Tsinghua University Press

In almost all the realistic circumstances, such as health risk assessment and uncertainty analysis of atmospheric dispersion, it is very essential to include all the information into modelling. The parameters associated to a particular model may include different kind of variability, imprecision and uncertainty. More often, it is seen that available informations are interpreted in probabilistic sense. Probability theory is a well-established theory to measure such kind of variability. However, not all of available information, data or model parameters affected by variability, imprecision and uncertainty can be handled by traditional probability theory. Uncertainty or imprecision may occur due to incomplete information or data, measurement errors or data obtained from expert judgement or subjective interpretation of available data or information. Thus, model parameters, data may be affected by subjective uncertainty. Traditional probability theory is inappropriate to represent them. Possibility theory and fuzzy set theory is another branch of mathematics which is used as a tool to describe the parameters with insufficient or vague knowledge. In this paper, an attempt has been made to combine probability knowledge and possibility knowledge and draw the uncertainty. The paper describes an algorithm for combining probability distribution and interval-valued fuzzy number and applied to environmental risk modelling with a case study. The primary aim of this paper is to propagate the proposed method. Computer codes are prepared for the proposed method using MATLAB.

Decision making in real world is usually made in fuzzy environment and subject to fuzzy risks. The value at risk (VaR) is a widely used tool in risk management and the average value at risk (AVaR) is a risk measure which is a superior alternative to VaR. In this paper, we present a methodology for fuzzy risk analysis based on credibility theory. First, we present the new concepts of the credibilistic VaR and credibilistic AVaR. Next, we examine some properties of the proposed credibilistic VaR and credibilistic AVaR. After that, a kind of fuzzy simulation algorithms are given to show how to calculate them. Finally, a numerical example is illustrated. The proposed credibilistic VaR and credibilistic AVaR are suitable for use in many real problems of fuzzy risk analysis.

The interrelationship of notions is presented in fuzzy transitivity and monotonicity of fuzzy similarity measures. It is observed that the axiom of fuzzy transitivity may replace that of monotonicity in the definition of fuzzy similarity measures.

In this paper we study some single-machine scheduling problems with learning effects where the actual processing time of a job serves as a function of the total actual processing times of the jobs already processed and of its scheduled position. We show by examples that the optimal schedules for the classical version of problems are not optimal under this actual time and position dependent learning effect model for the following objectives: makespan, sum of kth power of the completion times, total weighted completion times, maximum lateness and number of tardy jobs. But under certain conditions, we show that the shortest processing time (SPT) rule, the weighted shortest processing time (WSPT) rule, the earliest due date (EDD) rule and the modified Moore’s Algorithm can also construct an optimal schedule for the problem of minimizing these objective functions, respectively.

A dynamical model is presented for autonomous mobile intelligent agents. Based on the local information of the swarm, a fuzzy logical controller (FLC) is built for the attraction/repulsion function. The flocking of the separation, cohesion and alignment are achieved by combining with the rate consensus algorithm. Based on the optimal controller theories, a performance target is used to measure the states of the system. By applying the connected network from the individual local perceived information, the aggregation of the multi-agent systems can swarm following a whole consensus in the computer simulations.

Combined forecasts is a well-established procedure for improving forecasting accuracy which takes advantage of the availability of both multiple information and computing resources for data-intensive forecasting. Therefore, based on the combination of engineering fuzzy set theory and artificial neural network theory as well as genetic algorithms and combined forecast theory, the system Non-linear Combined Forecast (NCF) method is established for accuracy enhancement of prediction, especially of ice flood prediction. The NCF values from single forecast model for Inner Mongolia Reach of the Yellow River are given. The case shows that the method has clear physical meanings and precise consequences. Compared with any single model, the system NCF method is more rational, effective and accurate.