapes. The study demonstrates that the Mamdani FIS outperforms the traditional methods in both predictive accuracy and profitability of betting strategies. Through extensive validation, the model achieves higher accuracy and lower log loss metrics, indicating improved reliability in prediction outcomes. Additionally, the Mamdani FIS consistently yields higher returns on investment across various betting scenarios, showcasing its practical utility in sports betting applications. Overall, the proposed Mamdani FIS represents a robust tool for tennis match prediction, with potential extensions to other sports and predictive contexts. Future research may explore incorporating additional variables and applying this fuzzy inference approach to broader areas of sports analytics.
PubDate: 2025-02-07
- On disaggregation modeling of uncertainty group preferences considering
trust networks-
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Abstract: Preference disaggregation is a common method used in multi-criteria decision aid (MCDA) to derive preference models and reproduce the preference information of decision makers (DMs). Due to cognitive uncertainty, DMs may not be able to accurately, directly, and deterministically portray their preferences based on their own cognition, causing difficulties when trying to efficiently merging group information. To explore reasonable resolutions, this article addresses the uncertainty in the preference information provided by DMs and portrays this information by utilizing uncertainty theory. Furthermore, it integrates group information by constructing social networks and analyzing the similarity of decision results of DMs. Specifically, a group preference learning model is designed to aggregate the diverse individual preference information into group decision-making in accordance with trust-similarity centrality. Ultimately, by fully utilizing this integrated information, a group decision-making recommendation is produced. For missing values in the trust network, the product axiom is used as a propagation operator to maximize the propagated trust. To illustrate the proposed model, it is applied to rank European countries in terms of their university qualities. Finally, the proposed model is compared with the existing models that incorporate preference disaggregation or social networks, and the effectiveness of the proposed model in handling uncertainty and the advantages in interpretability are demonstrated.
PubDate: 2025-01-24
- Multi-period fuzzy portfolio selection model with preference-regret
criterion-
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Abstract: In this paper, we explore a preference-regret decision problem for multi-period portfolio selection in a fuzzy environment. To do this, we first define a possibilistic preference-regret measure to quantify an investor’s regret for not holding the ex-post best-performing strategy. Then, we present a possibilistic preference-regret model with real investment constraints for multi-period fuzzy portfolio selection. In our proposed model, we assume that the investor aims to identify an optimal investment strategy that maximizes the cumulative possibilistic preference-regret concerning portfolio returns over the entire investment horizon. To enhance the practicality of our model, we incorporate several real-world investment constraints, including transaction costs, cardinality constraint, dependency constraint, and budget constraint. Furthermore, we develop an improved co-evolutionary particle swarm optimization algorithm to solve our proposed model. Finally, we conduct a comparative analysis using a numerical example to demonstrate the practicality of our model and validate the effectiveness of the solution algorithm.
PubDate: 2024-11-15
- Supply chain management based on uncertainty theory: a bibliometric
analysis and future prospects-
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Abstract: Uncertainty in the environment poses a significant challenge for supply chain management, and uncertainty theory is a branch of mathematics that focuses on analyzing uncertain phenomena. In this context, an increasing number of scholars have begun to use the uncertainty theory to study uncertain phenomena in the supply chain management, but there is still a lack of systematic literature reviews and research outlooks in this research field. To fill this gap, this paper provides a comprehensive and systematic review of the relevant literature in the Web of Science database from 2015 to May 2024 using bibliometric analysis and content analysis. First, bibliometric analysis is conducted to visualize the current state of research, including publication trends, keywords, authors, and geographical distribution. Then, through content analysis, the selected literature is categorized into seven subfields according to the research questions, including supply chain pricing decision, supply chain network disruption, supply chain network design, supply chain management considering sales efforts, sustainable supply chain management, supply chain contract design, and general supply chain management. The results indicate that the literature on the supply chain management based on the uncertainty theory is not yet mature. The research has begun to shift from single uncertainty to multidimensional uncertainty and from single-objective decision-making to multi-objective decision-making. The research direction has also shifted towards sustainability and resilience design in supply chain networks, gradually incorporating environmental and social benefits into supply chain decision-making. Based on the results of the bibliometric analysis and content analysis, future research directions are identified and potential related research opportunities are proposed, including the impact of consumer behavior, channel interaction, corporate social responsibility, and logistics service strategies on the supply chain management based on the uncertainty theory.
