Discrimination Analysis On Fuzzy Random Populations

Discrimination analysis originated in the 20th century, 30's, it is a statistical method, using the known types of samples to establish a discrimination model, in order to determine the types of unknown samples. In recent years, discrimination analysis has been widely used in various disciplines, such as in the natural sciences, sociology, medicine, and economic management, and so on. For example, in economics, we usually need to use different indicators including the level of per capita income, per capita industrial and agricultural output and per capita consumption level to determine economic development level type of a country; another example, in recent years, there are frequent earthquakes in the world. It takes a crucial role for the protection of people's lives and reducing property damage, if we could have a exact recognition the earthquake type and an accurate degree forecasting of a aftershock. Therefore, it's of great importance to study on discrimination analysis methods.With the deepening of research and the popularization of computers, A type of pattern recognition method of computer-based information processing and classification came into being. With the advancement of technology and social development, pattern recognition in the information age is playing an increasingly important role. Statistical pattern recognition method which is an important recognition from Criterion is one of the basic methods, which depicts by random variable and its distribution. It makes discrimination with the distances that the individual to the populations, and classified according to the minimum distance principle. Complicated sequence of data propels the classical mathematical and statistical probability theory to develop toward the direction of uncertainty continuously. Thus the theory of fuzzy discrimination analysis methods and pattern recognition appears.However, with advances in science technology and continuous development of information technology, complex data will appears endlessly to promote the classical theory of probability and mathematical statistics continue to develop and thorough towards the direction of fuzzy uncertainty science. So, fuzzy random model exits widespread in practical study. For example, the complicated system of natural disasters is full of uncertainty, contains a large amount of randomness and fuzziness. At present, the probability and statistical methods are often used in seismic risk analysis. However, there are coexistence of randomness and fuzziness in many cases. Sometimes, people have to identify these objects. For example, to evaluate he overall quality, and it is classified as "very good", "good" and "normal"; the random description is expressed in only from the three grade, and the fuzziness is reflected in the integrated evaluation of the quality. If we see the waiter's overall quality as a variable, it is a fuzzy random variable with both fuzzy uncertainty and also random- ness. To judge a specific individual of this type, neither classical discrimination analysis nor fuzzy discrimination analysis method is clearly valid. In the existing research results, also found no literature about discrimination analysis under fuzzy random environment. Therefore, in order to solve these identification problems existing both fuzziness and randomness, discrimination analysis method of classical probability theory will be extended to the case of fuzzy random in the paper. First, it gives a new definition of the fuzzy distance between the individual and gropes, for the inaccurate of distance in fuzzy set theory. Then, it constructs discrimination models on two and multiple fuzzy random populations respectively, basing on the minimal distance rule in classical probability theory, accompanying with the sort theory of fuzzy number. And finally, it proves the feasibility and validity about the proposed discrimination analysis method, using specific examples.