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Abstract: Abstract Theoretical analysis and empirical study results all show that there are situations in reality where observed data are not random variables. Thus, decision-making criteria based on probability theory are not suitable for people to make decisions. This paper proposes an uncertain dominance based on uncertainty theory to offer an alternative decision-making criterion for such situations. The paper first defines a new criterion of first- and second-order uncertain dominance, then proves some necessary conditions of them based on uncertainty theory. Some sufficient and necessary conditions of the first- and second-order uncertain dominance are given when uncertain variables are all normal or linear uncertain variables. In addition, the paper proves the link between the uncertain dominance criterion and the expected utility criterion and shows that the first-order uncertain dominance is suitable for all people to make decisions and the second-order uncertain dominance is suitable for risk-averse people to make decisions. PubDate: 2023-12-01
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Abstract: Abstract This paper deals with an inverse data envelopment analysis (DEA) based on the non-radial slacks-based model in the presence of uncertainty employing both integer and continuous interval data. To this matter, suitable technology and formulation for the DEA are proposed using arithmetic and partial orders for interval numbers. The inverse DEA is discussed from the following question: if the output of \(DMU_o\) increases from \(Y_o\) to \(\beta _o\) , such the new DMU is given by \((\alpha _o^*,\beta )\) belongs to the technology, and its inefficiency score is not less than t-percent, how much should the inputs of the DMU increase' A new model of inverse DEA is offered to respond to the previous question, whose interval Pareto solutions are characterized using the Pareto solution of a related multiple-objective nonlinear programming (MONLP). Necessary and sufficient conditions for input estimation are proposed when output is increased. A functional example is presented on data to illustrate the new model and methodology, with continuous and integer interval variables. PubDate: 2023-12-01
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Abstract: Abstract The price prediction is valuable in energy management system (EMS) because it allows making informed decisions and solving the problem of the uncertainty related to the future ignorance based only on the past knowledge. To this goal, we present in this paper a two-steps EMS in order to control the different operations of a micro-grid (MG). In the first step, we exploit the advantages of the Bidirectional Long-Short Term Memory (BiLSTM) deep learning model to predict the next daily electricity price based on time series. In the second step, we use a type-2 fuzzy logic controller to decide which energy source will exploit the excess energy produced or meet the MG need. Real data is used in this paper to test the effectiveness of the proposed EMS whose superiority is proved through the test period. The BiLSTM forecasting model better performs compared to other related algorithms designed to the electricity price prediction. In addition, the proposed decision-making process can reduce the total MG cost and protect the batteries against the deep discharge and maximum charge in order to prolong their lifespan. We expect that this work can contribute to meet the real-world needs in the management of the electrical system. PubDate: 2023-12-01
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Abstract: Abstract Support vector machines have been widely applied in binary classification, which are constructed based on crisp data. However, the data obtained in practice are sometimes imprecise, in which classical support vector machines fail in these situations. In order to handle such cases, this paper employs uncertain variables to describe imprecise observations and further proposes a hard margin uncertain support vector machine for the problem with imprecise observations. Specifically, we first define the distance from an uncertain vector to a hyperplane and give the concept of a linearly α-separable data set. Then, based on maximum margin criterion, we propose an uncertain support vector machine for the linearly α-separable data set, and derive the corresponding crisp equivalent forms. New observations can be classified through the optimal hyperplane derived from the model. Finally, a numerical example is given to illustrate the uncertain support vector machine. PubDate: 2023-12-01
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Abstract: Abstract COVID-19 has been declared a pandemic and countries are tackling this disease either through preventative measures such as lockdown and sanitization or through curative ones such as medication, isolation, and so on. Some people believe that vaccination is the best way to prevent this disease, while others disagree. Society’s attitudes toward vaccination can be influenced by a variety of factors such as misunderstanding, ambiguity, lack of knowledge. The proposed study’s goal is to better understand people’s attitudes regarding vaccination by focusing on key topics related to COVID-19 anti-vaccine tweets. Tweets are obtained over a period based on the number of COVID-19 cases by utilizing the “anti-vaccine” keyword rather than the “vaccine” keyword. Furthermore, in addition to people perceptions and attitudes toward anti-vaccination, the causal relationship between each topic is investigated. As a result, latent dirichlet allocation (LDA), fuzzy association rule mining (FARM), fuzzy cognitive map (FCM), and fuzzy c-means are used to conduct a complete study. Topics are analyzed independently using clustering and scenario analysis. The findings demonstrate the most common topics in anti-vaccination tweets, as well as the influence of each topic on the others. PubDate: 2023-12-01
