Learning Generalized Weighted Relevance Aggregation Operators Using Levenberg-Marquardt Method

We previously introduced the generalized Weighted Relevance Aggregation Operators (WRAO) for hierarchical fuzzy signatures. WRAO enhances the ability of the fuzzy signature model to adapt to different applications and simplifies the learning of fuzzy signature models from data. In this paper we overcome the practical issues which occur when learning WRAO from data. This paper discuss an algorithm for learning WRAO using the Levenberg- Marquardt (LM) method, which is one of the most sophisticated and widely used gradient based optimization method. Also, this paper shows the successful results of applying the proposed algorithm to extract WRAO for two real world problems namely High Salary Selection and SARS Patient Classification.

1. Introduction

Fuzzy signatures can model complex structured problems with the help of hierarchically structured vector valued fuzzy sets, and a set of aggregation functions [3]. The hierarchically structured vector valued fuzzy sets represent the degree of relationship of the attributes of the object. The set of aggregation functions map, from lower branches to the higher branches, the different universes of discourse of the hierarchical fuzzy signature structure. Further, these aggregation functions are non-homogenous. We argue that these properties help fuzzy signatures to model problems similar to the nature of human approaches to problem solving [3].