Approximating fuzzy membership functions from clustered raw data

Clustering is the process of identifying groups of similar data fulfilling certain criteria. Fuzzy c-means clustering algorithm generates cluster centers and degree of memberships of each pattern to each fuzzy cluster. However, this clustered raw data is not of much benefit for the symbolic representation of fuzzy rule base which can be generated using standard algorithms like fuzzy decision trees and others. Also human interpretability is improved when clustered raw data is represented by Triangular, Trapezoidal, or Gaussian kind of membership functions, rather than representing as matrix of raw membership values. The convex hull method for the estimation of trapezoidal membership functions from the clustered raw data is of limited use and many a times generates membership functions that are either highly overlapped or highly separated. In this article, two heuristic algorithms are presented for the estimation of parameterized family of membership functions, namely, triangular and trapezoidal. Each of these algorithms has been explained formally and then stated in pseudo code form and illustrated with a sample dataset. Finally, the practical application of these algorithms is given in the context of our recent research.