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What is Footprint of Uncertainty (FOU)

Chapter 1
Handbook of Research on Computational Intelligence for Engineering, Science, and Business
To indicate a graph of type-2 fuzzy set more easily, the concept of the footprint of uncertainty is used. The membership function of a general type-2 fuzzy set, Ã, is three-dimensional ( Figure 1 ), where the third dimension is the value of the membership function at each point on its two-dimensional domain that is called its footprint of uncertainty (FOU). The footprint of uncertainty (FOU) of a type-2 fuzzy set à is a region with boundaries covering all the primary membership points of elements x, and is defined as follows: The more (less) area in the FOU the more (less) is the uncertainty.
Published in Chapter:
Computational Intelligence Using Type-2 Fuzzy Logic Framework
A. Neogi (The University of Burdwan, India), A.C. Mondal (The University of Burdwan, India), and S.K. Mandal (National Institute of Technical Teachers’ Training & Research, India)
Copyright: © 2013 |Pages: 29
DOI: 10.4018/978-1-4666-2518-1.ch001
Abstract
In this chapter, the authors expand the notion of type-2 fuzzy sets. An introduction to standard and interval (type-2) fuzzy sets and systems is explained in the early part of the discussion. The chapter also covers the ideas of hybrid type-2 fuzzy system. Next, the authors study the applicability of type-2 fuzzy logic (FL) system in student’s performance in oral presentation as it is clearly new field of research topic and have an excellent opportunity to combine several fuzzy set method developed in the recent years. The proposed application shows the linkage of type-2 fuzzy system with TOPSIS. The present chapter also highlights the possible future directions for type-2 FL system research. By the end of the chapter, the authors hope that even those with little previous experience of fuzzy logic should be enabled to apply these methods in their own application areas and/or begin research in this fascinating and exciting area.
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More Results
Chapter 14
Computing with Words Model for Emotion Recognition Using Interval Type-2 Fuzzy Sets
The region bounded by UMF and LMF of the IT2FS is called FOU. A larger FOU will imply that the problem is characterized by a higher amount of uncertainty. It is desirable to reduce the footprint of uncertainty without comprising on the information contained in it to make classification more accurate.
Published in Chapter: Computing with Words Model for Emotion Recognition Using Interval Type-2 Fuzzy Sets; From: Handbook of Research on Synthesizing Human Emotion in Intelligent Systems and Robotics
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