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Abstract: Abstract One of the main challenges in the security of energy supply in modern power systems is the frequency deviation. Appearance of an imbalance between the demand and supply of electrical energy is the main reason for any change in the frequency level of the grid. Thus, the Load Frequency Control (LFC) operation is usually performed automatically to restore the stability in the frequency level of the system. LFC has been studied with different controllers previously. However, this study concentrates on proposing a new configuration for the Fuzzy Logic Controller (FLC) to be implemented in the modeling of a test two-area power system under two different operational conditions and challenges to analyze its performance. A Third-Order Fermat Curve-based Fuzzy Inference System (TOFC-FIS) is designed for the FLC with the aim of optimizing the performance of type-I FLCs in the LFC application. The motive for this study was to mathematize the FIS of FLC to prepare a basis for further performance enhancement using optimization algorithms. Thus, the proposed FIS is optimized using a Neural Network (NN) to create an Adaptive Neuro-Fuzzy Inference System for the FLC in the studied scenarios. The results of typical and NN-trained TOFC-FIS-based FLC illustrate the considerable improvement in performance indexes of LFC in two-area power systems compared to both conventional and intelligent control methods. PubDate: 2023-12-01
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Abstract: Abstract In recent years, the researches on parameter estimation of uncertain differential equations have developed significantly. However, when we deal with some nonparametric uncertain differential equations, the parameter estimation may not be used directly. To deal with these uncertain differential equations, it is important to consider the nonparametric estimation with the help of the observations. As an important branch of uncertain differential equation, autonomous uncertain differential equation may be properly applied to model some uncertain autonomous dynamic systems. In this paper, we propose a Legendre polynomial based method for the nonparametric estimation of autonomous uncertain differential equations. After that, some numerical examples are given and the residuals as well as uncertain hypothesis tests are used to prove the acceptability of these estimations. In application, we consider an atmospheric carbon dioxide model by the proposed method of nonparametric estimation. PubDate: 2023-12-01
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Abstract: Abstract Multivariate uncertain calculus is a branch of mathematics that deals with differentiation and integration of uncertain fields based on uncertainty theory. This paper defines partial derivatives of uncertain fields for the first time by putting forward the concept of Liu field. Then the fundamental theorem, chain rule and integration by parts of multivariate uncertain calculus are derived. Finally, this paper presents an uncertain partial differential equation, and gives its integral form. PubDate: 2023-11-20
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Abstract: Abstract Uncertain partial differential equation (UPDE) was introduced in literature. But the solution of a UPDE was not defined well. In this article, we will rigorously give a suitable concept of a UPDE and define its solution by an integral equation. Then, some examples are given to show the rationality of the definition. Uncertain heat conduction equation is presented as an application of UPDE. For those UPDEs having no analytic solutions, \(\alpha\) -path method is introduced to obtain the inverse uncertainty distributions of solutions to UPDEs. PubDate: 2023-11-19
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Abstract: Abstract Pairwise comparisons have been a long-standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision-making methods such as the Analytic Hierarchy/Network Process (AHP/ANP), the Best-Worst method (BWM), PROMETHEE and many others. Pairwise comparisons can be performed within several frameworks such as multiplicative, additive and fuzzy representations of preferences, which are particular instances of a more general framework based on Abelian linearly ordered groups. Though multiplicative, additive and fuzzy representations of preferences are widely used in practice, it is unknown whether decision makers are equally precise in the three aforementioned representations when they measure objective data. Therefore, the aim of this paper is to design, carry out and analyse an experiment with over 200 respondents (undergraduate university students) from two countries, Czechia and Italy, to compare precision of the respondents in all three representations. In the experiment, respondents pairwise compared (by approximation) the areas of four geometric figures and then, the imprecision of their assessments was measured by computing the distance with the exact pairwise comparisons. We grouped the respondents in such a way that each participant was allowed to deal with a unique type of representation. The outcomes of the experiment indicate that the multiplicative approach is the most precise. PubDate: 2023-11-03
