SimE: A Geometric Approach for Similarity Estimation of Fuzzy Sets

M. Shanmugapriya ； H. Khanna Nehemiah ； R.S. Bhuvaneswaran ； Kannan Arputharaj ； J. Jabez Christopher

《Research Journal of Applied Sciences, Engineering and Technology》 13卷5期 (2016/09) Pp. 345-353

https://doi.org/10.19026/rjaset.13.2952

摘要

The characteristics of a fuzzy set are decided by its membership function. This work aims to provide a geometric approach for enhancing the design and performance of fuzzy systems. Similarity Estimator (SimE) evaluates the membership functions of fuzzy sets on Euclidean space based on geometric area. The overlapping regions between the sets are partitioned into geometric structures. The area of overlapping is computed by summing the area of polygons and integrating the area under curves. Similarity between fuzzy sets is directly proportional to the area of overlapping between them. SimE was tested over a range of real numbers with finite intervals. Fuzzy sets using different membership functions were created for the same data distribution. From the test results it can be inferred that fuzzy sets defined using triangular membership functions have a minimum overlapping area when compared to fuzzy sets defined using other membership function. Optimal overlapping area of fuzzy sets improves the semantic representation and the performance of the system. SimE can be used by knowledge engineers to design efficient fuzzy systems.

關鍵字

Design automation ； fuzzy systems ； fuzzy set theory ； geometric area ； membership function ； similarity measure