Interval-valued Level Cut Set On The Interval-valued Fuzzy Set And Its Application

The concept of interval-valued fuzzy sets is an extension of Zadeh's fuzzy sets. In recent years, many researchers are interested in interval-valued fuzzy sets. The main reason is that, in practice, the interval-valued results obtained in handling information can effectively reflect the fuzziness and uncertainty of the fact. And the interval-valued fuzzy sets can also reduce the loss of fuzzy information. In application, interval-valued fuzzy sets have been applied to lost of fields such as artificial intelligence, decision-making analysis and so on.In this paper, the level cut sets, decomposition theorems and representation theorems of interval-valued fuzzy sets and interval-valued fuzzy sets are researched indail. Firstly, the level cut sets of interval-valued fuzzy sets are defined as the 3-dimensional sets. Then new definitions of four kinds of cut sets on interval-valued fuzzy sets are introduced, which are generalizations of level cut sets on Zadeh fuzzy sets and have the same properties as that of Zadeh fuzzy sets. Secondly, based on these new level cut sets, the decomposition theorems and representation theorems on interval-valued fuzzy sets are established, re-spectively. Thirdly, based on these new level cut sets, the interval-valued fuzzy subgroup is established. Finally, by use of these level cut sets, we studied the ranking interval numbers and fuzzy numbers. Therefore, the level cut sets on interval-valued fuzzy sets can provide a useful way in the application.