The Research Of Learning From Examples Based On Interval Numbers And Interval-Valued Programming

In realistic life and many fields including engineering technology, life science, economy management, there exist lots of uncertainty including stochastic and fuzzy. As the generalizing of the classical mathematic set theory, the fuzzy set can express so many fuzzy concepts in human knowledge. Interval numbers as the special case of fuzzy numbers exist in engineering application and realistic life, for instance, broken-down point in power network, the time of virus infection etc, witch expressed by interval numbers are more natural.This paper mainly explores the method of process for objects expressed by interval-valued data. The main contributions of this dissertation can be summarized as following two fields: firstly, learning from examples of decision tree based on interval-valued data. In the learning proceeding of decision tree based on interval-valued data, owing to attributes denoted by interval-valued data, we considered that the interval values of the same attributes of all the samples could satisfy certain distribution rule or form some centers. Therefore interval-valued data of certain attributes of all the samples could be clustered by the algorithm of FCM (fuzzy C-meaning) to produce some central interval numbers. At the same time, we could gain the degrees of membership of others interval-valued data to those central interval numbers. Consequently, the format of interval-valued attributes is transformed to the format of the attributes denoted by degree of membership, and then which could be disposed directly by the algorithm of fuzzy ID3, in the end, to form decision tree. Contrast to presently the measure which divides simply the split points in the interval-valued data, the former could not only better remain the character of interval numbers but also consider the distribution rule of the same attributes value, and then to process scientifically the knowledge in the form of interval number. Secondly, interval-valued programming, interval-valued programming has evolved to solve the problem of interval-valued modulus and general variable. This paper proposes the novel idea that how to convert the interval-valued modulus into the stochastic variable, which arose from fact that interval-valued data could correspond the normal school of the appraised value. Uncertainness of the stochastic variable is substituted for the fuzzy of interval-valued data. Therefore, the model of ILP (interval-valued linear programming) would be transformed into the model of stochastic expectation-valued programming. Based on this theory, GA(genetic algorithm) with stochastic simulation was designed to seek the optimum solution to the original problem.