The main difference between them is that the type-2 fuzzy set itself is fuzzy, with a new dimension called the footprint of uncertainty, which characterizes type-2 fuzzy logic.
The rule structure of both types are the same, except for the antecedent and consequent are of the respective types.
You may refer to
http://www.aensiweb.com/jasr/jasr/2012/2564-2574.pdf
or
http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6669886&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6669886
The type-2 fuzzy sets generalize type-1 fuzzy sets. A type-2 fuzzy set lets us incorporate uncertainty about the membership function into fuzzy set theory. The first mention was publicised by L. A. Zadeh: "The Concept of a Linguistic Variable and Its Application to Approximate Reasoning–1," Information Sciences, vol. 8, pp. 199–249, 1975.
Membership functions are used to describe these fuzzy sets, and in a type-1 FLS they are all type-1 fuzzy sets, whereas in an interval type-2 FLS at least one membership function is an interval type-2 fuzzy set.
While I clearly understand the differences, I'm not very sure that for control system applications the additional computational effort required for a Type II is justified in comparison to a well tuned type I fuzzy logic control system.
One of main differences between fuzzy type 2 and 1 is in fuzzy type 2 we have the so-called type reduction before defuzzification level.
Fuzzy type 2 makes our system more noise tolerant but also may be computationally costly. I you could get a good result with fuzzy type 1, don't use Fuzzy type 2.
The work "A study of the subjectivities of Type 1 and Type 2 in parameters of differential equations" (Bertone, Jafelice and Bassanezi) is a comparative study between the solutions obtained from the logistic model for the two types of fuzzy subjectivities. When using Type 2 we obtain the response more accurately.
The concept of type-2 fuzzy sets (T2FSs) as an extension of the type-1 fuzzy sets (T1FSs) was first introduced in . Type-2 fuzzy sets can handle such uncertainties because their membership functions are fuzzy. A FLS described using at least one T2FS is called a type-2 fuzzy logic system (T2FLS). T2FLS can be used in circumstances where it is difficult to determine an exact membership function such as when the training data are corrupted by noise .
"Jerry Mendel" has great articles in this field !!!
In Type 1 fuzzy set , Expert should determine the degree of achieving the characteristics of the object. For example, if you have a 3 different red balls. The first is red by 75%, second is red 85%, Third is red 95%.
In Type 2 Fuzzy set, Expert can't determine exactly the degree of achieving the characteristics. For example, if you have a 3 different red balls. The first is red by 75%-80%, second is red 85%-90%, Third is red 95%-100%. So it presents an interval fuzzy set.
Type 1 FS membership ftn is certain value lies in [0,1], while type 2 FS MS is uncertain or vague i.e fuzzy. So may be lies in an interval rather than a specific value.
In Type 2 FS, the decision boundary is uncertain and thus is not sharp
Ye in fuzzy type -2 we will discuss the fuzziness of those set In which memebrship value can be achieved by T-1 fuzzy set
Simply type 1 attributes are crispy or precise but allow fuzzy queries, while type2 is a collection of imprecise data ordered over possibility distribution
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