Ordering fuzzy sets generated by a neural network algorithm

Ordering fuzzy subsets is an important event in dealing with fuzzy decision problems in many areas. This issue has been of concern for many researchers over the years. Also, in the last several years, there has been a large and energetic upswing in neuroengineering research aimed at synthesizing fuzzy logic with computational neural networks. The two technologies often complement each other: neural networks supply the brute force necessary to accommodate and interpret large amounts of sensor data and fuzzy logic provides a structural framework that utilizes and exploits these low-level results. As a neural network is well known for its ability to represent functions, and the basis of every fuzzy model is the membership function, so the natural application of neural networks in fuzzy models has emerged to provide good approximations to the membership functions that are essential to the success of the fuzzy approach. This paper evaluates and analyzes the performance of available methods of ranking fuzzy subsets on a set of selected examples that cover possible situations we might encounter as defining fuzzy subsets at each node of a neural network. Through this analysis, suggestions as to which methods have better performance for utilization in neural network architectures, as well as criteria for choosing an appropriate method for ranking are made.