The fuzzy sets, discussed in the previous chapter, are called type-1 fuzzy sets. They are characterized by the membership function, while the value of this function for a given element x is called the grade of membership of this element to a fuzzy set. In case of type-1 fuzzy sets, the membership grade is a real number taking values in the interval [0,1]. This chapter will present another concept of a fuzzy description of uncertainty. According to this concept, the membership grade is not a number any more, but it has a fuzzy character. Figure 5.1 shows a graphic illustration of type-1 fuzzy sets A1,…,A5 and corresponding type-2 fuzzy sets Ã1,…, Ã5. It should be noted that in case of type-2 fuzzy sets, for any given element x, we cannot speak of an unambiguously specified value of the membership function. In other words, the membership grade is not a number, as in case of type-1 fuzzy sets.
In subsequent points of this chapter, basic definitions concerning type-2 fuzzy sets will be presented and operations on these sets will be discussed. Then type-2 fuzzy relations and methods of transformation of type-2 fuzzy sets into type-1 fuzzy sets will be introduced.
In the last part of this chapter, the theory of type-2 fuzzy sets will serve for the construction of the fuzzy inference system. Particular blocks of such system will be discussed in details, including type-2 fuzzification, type-2 rules base, type-2 inference mechanisms and the two-stage defuzzification consisting of type-reduction and defuzzification.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Methods of knowledge representation using type-2 fuzzy sets. In: Computational Intelligence. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76288-1_5
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DOI: https://doi.org/10.1007/978-3-540-76288-1_5
Publisher Name: Springer, Berlin, Heidelberg
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