Analysis on Random Fuzzy Queueing Systems with Finite Capacity

This paper discusses random fuzzy queueing systems with finite capacity, where the interarrival times and service times are characterized as random fuzzy variables. Fuzzy simulation techniques are designed to estimate the membership degree, the expected value of system length, and the credibility measure that the system length does not exceed a predetermined level. Furthermore, the rough figures of the membership function and credibility distribution function of the system length can be obtained. Finally, an example is given to illustrate the effectiveness of the presented techniques

Two-stage Supply Chain Model with Uncertain Demand

Based on uncertainty theory, a two-stage supply chain model is presented, where the customers’ demands are characterized as uncertain variables. The objective is to minimize the combined costs incurred in the manufacturing and logistics phases. When these uncertain variables are linear, the objective function and constraints can be converted into crisp equivalents, then can be solved by traditional methods. An example is given to illustrate the model and the converting method

Evaluation of six satellite-based terrestrial latent heat flux products in the vegetation dominated Haihe river basin of north China

In this study, six satellite-based terrestrial latent heat flux (LE) products were evaluated in the vegetation dominated Haihe River basin of North China. These LE products include Global Land Surface Satellite (GLASS) LE product, FLUXCOM LE product, Penman-Monteith-Leuning V2 (PML_V2) LE product, Global Land Evaporation Amsterdam Model datasets (GLEAM) LE product, Breathing Earth System Simulator (BESS) LE product, and Moderate Resolution Imaging Spectroradiometer (MODIS) (MOD16) LE product. Eddy covariance (EC) data collected from six flux tower sites and water balance method derived evapotranspiration (WBET) were used to evaluate these LE products at site and basin scales. The results indicated that all six LE products were able to capture the seasonal cycle of LE in comparison to EC observations. At site scale, GLASS LE product showed the highest coefficients of determination (R2) (0.58, p 2), followed by FLUXCOM and PML products. At basin scale, the LE estimates from GLASS product provided comparable performance (R2 = 0.79, RMSE = 18.8 mm) against WBET, compared with other LE products. Additionally, there was similar spatiotemporal variability of estimated LE from the six LE products. This study provides a vital basis for choosing LE datasets to assess regional water budget

Risk-Neutral Pricing Method of Options Based on Uncertainty Theory

In order to rationally deal with the belief degree, Liu proposed uncertainty theory and refined into a branch of mathematics based on normality, self-duality, sub-additivity and product axioms. Subsequently, Liu defined the uncertainty process to describe the evolution of uncertainty phenomena over time. This paper proposes a risk-neutral option pricing method under the assumption that the stock price is driven by Liu process, which is a special kind of uncertain process with a stationary independent increment. Based on uncertainty theory, the stock price’s distribution and inverse distribution function under the risk-neutral measure are first derived. Then these two proposed functions are applied to price the European and American options, and verify the parity relationship of European call and put options

A New Stability Analysis of Uncertain Delay Differential Equations

This paper first provides a concept of almost sure stability for uncertain delay differential equations and analyzes this new sort of stability. In addition, this paper derives three sufficient conditions for uncertain delay differential equations being stable almost surely. Finally, the relationship between almost sure stability and stability in measure for uncertain delay differential equations is discussed

Risk-Neutral Pricing Method of Options Based on Uncertainty Theory

In order to rationally deal with the belief degree, Liu proposed uncertainty theory and refined into a branch of mathematics based on normality, self-duality, sub-additivity and product axioms. Subsequently, Liu defined the uncertainty process to describe the evolution of uncertainty phenomena over time. This paper proposes a risk-neutral option pricing method under the assumption that the stock price is driven by Liu process, which is a special kind of uncertain process with a stationary independent increment. Based on uncertainty theory, the stock price’s distribution and inverse distribution function under the risk-neutral measure are first derived. Then these two proposed functions are applied to price the European and American options, and verify the parity relationship of European call and put options

A Structural Credit Risk Model Driven by the Lévy Process under Knightian Uncertainty

The classic credit risk structured model assumes that risky asset values obey geometric Brownian motion. In reality, however, risky asset values are often not a continuous and symmetrical process, but rather they appear to jump and have asymmetric characteristics, such as higher peaks and fat tails. On the other hand, there are real Knight uncertainty risks in financial markets that cannot be measured by a single probability measure. This work examined a structural credit risk model in the Lévy market under Knight uncertainty. Using the Lévy–Laplace exponent, we established dynamic pricing models and obtained intervals of prices for default probability, stock values, and bond values of enterprise, respectively. In particular, we also proved the explicit solutions for the three value processes above when the jump process is assumed to follow a log-normal distribution. Finally, the important impacts of Knightian uncertainty on the pricing of default probability and stock values of enterprise were studied through numerical analysis. The results showed that the default probability of enterprise, the stock values, and bond values were no longer a certain value, but an interval under Knightian uncertainty. In addition, the interval changed continuously with the increase in Knightian uncertainty. This result better reflected the impact of different market sentiments on the equilibrium value of assets, and expanded decision-making flexibility for investors

An Uncertain APP Model with Allowed Stockout and Service Level Constraint for Vegetables

Volatile markets and uncertain deterioration rate make it extremely difficult for manufacturers to make the quantity of saleable vegetables just meet the fluctuating demands, which will lead to inevitable out of stock or over production. Aggregate production planning (APP) is to find the optimal yield of vegetables, shortage and overstock symmetry, are not conducive to the final benefit.The essence of aggregate production planning is to deal with the symmetrical relation between shortage and overproduction. In order to reduce the adverse effects caused by shortage, we regard the service level as an important constraint to meet the customer demand and ensure the market share. So an uncertain aggregate production planning model for vegetables under condition of allowed stockout and considering service level constraint is constructed, whose objective is to find the optimal output while minimizing the expected total cost. Moreover, two methods are proposed in different cases to solve the model. A crisp equivalent form can be transformed when uncertain variables obey linear uncertain distributions and for general case, a hybrid intelligent algorithm integrating the 99-method and genetic algorithm is employed. Finally, two numerical examples are carried out to illustrate the effectiveness of the proposed model