MATHEMATICAL EXPECTATION ABOUT DISCRETE RANDOM VARIABLE WITH INTERVAL PROBABILITY OR FUZZY PROBABILITY

The character and an algorithm about DRVIP（ discrete random variable with interval probability） and the secured kind DRVFP （discrete random variable with crisp event-fuzzy probability） are researched. Using the fuzzy resolution theorem, the solving mathematical expectation of a DRVFP can be translated into solving mathematical expectation of a series of RVIP. It is obvious that solving mathematical expectation of a DRVIP is a typical linear programming problem. A very functional calculating formula for solving mathematical expectation of DRVIP was obtained by using the Dantzig＇s simplex method. The example indicates that the result obtained by using the functional calculating formula fits together completely with the result obtained by using the linear programming method, but the process using the formula deduced is simpler.

Risk Decision Analysis of Logistics Purchasing Based on Mathematical Expectation

The mathematical expectation value method is a commonly used method in risk decision-making. This paper studies the problem of how to arrange the purchase plan in order to get the maximum expected profit;considering the applicable principles of mathematical expectation, the decision method for getting the optimal decision scheme is given. Finally, we do simulation and stability analysis on an example and obtain the reasonable result. This result shows that mathematical expectation value method is effective in solving the problem of risk decision.

Progress and Challenge of the Short-Term Climate Prediction

The experience of developing a short-term climate prediction system at the Institute of Atmospheric Science of the Chinese Academy of Sciences is summarized,and some problems to be solved in future are discussed in this paper.It is suggested that a good system for short-term climate prediction should at least consist of (1) well-tested model(s),(2) sufficient data and good methods for the initialization and assimilation,(3) a good system for quantitative corrections,(4) a good ensemble prediction method,and (5) appropriate prediction products,such as mathematical expectation,standard deviation,probability,among others.

An Approach to Resolving Two Paradoxes in Probability Theory

A new mathematical expectation formula with some hypotheses, notions and propositions was given to get rid of the challenge of St. Petersburg paradox and Pascal's wager. Relevant results show that it is very effective to apply the model to solve the expected revenue problems containing random events with low proba-bility but high revenue. This work also provides the probability theory with a more widely applied perspective in group decision-making.

RANDOM VARIABLE WITH FUZZY PROBABILITY

Mathematic description about the second kind fuzzy random variable namely the random variable with crisp event-fuzzy probability was studied. Based on the interval probability and using the fuzzy resolution theorem, the feasible condition about a probability fuzzy number set was given,go a step further the definition and characters of random variable with fuzzy probability (RVFP) and the fuzzy distribution function and fuzzy probability distribution sequence of the RVFP were put forward. The fuzzy probability resolution theorem with the closing operation of fuzzy probability was given and proved. The definition and characters of mathematical expectation and variance of the RVFP were studied also. All mathematic description about the RVFP has the closing operation for fuzzy probability,as a result, the foundation of perfecting fuzzy probability operation method is laid.

Probability representations of fuzzy systems

In this paper, the probability significance of fuzzy systems is revealed. It is pointed out that COG method, a defuzzification technique used commonly in fuzzy systems, is reasonable and is the optimal method in the sense of mean square. Based on different fuzzy implication operators, several typical probability distributions such as Zadeh distribution, Mamdani distribution, Lukasiewicz distribution, etc, are given. Those distributions act as ＂inner kernels＂ of fuzzy systems. Furthermore, by some properties of probability distributions of fuzzy systems, it is also demonstrated that CRI method, proposed by Zadeh, for constructing fuzzy systems is basically reasonable and effective. Besides, the special action of uniform probability distributions in fuzzy systems is characterized. Finally, the relationship between CRI method and triple I method is discussed. In the sense of construction of fuzzy systems, when restricting three fuzzy implication operators in triple I method to the same operator, CRI method and triple I method may be related in the following three basic ways： 1） Two methods are equivalent; 2） the latter is a degeneration of the former; 3） the latter is trivial whereas the former is not. When three fuzzy implication operators in triple I method are not restricted to the same operator, CRI method is a special case of triple I method; that is, triple I method is a more comprehensive algorithm. Since triple I method has a good logical foundation and comprises an idea of optimization of reasoning, triple I method will possess a beautiful vista of application.

Some Statistical Properties of the Correlation Function of Combination Sequences

in this paper,the statistical prOPerties of random combination sequences are discussed.Thevalue of E{R(r)}and the upper bound of E{A(r)}are derived.In the end,a new method to find a longsequence with low autocorrelation value is given.