On the convergence of HLMS Algorithm

Abstract

In multicriteria decision making, the study of attribute contributions is crucial to attain correct decisions. Fuzzy measures allow a complete description of the joint behavior of attribute subsets. However, the determination of fuzzy measures is often hard. A common way to identify fuzzy measures is HLMS (Heuristic Least Mean Squares) algorithm. In this paper, the convergence of the HLMS algorithm is analyzed. First, we show that the learning rate parameter ( ) dominates the convergence of HLMS. Second, we provide an upper bound for that guarantees HLMS convergence. In addition, a toy example shows the descriptive power of fuzzy measures versus the poverty of individual measures.