PubDate: 2024-10-10
- Music statistics: uncertain logistic regression models with applications
in analyzing music-
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Abstract: In the realm of data analysis, traditional statistical methods often struggle when faced with ambiguity and uncertainty inherent in real world data. Uncerainty theory, developed to better model and interpret such data, offers a promising alternative to conventional techniques. In this paper, we establish logistic regression models to initiate music statistics based on uncertainty theory. In particular, we will classify the music into different types named Baroque, Classical, Romantic, and Impressionism based on four characteristics: harmonic complexity, rhythmic complexity, texture complexity, and formal structure, with the help of the uncertain logistic models proposed. This theoretical framework for music classification provides a nuanced understanding of how music is interpreted under conditions of ambiguity and variability. Compared with the probabilistic counterpart, our approach highlights the versatility of uncertainty theory and provides researchers one much more feasible method to analyze the often-subjective nature of music reception, as well as broadening the potential applications of uncertainty theory.
PubDate: 2024-10-04
- LQ optimal control of uncertain fractional differential systems
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Abstract: This paper mainly emphasizes the linear quadratic optimal control problem of fractional differential systems based on uncertainty theory, which is an important tool for modeling belief degrees. First, a class of linear uncertain fractional differential equations is solved analytically by solving auxiliary linear uncertain differential equations. Then an equivalent uncertain optimal control model of the uncertain fractional LQ optimal control model is obtained, and the feedback form of its optimal control is deduced by dynamic programming. Finally, a numerical example is analyzed based on the obtained results.
PubDate: 2024-09-22
- Portfolio selection with second order uncertain dominance constraint
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Abstract: This paper proposes an uncertain mean-second order dominance model in the framework of uncertainty theory. By giving mean-expected utility equivalent, we show that the proposed model is suitable for rational and risk-averse investors because the portfolio produced by the model can give the investors the maximum expected return and in the meantime bring the investors expected utility value equal to or higher than the reference return no matter what specific utility functions the investors may take. By offering deterministic equivalents and comparing them with the uncertain mean-variance and uncertain mean-risk index models, we clarify the advantages of the proposed model, i.e., being easier to use and safer in investment. Furthermore, we give a numerical example and some experiments to illustrate the application of the model and the advantages of it.
PubDate: 2024-09-17
- Valuation of convertible bond based on uncertain fractional differential
equation-
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Abstract: Convertible bond is a hybrid financial derivative with the properties of debt and equity, which provides the holder with a right to convert bond into the issuer’s stock at a prescribed ratio in the future. This paper analyzes the valuation problems of convertible bond on the basis of uncertain fractional differential equation. Then the prices of convertible bond are obtained by means of expected value criterion and optimistic value criterion, respectively. Besides, numerical examples are given to compare expected value models with optimistic value models. Finally, an empirical study is provided to illustrate that the uncertain fractional stock model is superior to the classical stochastic model.
PubDate: 2024-09-14
- China’s carbon emission allowance prices forecasting and option
designing in uncertain environment-
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Abstract: Carbon emissions trading is pivotal for advancing China’s low-carbon goals. As the primary tradable asset in the carbon market, carbon emission allowances inevitably experience price fluctuations. However, numerous empirical studies show that the frequency of real-world data is highly unstable, which results in the failure of probabilistic modeling. Therefore, this paper aims to model the dynamics of carbon emission allowance prices in China using four mainstream uncertain differential equations. The optimal model is chosen through rolling window cross-validation using the criterion of minimizing average testing errors. Parameters of the optimal model are determined by moment estimation based on residuals, and the model’s effectiveness is also assessed through uncertain two-sided hypothesis testing. Additionally, we forecast carbon emission allowance prices and their 95% confidence intervals for the next 14 business days. To manage trading risks, we propose a customized carbon option contract for pricing European carbon options and conduct sensitivity analysis on key parameters. Finally, we present a paradox of stochastic differential equations for modeling carbon emission allowance prices.
PubDate: 2024-09-09
- Are the queueing systems in practice random or uncertain' Evidence from
online car-hailing data in Beijing-
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Abstract: In order to rationally characterize the nondeterministic phenomena in queueing systems, there exist two mathematical systems, one is probability theory concerned with the analysis of random phenomena and the other is uncertainty theory concerned with the analysis of uncertain phenomena. Before using the above two mathematical systems to model the real queueing systems, we often need to face such a question, are the real queueing systems random or uncertain' In order to answer this question, we collect the arriving times of passengers from online car-hailing platform in Beijing, and then analyze the collected data based on stochastic renewal process and uncertain renewal process. Finally, by comparing samples and confidence intervals of the total numbers of passengers arriving on the online car-hailing platform under two mathematical systems, we come to the conclusion that the queueing systems in the real world are uncertain rather than random.
