CCI & ElderTech
Uncertainty Modelling in Technologies for the Elderly
Type-2 Fuzzy Logic Questions:
Type-2 Fuzzy Logic Questions Answered:
- What does fuzzy logic do?
- What's the difference between type-1 and type-2?
- What's a type-2 fuzzy set?
- What evidence is there that type-2 works better than type-1?
- Where can I find out more?
Type-2 Fuzzy Logic Questions Answered:
- What does fuzzy logic do?
Fuzzy logic is a way of representing and modelling uncertainty and imprecision. The basic premise is that most (all) applications in the general area of modelling decision making have to cope with imprecision in data, knowledge, rules etc. It provides a way of not ignoring this imprecision but using it to make better computer systems. It is used heavily in control applications and, the argument by some is, has not made as big an impact as expected in modelling human decision making. Hence the interest in type-2 fuzzy sets.
Back to top - What's the difference between type-1 and type-2?
A type-1 approach models uncertainty using a number between zero and one. It is crisp. Type-2 fuzzy logic represents uncertainty using a function which is itself a type-1 fuzzy number. Sometimes type-2 is referred to as fuzzy fuzzy because of this.
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What's a type-2 fuzzy set?
A type-2 fuzzy set maps elements in a crisp domain to type-1 fuzzy numbers bounded in the range [0,1]. We denote a fuzzy set as type-2 by placing a tilde character above the name of the set. For example a the type-2 fuzzy set fast would be denoted as
.
Since the value at each point in a type-2 fuzzy set is given as a function, type-2 fuzzy sets are three-dimensional. The type-2 fuzzy set fast is depicted below:
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What evidence is there that type-2 works better than type-1?
A number of researchers have recently shown in certain applications that type-2 can outperform type-1. If you look at papers by Hagras (Essex University), John (De Montfort University) and Mendel (University of Southern California) you will see number of application led papers. The number of application papers is growing and they all show an improvement over type-1.
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Where can I find out more?
Jerry Mendel has a book (Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions) which is a very good starting point. The paper by mendel and John (Type-2 Fuzzy Sets Made Simple) gives a good explanation of some of the basics and the various operations. There is general type-2 fuzzy logic web portal host by the CCI, http://www.type2fuzzylogic.org/, that hosts a online publications database and a directory of type-2 fuzzy logic researchers.
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