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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: 2023-03-20
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Abstract: Abstract Explainability is considered essential in enabling artificial intelligence (AI) in some crucial industries, e.g., healthcare and banking. However, conventional algorithms suffer a trade-off between readability and performance, encouraging the emergence of explainable AI. In this paper, we propose a novel method to form the hierarchical Choquet integral (HCI) as an explainable AI to retain the model's accuracy and explainability. To achieve this purpose, we first adopted neuroevolution, which combines a genetic algorithm (GA) and a neural network (NN), and pruned weights to obtain information about the hierarchical decomposition of the Choquet integral. We then fine-tuned the weights of the HCI model for the classification problem. In addition, we use four datasets to illustrate the proposed algorithm and compare the results with the conventional classifiers: decision tree, deep learning, and support vector machine (SVM). The empirical results indicate that the proposed algorithm outperforms others in terms of accuracy, and keeps the Choquet integral's explainable property, justifying this paper's contribution. PubDate: 2023-03-01
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Abstract: Abstract It is very common to use linguistic information to solve decision-making problems in real life, and the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) has been widely used because of its powerful ability of expressing complex linguistic information. There is no doubt that the comparison method of double hierarchy hesitant fuzzy linguistic elements (DHHFLEs) not only occupies an important theoretical and practical position, but also is the basis for further study of DHHFLTSs. However, the existing comparison methods of DHHFLEs still have some limitations. Therefore, this paper proposes a new DHHFLE comparison method, which is an improvement and perfection of the existing DHHFLE comparison methods. In addition, considering that the current research on distance and similarity measures of DHHFLEs is mostly based on the algebraic point of view, this paper proposes a cosine similarity measure of DHHFLEs, which fills the gap in the study of distance and similarity measures from the geometric point of view. Then, the cosine similarity-based DHHFL-ELECTRE II method is proposed to solve the multi-attribute decision-making (MADM) problem in the double hierarchy hesitant fuzzy linguistic environment. Finally, this method is used to solve a MADM problem in the performance evaluation of financial logistics enterprises. The results show that the proposed method has certain applicability and feasibility. PubDate: 2023-03-01
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Abstract: Abstract This work implements the BFGS (Broyden-Fletcher-Goldfarb-Shanno) optimization method for training the type-1 and singleton fuzzy logic system applied to solve binary classification problems. The BFGS is a quasi-Newton method that approximates the second-order information using the gradient of the cost function. Additionally, the Golden Section method is used to obtain the step size for each line search in a descent direction. The effectiveness of the proposed method is demonstrated by using well-established classification metrics evaluated in popular datasets from the literature. Comparisons between the proposed approach and well-known gradient-based methods available are also provided, showing that the BFGS achieves improved performance in terms of accuracy, mean squared error, and the number of epoch demanded during the training phase. PubDate: 2023-03-01
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Abstract: Abstract Since the concept of uncertain fractional differential equations was proposed, its wide range of applications have urged us to consider parameter estimation for uncertain fractional differential equations. In this paper, based on the definition of Liu process, we construct a function of unknown parameters which follows a standard normal uncertainty distribution. Then the method of moments is used to build a system of equations whose solutions are the estimated values of unknown parameters. After that, an algorithm of parameter estimation for a special uncertain fractional differential equation is proposed. Finally, the algorithm is applied to two numerical examples and the acceptability of the estimated parameters is proved by using uncertain hypothesis test. PubDate: 2023-03-01
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Abstract: Abstract The necessarily optimal solution is known as the most reasonable solution to linear programming problems with interval/fuzzy objective function coefficients. As it remains optimal against the certain fluctuations of objective function coefficients, the necessarily optimal solution can be seen as a robust optimal solution. In this paper, we demonstrate that the necessary optimality degree of a non-degenerate basic feasible solution can be obtained easily by utilizing the tolerance approach. The necessary optimality degree evaluates to what extent the solution remains optimal against the fluctuations of objective function coefficients. Several types of fuzzy subsets showing the possible range of the objective function coefficient vector are considered. For each type of fuzzy subset, an efficient calculation method of necessary optimality degree is proposed. Numerical examples are given to illustrate the proposed methods. PubDate: 2023-03-01
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Abstract: Abstract In this paper, the definitions of Clarke generalized directional \(\alpha \) -derivative and Clarke generalized gradient are introduced for a locally Lipschitz fuzzy function. Further, a nonconvex nonsmooth optimization problem with fuzzy objective function and both inequality and equality constraints is considered. The Karush-Kuhn-Tucker optimality conditions are established for such a nonsmooth extremum problem. For proving these conditions, the approach is used in which, for the considered nonsmooth fuzzy optimization problem, its associated bi-objective optimization problem is constructed. The bi-objective optimization problem is solved by its associated scalarized problem constructed in the weighting method. Then, under invexity hypotheses, (weakly) nondominated solutions in the considered nonsmooth fuzzy minimization problem are characterized through Pareto solutions in its associated bi-objective optimization problem and Karush-Kuhn-Tucker points of the weighting problem. PubDate: 2023-03-01
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Abstract: Abstract In this paper, we propose an uncertain energy model with a time-varying volatility factor to describe the electricity and gas futures price dynamics. The corresponding spark-spread option pricing problem is also discussed. Numerical experiments show the effectiveness of proposed pricing method. Compared with the existing stochastic models, our uncertain energy model has a better performance to catch the price evolution of both gas and electricity futures. PubDate: 2023-03-01
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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: 2023-01-21
