Describing Fuzzy Membership Function and Detecting the Outlier by Using Five Number Summary of Data

Abstract

One of the most important activities in data science is defining a membership function in fuzzy system. Although there are few ways to describe membership function like artificial neural networks, genetic algorithms etc.; they are very complex and time consuming. On the other hand, the presence of outlier in a data set produces deceptive results in the modeling. So it is important to detect and eliminate them to prevent their negative effect on the modeling. This paper describes a new and simple way of constructing fuzzy membership function by using five-number summary of a data set. Five states membership function can be created in this new method. At the same time, if there is any outlier in the data set, it can be detected with the help of this method. Usually box plot is used to identify the outliers of a data set. So along with the new approach, the box plot has also been drawn so that it is understood that the results obtained in the new method are accurate. Several real life examples and their analysis have been discussed with graph to demonstrate the potential of the proposed method. The results obtained show that the proposed method has given good results. In the case of outlier, the proposed method and the box plot method have shown similar results. Primary advantage of this new procedure is that it is not as expensive as neural networks, and genetic algorithms.