Fuzzy logic became the core of a different approach to computing. Whereas traditional approaches to computing were precise, or hard edged, fuzzy logic allowed for the possibility of a less precise or softer approach (Klir et al., 1995, pp. 212-242). An approach where precision is not paramount is not only closer to the way humans thought, but may be in fact easier to create as well (Jin, 2000). Thus was born the field of soft computing (Zadeh, 1994). Other techniques were added to this field, such as Artificial Neural Networks (ANN), and genetic algorithms, both modeled on biological systems. Soon it was realized that these tools could be combined, and by mixing them together, they could cover their respective weaknesses while at the same time generate something that is greater than its parts, or in short, creating synergy. Adaptive Neuro-fuzzy is perhaps the most prominent of these admixtures of soft computing technologies (Mitra et al., 2000). The technique was first created when artificial neural networks were modified to work with fuzzy logic, hence the Neuro-fuzzy name (Jang et al., 1997, pp. 1-7). This combination provides fuzzy systems with adaptability and the ability to learn. It was later shown that adaptive fuzzy systems could be created with other soft computing techniques, such as genetic algorithms (Yen et al., 1998, pp. 469-490), Rough sets (Pal et al., 2003; Jensen et al., 2004, Ang et al., 2005) and Bayesian networks (Muller et al., 1995), but the Neuro-fuzzy name was widely used, so it stayed. In this chapter we are using the most widely used terminology in the field. Neuro-fuzzy is a blanket description of a wide variety of tools and techniques used to combine any aspect of fuzzy logic with any aspect of artificial neural networks. For the most part, these combinations are just extensions of one technology or the other. For example, neural networks usually take binary inputs, but use weights that vary in value from 0 to 1. Adding fuzzy sets to ANN to convert a range of input values into values that can be used as weights is considered a Neuro-fuzzy solution. This chapter will pay particular interest to the sub-field where the fuzzy logic rules are modified by the adaptive aspect of the system. The next part of this chapter will be organized as follows: in section 1 we examine models and techniques used to combine fuzzy logic and neural networks together to create Neuro-fuzzy systems. Section 2 provides an overview of the main steps involved in the development of adaptive Neuro-fuzzy systems. Section 3 concludes this chapter with some recommendations and future developments.
GPS Data Correction Based on Fuzzy Logic for Tracking Land Vehicles
