Interval Type-2 Fuzzy Sets
Interval type-2 fuzzy sets have received the most attention because the mathematics that is needed for such sets—primarily Interval arithmetic—is much simpler than the mathematics that is needed for general type-2 fuzzy sets. So, the literature about interval type-2 fuzzy sets is large, whereas the literature about general type-2 fuzzy sets is much smaller. Both kinds of fuzzy sets are being actively researched by an ever-growing number of researchers around the world.
Formulas for the following have already been worked out for interval type-2 fuzzy sets:
- Fuzzy set operations: union, intersection and complement (, )
- Centroid (a very widely used operation by practitioners of such sets, and also an important uncertainty measure for them) (, )
- Other uncertainty measures and uncertainty bounds
- Similarity (, )
- Subsethood
- Fuzzy set ranking
- Fuzzy rule ranking and selection
- Type-reduction methods (, )
- Firing intervals for an interval type-2 fuzzy logic system (, )
- Fuzzy weighted average
- Linguistic weighted average
- Synthesizing an FOU from data that are collected from a group of subject
Read more about this topic: Type-2 Fuzzy Sets And Systems
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