The Deeper Research On Fuzzy Number In Fuzzy Mathematics And Their Applications

Fuzzy theory has been widely present in every corner of society, serving as the mathematical tools that deal with the uncertainty of things, which has a very wide range of applications in the information age. All the applications must be based on the precise and impeccable theory system. The work we study the theory of fuzzy numbers is not only the replenishment to the theory of fuzzy mathematic, but also an expansion and a creation to the real analysis and the theory of the probability.The thesis mainly has finished three important works.â… :make a summary and develop a systematic theory to the fuzzy number, and make corrections to the wrong discussion on theorem of supremum and the matter that the monotonous numbers has a necessary limit.â…¡:give a new definition to the distance of the fuzzy numbers. We get the relevant theorems and conclusions based on the new definition, imitating the real analysis. We find a new viewpoint to study the fuzzy number, which makes us to solve the problems frequently faced in the practice and study.â…¢:introduce the applications of the fuzzy number in the AHP.