Research On Fuzzy Probability Based On Interval Probability

Fuzzy probability falls into three categories according to fuzzy situation:fuzzy events--accurate probability; clear events-fuzzy probability; fuzzy events-fuzzy probability. In recent years, many scholars have made many achievements about the first kind of fuzzy probability. Some scholars have also made some progress about the second kind of fuzzy probability, but are not in-depth study, mainly because that the calculation methods of fuzzy probability are not yet ripe.In 1998, Wang Baisheng presented the idea about fuzzy number origin, the idea has great inspirational for exploring the fuzzy numbers reasonable computing. Based on this idea, random variable of interval probability and its digital features have been relatively detailed studied. On this basis, the second kind of fuzzy probability has been study in some of the literature, mainly on the discrete fuzzy random problems. In continuous random problems, the random variable has been fully described by the probability density function, but it is not an easy task to get the accurate probability density function. So it will be of practical significance to describe the fuzzy probability density function using fuzzy-valued function if the data is not complete and the probability density function can not be fully defined. The fuzzy-valued function is said to be fuzzy probability density function, and the corresponding random variables is said to be fuzzy random variables. On this basis, the problem of the second kind of continuous fuzzy probability random variables has been studied.In this paper, the knowledge of interval probability and its random problem has been first introduced, and then conclusions about the second type of fuzzy probability and its random problem have been detailed and specific summarized, including discrete fuzzy random problems and continuous fuzzy random problems. Based on the idea of fuzzy number origin, an interval probability space of the finite origin is established by the operation of fuzzy probability. Definitions of interval probability random variable (random vecter) and its distribution function, distribution sequence, math expectation, variance and so on are given, and the specific nature and operational law have been studied too. The discrete random question of the second kind of fuzzy probability is based on the discrete random problem of interval probability and then gets a series of corresponding conclusions:definitions of fuzzy probability random variable (random vecter) and its distribution function, distribution sequence, fuzzy math expectation, fuzzy variance and so on are given, and the specific nature and operational law have been studied too. The problem of the second kind of continuous fuzzy probability random variables is the problem of fuzzy probability random because of the fuzziness of probability density function, the definition and basic nature of the fuzzy random variable with fuzzy density and its distribution function on the basis of interval probability density, the definition and calculation methods of fuzzy mathematical expectation sand the fuzzy variance have been also given. Secondly, the proof of some nature which has not been given in the literature is given in this paper.Finally, the third kind of fuzzy probability is studied using the above conclusions, and get some preliminary conclusions include:the problem about the third kind of discrete and continuous fuzzy random. Definitions of fuzzy probability random variable (random vecter) and its distribution function, distribution sequence, fuzzy math expectation, fuzzy variance and so on are given about the third kind of discrete fuzzy random; definitions and basic nature of the fuzzy random variable with fuzzy density and its distribution function and fuzzy mathematical expectations and the fuzzy variance are given too.Some of the conclusions are not yet ripe about the study of the third kind of fuzzy probability, which needing further study and explore.