PubDate: 2024-09-05
- Modeling of linear uncertain portfolio selection with uncertain constraint
and risk index-
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Abstract: Since securities market is subject to a great deal of uncertainty and complexity, the return of securities cannot be accurately estimated by historical data. In this case, it must use experts’ knowledge and judgment. Therefore, we investigate portfolio selection problems in such uncertain environments. First, this paper regards the rate of return on security as an uncertain variable which obeys linear uncertainty distribution, and then provides the analytical expressions of the corresponding risk, return and risk index in the uncertain portfolio selection environment. Afterwards, we construct three types uncertain portfolio selection models with uncertain constraint, namely, the minimizing risk, the maximizing return and the maximizing belief degree. Meanwhile, in order to more intuitively reflect the investor’s sense of loss, three types uncertain portfolio selection models considering both uncertain constraint and risk index are also constructed. These models are transformed into corresponding deterministic models. Finally, through an example analysis, this paper obtains the portfolio selection strategies under different objectives, compares the results under different models, and analyzes the sensitivity of the parameters.
PubDate: 2024-07-24
- Prediction of global trade network evolution with uncertain multi-step
time series forecasting method-
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Abstract: Predicting the evolutionary trends of complex systems is a critical issue in the field of complex system science. Based on the uncertain theory framework, this study proposes an uncertain multi-step time series forecasting aimed at predicting trends of network evolution, and applies it to the prediction of the future development of the global trade network. Specifically, this study utilizes inter-country input–output tables to construct the global trade network based on social network analysis methods. Furthermore, supply-side and demand-side trade dependency indicators are proposed to identify the evolutionary characteristics of the global trade network. The uncertain multi-step time series forecasting is subsequently utilized to predict network evolution in 2025–2035, and the network associations between China and the five regional trading blocs and countries are mainly analyzed. This study broadens the theoretical approaches for predicting the future evolution of complex systems.
PubDate: 2024-07-18
- Pricing of shout option in uncertain financial market
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Abstract: The shout option allows the investors to make "shouts" to the seller throughout the option’s duration. The investors’ payoff is higher between the intrinsic value at shout time and the intrinsic value at the maturity time. Previous shout option pricing is in the framework of probability theory. However, some unexpected events in real life can make the frequency deviate from the estimated distribution function, in which case we should use the uncertainty theory. This study investigates shout option pricing problems under uncertainty theory. It also derives pricing formulas for shout-call and shout-put options. Additionally, we design a numerical algorithm to compute the price of the shout options. Finally, this study applies the concept of the shout option to Microsoft’s stock data and examines the relationship between the option price and crucial parameters.
PubDate: 2024-07-12
- Pricing and carbon reduction decisions for a new uncertain dual-channel
supply chain under cap-and-trade regulation-
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Abstract: This study concentrates on the pricing issue in a low-carbon dual-channel (DC) supply chain, where the upper-level manufacturer is regulated by the cap-and-trade (CAT) mechanisms. Market demand is a key factor affecting pricing decision and demand uncertainty complicates the pricing problem. To deal with the challenge that only partial demand distribution information is available, this paper proposes a novel ambiguity distribution set to depict the uncertain demand. Under the proposed ambiguity distribution set, a robust fuzzy bi-level optimization pricing model is developed for the low-carbon DC supply chain. Three CAT regulation mechanisms, no CAT regulation, grandfathering (GF) mechanism and benchmarking (BM) mechanism, are considered to address the manufacturer’s CAT regulation. The analytically tractable counterpart of the proposed model is derived and the corresponding robust equilibrium solutions are obtained under three CAT mechanisms. Numerical analyses are carried out to explore the impact of the demand uncertainty on the manufacturer’s selection of the CAT regulation mechanism. The numerical results indicate that the uncertainty degree can change the manufacturer’s selection of the regulated mechanisms. Specifically, when the uncertainty degree is smaller, the BM mechanism is beneficial for the manufacturer comparing with the GF mechanism; when the uncertainty degree is bigger, the manufacturer prefers to GF mechanism rather than BM mechanism.
PubDate: 2024-06-27
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