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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: 2023-01-17 DOI: 10.1007/s10700-023-09407-5
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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: 2023-01-06 DOI: 10.1007/s10700-022-09406-y
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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: 2023-01-02 DOI: 10.1007/s10700-022-09405-z
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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: 2023-01-01 DOI: 10.1007/s10700-022-09403-1
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Abstract: Abstract All existing methods to estimate unknown parameters in uncertain differential equations are based on difference scheme, and do not work when the time intervals between observations are not short enough. In order to overcome this shortage, this paper presents a concept of residual. Afterwards, an algorithm is designed for calculating residuals of uncertain differential equation corresponding to observed data. In addition, this paper presents a method of moments based on residuals to estimate the unknown parameters in uncertain differential equations. Finally, some examples (including Alibaba stock price) are provided to illustrate the parameter estimation method. PubDate: 2022-12-01 DOI: 10.1007/s10700-021-09379-4
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Abstract: Abstract In the literature, a BitTorrent-like peer-to-peer file-sharing system has been modelled as a system of addition-min fuzzy relational inequalities (FRIs). Finding all minimal solutions of such a system is considered a difficult task because the minimal solutions to addition-min FRIs are usually not unique and are often infinite in number. In this paper, we study the properties of the minimal solutions of such a system and propose an iterative algorithm to find the minimal solutions for any given solution (included the maximum solution). The proposed algorithm not only finds the minimal solutions efficiently, but also finds many minimal solutions in different iterative sequences of variables. PubDate: 2022-12-01 DOI: 10.1007/s10700-021-09377-6
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Abstract: Abstract Cost-allocation problems in a fixed network are concerned with distributing the costs for use by a group of clients who cooperate in order to reduce such costs. We work only with tree networks and we assume that a minimum cost spanning tree network has already been constructed and now we are interested in the maintenance costs. The classic problem supposes that each agent stays for the entire time in the same node of the network. This paper introduces cost-allocation problems in a fixed-tree network with a set of agents whose activity over the nodes is fuzzy. Agent’s needs to pay for each period of time may differ. Moreover, the agents do not always remain in the same node for each period. We propose the extension of a very well-known solution for these problems: Bird’s rule. PubDate: 2022-12-01 DOI: 10.1007/s10700-021-09375-8
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Abstract: Abstract For several classes of decisions, the use of target-based decision analysis (TBDA) is more appropriate than utility analysis. Recent literature on TBDA mainly focuses on different expression forms of targets and performance levels, and on different types of aggregation operators in terms of multi-attribute preference functions. However, different expression forms are usually introduced separately in literature, which cannot fully support the inherent complexity of problems along with different perception and knowledge levels of decision makers during assessing targets and performance levels. Furthermore, although there are attractive features of multilinear target-based preference functions (MTPFs), its applications are seldom considered because of the complexity of identifying their coefficients. In order to solve these two issues, an integrated approach is proposed for multilinear hybrid-information target-based decision analysis, which can deal with diverse forms of targets and performance levels, and identify the coefficients of MTPFs. First, given targets and performance levels for each attribute being expressed in multiple forms simultaneously, a generalized procedure is proposed to transform different forms into probability distributions, and to measure probability of target achievement for each attribute. Second, a novel procedure to identify the coefficients of MTPFs is proposed. This procedure is based on the multilinear model and 2-additive fuzzy measures, which is based on the equivalence between multilinear model based on fuzzy measures and MTPFs. The approach is applied to a case study involving customer competitive evaluation of smart thermometer patches to demonstrate its feasibility and advantages. PubDate: 2022-12-01 DOI: 10.1007/s10700-021-09378-5
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Abstract: Abstract As an important research direction, operational research (OR) has always attracted scholars worldwide. We study the structure, trend and prospect in the OR field by conducting a bibliometric analysis of publications in the period of 1952–2020, which are included in the Web of Science (WoS) database. Using three effective bibliometric tools, namely, VOS viewer, CiteSpace, and Bibliometrix, a total of 5,353 publications were retrieved to show clear visual results using a series of scientific analyses. First, a performance analysis revealed the basic characteristics of publications considering the type distribution, annual trend, quantity and quality. Then, a cooperation analysis presented the influential countries/regions and showed the relationships among countries/regions, institutions and authors during different periods based on bibliometric indicators and co-authorship networks. Moreover, a keyword analysis was conducted to investigate the hot topics and development of the OR field, using co-occurrence analysis, timeline view analysis and evolution analysis. Finally, we discussed the implications and limitations, and summarized the main findings. This study hopes to provide important and valuable references for future research on the OR field. PubDate: 2022-12-01 DOI: 10.1007/s10700-021-09380-x
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Abstract: Abstract Convexity is a deeply studied concept since it is very useful in many fields of mathematics, like optimization. When we deal with imprecision, the convexity is required as well and some important applications can be found fuzzy optimization, in particular convexity of fuzzy sets. In this paper we have extended the notion of convexity for interval-valued fuzzy sets in order to be able to cover some wider area of imprecision. We show some of its interesting properties, and study the preservation under the intersection and the cutworthy property. Finally, we applied convexity to decision-making problems. PubDate: 2022-12-01 DOI: 10.1007/s10700-021-09376-7
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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: 2022-11-16 DOI: 10.1007/s10700-022-09402-2
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