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Abstract: Abstract Uncertainty theory is an area in axiomatic mathematics recently proposed by Professor Baoding Liu and aiming to deal with belief degrees. Retrieving 1004 journal articles from the Web of Science database between 2008 and 2019, and utilizing CiteSpace and Pajek software, we analyze the publications per year and by geographical distribution, productive scholars and their cooperation, key journals, highly cited articles and main paths of the field. In this way, seven key sub-fields of uncertainty theory and their research potential are derived. The results show the following: (1) The literature on uncertainty theory follows a linear growth trend, involves an extensive network of 1000 scholars worldwide and is published in 300 journals, indicating thus that uncertainty theory has become increasingly attractive, and its academic influence is gradually expanding. (2) Seven key sub-fields of uncertainty theory have clearly been identified, including the axiomatic system, uncertain programming, uncertain sets, uncertain logic, uncertain differential equations, uncertain risk analysis, and uncertain processes. Among them, uncertain differential equations and programming are the two main sub-fields with the largest numbers of published papers. Furthermore, for evaluating the research potential of sub-fields, maturity and recent attention indicators are calculated using the citations, total number of publications, quantity of most cited literature and half-life. Based on these indicators, uncertain processes shows the greatest development potential, and has remained a hot topic in recent years, being mainly concentrated on the uncertain renewal reward process, optimal control of discrete-time uncertain systems, and uncertain linear quadratic optimal control. Additionally, uncertain risk analysis is ranked second, and focuses on the analysis of expected losses, investment risk, and structural reliability of uncertain systems. PubDate: 2023-09-01 DOI: 10.1007/s10700-022-09400-4
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Abstract: Abstract In fuzzy decision-making, the probabilistic linguistic term sets (PLTSs) are flexible in depicting people’s linguistic evaluations. As the uncertainty measures of PLTSs, entropy and cross-entropy are the important decision-making tools. Generally speaking, the uncertainty of PLTSs can be studied from two facets, which are known as hesitancy and fuzziness. To better reflect these uncertainties, some hybrid entropy and cross-entropy measures of PLTSs are developed in this work. It is shown that the hybrid entropy measures are simple in structure, clear in physical meaning and strong in discriminating ability, while the hybrid cross-entropy measures can avoid the design flaws of existing measures and possess natural symmetry. It is also shown that the hybrid entropy and cross-entropy measures can be designed in pairs, mutually supportive and inherently unified as the uncertainty measures. In the ends, a multi-attribute decision-making (MADM) model, based on these uncertainty measures of PLTSs, is developed within the famous TOPSIS framework to select the best cloud computing platform. PubDate: 2023-09-01 DOI: 10.1007/s10700-022-09398-9
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Abstract: Abstract In actual dynamic system, uncertainty is absolute and certainty is relative. This paper presents the optimal dynamic pricing and production control strategy for perishable products in finite horizon. The influence of external environmental disturbance on the system is considered by means of a special uncertain process (Liu process). Then based on uncertainty theory and Hurwicz criterion, the optimization model is built, where control variables are restricted to an admissible control set. In addition, uncertain differential equation is used to describe the changes of inventory. By applying the optimality equation, we determine the optimal price and production strategy to maximize profit. Besides, both the optimal price and production rate are linearly decreasing with inventory. Afterwards, two numerical examples are given, the results reveal that reducing the uncertain disturbance of inventory and expanding the potential market size are beneficial to improving the optimal profit. Moreover, risk-loving decision makers can gain more profits while facing large risks. PubDate: 2023-09-01 DOI: 10.1007/s10700-022-09396-x
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Abstract: Abstract COVID-19's developing trend has put the waste management systems of governments all over the world in jeopardy. The increasing rise of infectious medical waste has now become a serious problem. This paper presents a multi-period multi-objective model for designing a medical waste management system during the COVID-19 pandemic. The model aims to reduce total costs of infectious medical waste management while also reducing the environmental impact of treatment centers, disposal centers, and transportation. It also aims to maximize the suitability of treatment technology based on social considerations and reduce the risk associated with processing and transporting COVID-19 waste. Different strategic and operational decisions are taken into account that include the selection of treatment technologies, the location of treatment and disposal centers, the flow of generated medical waste between facilities, and the number of vehicles required for the medical waste transport. The model tackles the uncertainty associated with model parameters, and it uses a credibility-based possibilistic programming method to deal with uncertainties. The suggested model is solved using an interactive fuzzy programming method and the importance of social indicators for selecting treatment technology is determined using the fuzzy best–worst approach. The effectiveness of the model is demonstrated by a practical case study in Shiraz, Iran. The numerical results can help system designers to achieve the most suitable trade-off between the sustainability goals and the safety viewpoint. PubDate: 2023-09-01 DOI: 10.1007/s10700-022-09401-3
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Abstract: Abstract In the framework of uncertainty theory, this paper investigates the pricing problem of American swaption. By assuming that the floating interest rate obeys an uncertain differential equation, the pricing formula of American swaption is derived. Furthermore, parameter estimation of the uncertain interest rate model is given, and the uncertain hypothesis test shows that the uncertain interest rate model fits the Shanghai interbank offered rate well. Finally, as a byproduct, this paper also indicates that stochastic differential equations cannot model real-world interest rates. PubDate: 2023-09-01 DOI: 10.1007/s10700-022-09399-8
