Developing algorithms for solving high-dimensional uncertain differential equations has been an exceedingly difficult task. This paper presents an \(\alpha \)-path-based approach that can handle the proposed high-dimensional uncertain SIR model. We apply the \(\alpha \)-path-based approach to calculating the uncertainty distributions and related expected values of the solutions. Furthermore, we employ

This paper finds a relation between moments of Liu process and Bernoulli numbers. Firstly, by an exponential generating function of Bernoulli numbers, a useful integral formula is obtained. Secondly, based on this integral formula, the moments of a normal uncertain variable and Liu process are expressed via Bernoulli numbers.

This paper presents an uncertain time series model to analyse and predict the evolution of confirmed COVID-19 cases in China, excluding imported cases. Compared with the results of the classical time series model, the uncertain time series model could better describe the COVID-19 epidemic by using an uncertain hypothesis test to filter out outliers. This improvement is reflected in the two observations

Assume an uncertain process follows an uncertain differential equation, and some realizations of this process are observed. Parameter estimation for the uncertain differential equation that fits the observed data as much as possible is a core problem in practice. This paper first presents a problem of initial value estimation for uncertain differential equations and proposes an estimation method. In

In the data security context, anomaly detection is a branch of intrusion detection that can detect emerging intrusions and security attacks. A number of anomaly detection systems (ADSs) have been proposed in the literature that using various algorithms and techniques try to detect the intrusions and anomalies. This paper focuses on the ADS schemes which have applied fuzzy logic in combination with

Uncertain differential equation is a type of differential equation driven by Liu process that is the counterpart of Wiener process in the framework of uncertainty theory. The stability theory is of particular interest among the properties of the solutions to uncertain differential equations. In this paper, we introduce the Lyapunov’s second method to study stability in measure and asymptotic stability

A behavioral multi-attribute decision making (BMADM) problem with probabilistic-based expressions is studied by considering decision-maker’s (DM) risk attitude and pre-evaluation. With consideration of information expressions for uncertainty, probabilistic interval numbers (PINs) and probabilistic linguistic terms (PLTs) are utilized to depict pre-evaluation information with respect to quantitative

Group decision making (GDM) can be defined as an environment where there exist a set of possible alternatives and a set of individuals (experts, judgements, etc.). Preference relation is one of the most widely used preference representation structures in GDM. Considering that the self-confidence degree is an important part to express preference information, and double hierarchy linguistic preference

As applications of the uncertainty theory to finance, uncertain stock models have been presented to describe the prices of stocks strongly influenced by human uncertainty. So far, large progress has been achieved on pricing problems of path-independent options of the uncertain stock models. This paper investigates a type of path-dependent exotic options of an uncertain stock model which are named barrier

The challenge of complex multi-attribute large group decision-making (CMALGDM) is reflected from three perspectives: interrelated attributes, large group decision makers (DMs) and dynamic decision environments. However, there are few decision techniques that can address the three perspectives simultaneously. This paper proposes a random intuitionistic fuzzy factor analysis model, aiming to address

The aim of the paper is to solve the group decision making problems which contain inconsistent probabilistic linguistic preference relations (PLPRs) and unknown expert weights. When the PLPRs are inconsistent, there are contradictories in the preference relations expressed by the experts. The evaluation value with contradictory information will bring out an incorrect consequence in decision making

In this paper, we study four projection-based normalization models and a decision-making method for probabilistic linguistic multi-criteria decision-making problems, in which the assessment information about an alternative with respect to a criterion is incomplete and the criteria weight values are not precisely known but the ranges are available. To apply the projection to the probabilistic linguistic

As a representative of the new economy, the web celebrity economy has achieved significant development in China with the rapid development of information technology and the Internet. In this environment, web celebrity shops encounter fierce business competition of peer competitors. Online reviews which imply the consumers’ attitudes and sentiments give the web celebrity shops good feedback to improve

When expressing preferences with different probability weights for different linguistic terms, only partial assessment information is usually to be provided. Then the probability information can be normalized to the interval probability, hence, using interval probabilistic linguistic term sets (IPLTs) is more appropriate. Considering this situation, interval probabilistic linguistic preference relation

