Relations between Interval Computing and Soft Computing

This volume is about knowledge processing with interval and soft computing, i.e., about techniques that use both interval and soft computing to process knowledge and about the results of applying these techniques. To better understand these techniques, in Chapter 1, we described fundamentals of interval computing, and in Chapter 2, we described the fundamentals of soft computing. Now it is time to explain how these techniques are related – and how they can be combined. Some examples of such a relation were already given in Chapter 2 – e.g., interval-valued fuzzy sets. Now it is time to provide a systematic description of this relation. After this chapter, we will be ready to describe how to combine interval and fuzzy techniques, and how the resulting combined techniques can be applied to real-life problems. This chapter starts with a brief reminder of why data processing and knowledge processing are needed in the first place, why interval and fuzzy methods are needed for data and knowledge processing, and which of the possible data and knowledge processing techniques we should use. Then, we explain how these reasonable soft computing techniques are naturally related with interval computing. Finally, we explain the need for interval-valued fuzzy techniques – techniques which will be used a lot in our future applications – and how the transition to such techniques is also related to interval computing.