A Method of Converting a Fuzzy System to a Two-Layered Hierarchical Fuzzy System and Its Run-Time Efficiency

Abstract

In classical single-layer fuzzy systems (FSs), the number of rules and the run-time computational requirements increase exponentially with the number of input domains. In this paper, we present a method for converting a multidimensional FS to a two-layer hierarchical FS that reduces the number of rules and improves the run-time efficiency. The first layer of the two-layer system consists of FSs whose rule bases can be represented as linearly independent vectors. The second layer constructs linear combinations of the rule base vectors. The effectiveness of the hierarchical conversion in reducing the number of rules and improving efficiency is demonstrated on a classic control problem and a simulated higher dimensional FS.

Multi-objective genetic learning of serial hierarchical fuzzy systems for large-scale problems

“…The JS algorithm (Joo and Sudkamp 2009) is one of the most recent approach in this area. For this reason, we thought it would be interesting to implement this approach to compare it with our algorithm.…”

“…The Joo and Sudkamp's (2009) algorithm consists of the conversion from a single-layer FS into a two-layer HFS. The first step is to establish what is the number of variables belonging to each layer is, as follows: let n be the number of variables and k the number of labels, with k !…”

“…The outputs of the modules in the first layer are the inputs of the modules which constitute the next layer, and so on. An aggregate operation might also exist in order to combine the outputs of one layer (Holve 1998;Joo and Lee 1999;Alimi 2005, 2010; Lee et al 2003;Salgado 2008;Zhang and Zhang 2006; Aja-Fernández and Alberola-López 2008; Joo and Sudkamp 2009). • Hybrid HFS (HHFS): This type of HFS is a mixture of the two previous ones (Joo and Lee 2002;Wang et al 2006;Chen et al 2004Chen et al , 2007; Aja-Fernández and Alberola-López 2008) (Fig.…”

“…The general way is to generate new linking variables without linguistic meanings (Lee et al 2003;Cheong 2007;Wang 1999;Zeng et al 2008;Holve 1998;Lee 1999, 2002;Alimi 2005, 2010;Salgado 2008;Zhang and Zhang 2006;Joo and Sudkamp 2009;Wang et al 2006;Chen et al 2004Chen et al , 2007Aja-Fernández and AlberolaLópez 2008;Zajaczkowski and Verma 2012). Gaweda and Scherer (2004) approach this task with fuzzy numbers.…”

Linguistic composition based modelling by fuzzy networks with modular rule bases

“…In this respect, uncertainty is an obstacle to accuracy as it is harder to build an accurate model from uncertain data [29][30][31][32]. Furthermore, dimensionality represents an obstacle to efficiency because it is more difficult to reduce the amount of computations in a FID sequence for a large number of rules [33][34][35][36]. Finally, structure is an obstacle to transparency as it is harder to understand the behaviour of a black-box model that does not reflect the interactions among subsystems [37][38][39][40].…”