Evaluating and selecting suitable sustainable recycling partners is a key work in sustainable supply chain management. In order to deal with the probabilistic linguistic influence relations between criteria and obtain the key factors that influence the evaluation results of sustainable recycling partners, we propose a new decision-making trial and evaluation laboratory (DEMATEL) method. First, we propose

The probabilistic linguistic term set (PLTS) is a powerful tool for describing linguistic evaluations derived from expert teams and has adequate capability to identify preferences among different evaluations. Due to the practicability of PLTSs, probabilistic linguistic decision making problems have been widely investigated in recent years. However, no study on probabilistic linguistic outranking relations

This paper investigates the problem of efficiency measurement for parallel systems with two components based on Stackelberg game theory, while some inputs/outputs are fuzzy numbers. Conventional DEA models treat DMUs as “Black Boxes”. While in this paper, we propose a new parallel fuzzy DEA model to calculate the efficiency scores for each DMU’s whole system and its sub-systems. Through the Stackelberg

The consistency test is a vital component of pairwise comparison matrices if meaningful results are to be guaranteed, and it has been studied extensively since the analytic hierarchy process was developed by Saaty. However, when using the existing methods, it is imperative to carry out matrix operations, which are usually not intuitional. In this paper, a direct method, from the perspective of 3 tuples

Smart manufacturing is an effective way to improve the efficiency of resource utilization and reduce the response time of making joint decisions for the enterprises. Though, with the globalization of manufacturing enterprises, manufacturing optimization problems often occur in complex manufacturing systems under the deteriorating and fuzzy environment, which brings many challenges to smart manufacturing

This paper introduces a class of differential fuzzy variational inequalities, the model provides an efficient approach for solving many dynamic multi-objective optimization problems in fuzzy environments. An existence theorem of the Carathéodory weak solution for the model is established under some suitable assumptions. An algorithm, supported by the convergence analysis, is developed to find the solution

This work proposes an inequality approach with the quasi-ordered set to evaluate the performances of decision making units (DMUs). In real world applications, input and output data are often imprecise and fluctuated. In this case, a fuzzy inequality approach is proposed to evaluate DMUs with fuzzy data. Fuzzy inequalities consist of fuzzy expressions of the production possibility set and the line segment

Automatic reasoning based on propositional logic is considered as an important tool in machine learning, and intuitionistic fuzzy sets have turned out to deal with vague and uncertain information effectively in real world. In this paper, a novel plausible reasoning based on intuitionistic fuzzy propositional logic is proposed. On the basis of it, the categories of intuitionistic fuzzy logic proposition

Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares, mostly due to the elegant theoretical foundation and ease of implementation. However, in many cases, we can only get imprecise observation values and the assumptions upon which the

With the wide applications of fuzzy theory in optimization, fuzzy arithmetic attracts great attention due to its inevitability in solution process. However, the complexity of the Zadeh extension principle significantly reduces the practicability of fuzzy optimization technology. In this paper, we prove some important properties on positive L-R fuzzy numbers, and propose a new calculation method for

Parameter estimation is a critical problem in the wide applications of uncertain differential equations. The method of moments is employed for the first time as an approach for estimating the parameters in uncertain differential equations. Based on the difference form of an uncertain differential equation, a function of the parameters is proved to follow a standard normal uncertainty distribution.

Probabilistic linguistic term set (PLTS) has been proposed to tackle qualitative information efficiently in the decision-making process to achieve computing with expressions, which can be regarded as an advanced process of computing with words. The PLTS plays an important role in decision making by providing a comprehensive way for representing complex linguistic information. Owning to its usefulness

In this paper, we formally discuss a computational scheme, which combines a local weighted regression model with fuzzy transform (or F-transform for short). The latter acts as a reduction technique on the cardinality of the learning problem, resulting in a more efficient algorithm. We tested the proposed approach first through two typical benchmark problems, that is the Hénon and the Mackey–Glass chaotic

Fuzzy regression models are widely used to investigate the relationship between explanatory and response variables for many decision-making applications in fuzzy environments. To include more fuzzy information in observations, this study uses intuitionistic fuzzy numbers (IFNs) to characterize the explanatory and response variables in formulating intuitionistic fuzzy regression (IFR) models. Different

The aim of this paper is to investigate the potential of fuzzy regression methods for computing more reliable estimates of higher-order moments of the risk-neutral distribution. We improve upon the formula of Bakshi et al. (RFS 16(1):101–143, 2003), which is used for the computation of market volatility and skewness indices (such as the VIX and the SKEW indices traded on the Chicago Board Options Exchange)

We prove a measurability result which implies that the measurable events concerning the values of a fuzzy random variable, in two related mathematical approaches wherein the codomains of the variables are different spaces, are the same (provided both approaches apply). Further results on the perfectness of probability distributions of fuzzy random variables are presented.