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Abstract: Abstract This paper extends the potential function and consistency to the Owen value for fuzzy cooperative games with a coalition structure. First, we prove that the unique payoff index satisfying the potential function is the Owen value. Then, we characterize the Owen value for fuzzy cooperative games with a coalition structure by fuzzy balanced contributions and fuzzy consistency, respectively. Finally, an example in supply chain is given to illustrate the relationship between the Owen value and potential function for fuzzy cooperative games with a coalition structure and solve the problem of payoff distribution in supply chain under fuzzy environment. PubDate: 2023-09-01 DOI: 10.1007/s10700-022-09397-w
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Abstract: Abstract In Bayesian rule an unknown parameter is thought to be a quantity whose variation can be characterized by a prior distribution. Then some data are observed from a population whose distribution function is indexed by the unknown parameter and then the prior distribution is updated according to the observed data. The updated prior distribution is named as the posterior distribution. Based on uncertainty theory, this paper first makes a connection between posterior uncertainty distribution and likelihood function, and proposes a new method to obtain the posterior uncertainty distribution from the prior uncertainty distribution with given observed data. Some examples with special uncertainty distributions are employed to explain the calculation. Furthermore, an uncertain urn problem is provided to illustrate the application of the new method. PubDate: 2023-09-01 DOI: 10.1007/s10700-022-09395-y
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Abstract: Abstract Since the concept of uncertain partial differential equations (UPDEs) was proposed, it has been developed significantly and led us to study parameter estimation for UPDEs. This paper proposes a concept of residual of a class of UPDEs, which follows a linear uncertainty distribution. Afterwards, an \(\alpha\) -path of a class of UPDEs is introduced and the important result that the inverse uncertainty distribution of solution of a class of UPDEs is just the \(\alpha\) -path of the corresponding UPDEs is reached. And a numerical method is designed to obtain the inverse uncertainty distribution of solution of UPDEs. In addition, based on the \(\alpha\) -path and the inverse uncertainty distribution, an algorithm is designed for calculating the residuals of UPDEs corresponding to the observed data. Then a method of moments to estimate unknown parameters in UPDEs is provided. Furthermore, uncertain hypothesis test is recast to evaluate whether an uncertain partial differential equation fits the observed data. Finally, the method of moments is applied to modeling China’s population and the fitness of the estimated parameters is verified by using uncertain hypothesis test. PubDate: 2023-08-01 DOI: 10.1007/s10700-023-09415-5
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Abstract: Abstract Uncertainty theory, founded in 2007, has become a branch of mathematics to model uncertainty rather than randomness. As an indispensable part of uncertainty theory, uncertain graph and uncertain network optimization has received the wide attention of many scholars. Naturally, a series of original research achievements have been obtained on uncertain graph and uncertain network optimization. This paper aims to present a state-of-the-art review on the recent advance in uncertain graph and uncertain network optimization. Furthermore, it hopes to predict the possible future research directions. Based on Web of Science database, this paper retrieves 144 related papers from 2011 to 2021 to analyze the features of published articles. More precisely, we analyze the annual number of publications, key topics and sub-fields, journals, and most-cited articles. In addition, the main results and models for uncertain graph and uncertain network optimization are summarized. Furthermore, the limitations of existing literature and the possible development trend are discussed. PubDate: 2023-06-08 DOI: 10.1007/s10700-023-09413-7
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Abstract: Abstract The Best–Worst Method (BWM) has been recently proposed to derive the weights of criteria using two vectors of the pairwise comparison. For BWM, the best criteria and the worst criteria of alternatives are first determined by the decision-maker (DM). Then, the DM gives his best-to-others vector (BV) and the others-to-worst vector (WV). In this paper, we show that the BV and WV can intrinsically be formulated as an incomplete reciprocal matrix, we call it BWM matrix. Thus, to derive the weights for BWM can be transformed to derive the weights from an incomplete reciprocal preference relation. In this view, we present several models to derive priority weights from a BWM matrix. Especially, we also show that the initial BWM model is a special case of our proposed method, the concept of efficiency is extended to the incomplete reciprocal preference relation. Furthermore, these methods are extended to derive the priority weights for group decision making problems. Additionally, some inconsistency indices are introduced to measure the inconsistency degree of a BWM matrix. Finally, one example is illustrated to derive the optimal weights from a BWM matrix and another example is illustrated to show the efficiency of the weight vectors, respectively. Monte Carlo simulations and comparative analyses are carried out to show the effectiveness of the proposed priority methods. PubDate: 2023-06-04 DOI: 10.1007/s10700-023-09410-w
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