The Similarity Measure Of Interval-Valued Fuzzy Sets And Its Applications

Since 1965, professor L.A.Zadeh put forward fuzzy theory, the fuzzy theory as well as its application has undergone substantial development.Because of the complexity of the objective world, the shortage of ability in people's cognitions, and potential error margins of measure the tools, people usually run into the incomplete and uncertain information, then we get the characterization of behavioural characteristics of things and often it is a scope or interval number. In view of this situation, people built interval-valued fuzzy sets, it is an extension of Zadeh's fuzzy sets. Recently, many researchers have discussed the fundamental theory of the interval-valued fuzzy sets and have obtained lots of meaningful results. In application, interval-valued fuzzy sets have been applied to lots of fields such as:decision-making analysis, pattern recognition, handling intelligence information and so on.In this paper, we will study the similarity measure of interval-valued fuzzy sets and its application problem. First we review the definition and basic properties of interval-valued and interval-valued fuzzy sets. Second according to two definition of the similarity measure of the interval-valued fuzzy sets and give several kinds of common similarity measure. And then considering the weights of attributes have the great influence to the results of evaluation in the interval-valued fuzzy sets, this paper summarized the common types of methods for weight and gives several kinds of new methods for weight, Final introduced similarity measure has been applied to lots of the pattern recognition and comprehensive evaluation, and with practical examples. This makes the basic theory and application of the interval-valued fuzzy sets more perfect.