In the present paper, we consider fuzzy optimization problems which involve fuzzy sets only in the objective mappings, and give two concepts of optimal solutions which are non-dominated solutions and weak non-dominated solutions based on orderings of fuzzy sets. First, by using level sets of fuzzy sets, the fuzzy optimization problems treated in this paper are reduced to set optimization problems,

When one estimates the importance of alternatives under rational choice, it is natural to avoid self-contradiction from the viewpoint of psychology. Due to the vagueness encountered in a manner analogous to human thought, decision makers always exhibit limited rationality. The judgements could be expressed as interval-valued comparison matrices within the framework of analytic hierarchy process. In

Uncertain fractional difference equations may preferably describe the behavior of the systems with the memory effect and discrete feature in the uncertain environment. So it is of great significance to investigate their stability. In this paper, the concept of finite-time stability almost surely for uncertain fractional difference equations is introduced. A finite-time stability theorem is then stated

In this paper, we study the min–max programming problem with n addition-min fuzzy relational inequality constraints. We prove that when the problem is feasible, an optimal solution always exists with all variables being of the same value. Based on this result, the min–max programming problem can be simplified as a single-variable optimization problem with the same optimal objective value. To solve

Based on uncertainty theory, this paper studies an uncertain SIS epidemic model with nonlinear incidence and demography. The solution, \(\alpha \)-paths and uncertainty distribution of uncertain model are discussed. Under threshold conditions, extinction and permanence of the disease are studied by \(\alpha \)-paths, which reveal the relationship of deterministic and uncertain models. An example is

Fuzzy relational inequalities with addition–min composition have been proposed to model the data transmission mechanism in a BitTorrent-like peer-to-peer file-sharing system. In this paper, we consider a multiple objective optimization problem which allows system manager to consider three objectives (system congestion, cost, and penalty) simultaneously. A quadratic program is then proposed for finding

To express the uncertain preferred and non-preferred qualitative judgments of decision makers, interval-valued intuitionistic linguistic fuzzy sets (IVILFSs) are proposed in a similar way as Atanassov and Gargov’s interval-valued intuitionistic fuzzy sets. Considering the application of IVILFSs, the concept of interval-valued intuitionistic linguistic fuzzy variables (IVILFVs) is defined and a ranking

Abstract The contractor’s procrastinating behavior owing to the psychology of cost salience exposes the project manager to the risk of time delay, which brings a significant challenge in project manager’s incentive contract design. This paper considers that a project manager pays a contractor over a menu of deadline-based incentive contracts to conduct a project which consists of two sequential tasks

Abstract The conventional extension principle is established on the Euclidean space and defined by considering the minimum or t-norm operator in which the fuzzy sets are usually assumed to be normal. The previous work on generalized extension principle was also based on the normal fuzzy sets. Since the non-normal fuzzy sets occur frequently in practical applications, in this paper, the generalized

Abstract Time series analysis is a method to predict future values based on previously observed values. Assuming the observed values are imprecise and described by uncertain variables, this paper proposes an approach of uncertain time series. By employing the principle of least squares, a minimization problem is derived to calculate the unknown parameters in the uncertain time series model. In addition

Abstract Fuzzy Optimization and Decision Making (FODM) is one of the influential journals in the research field of computer science and operation research, which was found in 2002. In this study, 370 publications published in FODM during 2002 and 2017 were retrieved from the Scopus database, and bibliometric methods are applied to analyze the structure of the FODM journal. First, general statistical

Abstract We investigate inhomogeneous fuzzy delay differential equation (FDDE) in which initial function and source function are fuzzy. We assume these functions be in a special form, which we call triangular fuzzy function. We define solution as a fuzzy bunch of real functions such that each real function satisfies the equation with certain membership degree. We develop an algorithm to find the solution