Name
Abstract | ||
|---|---|---|
This paper 1) reviews the alpha-plane representation of a type-2 fuzzy set (T2 FS), which is a representation that is comparable to the alpha-cut representation of a type-1 FS (T1 FS) and is useful for both theoretical and computational studies of and for T2 FSs; 2) proves that set theoretic operations for T2 FSs can be computed using very simple alpha-plane computations that are the set theoretic operations for interval T2 (IT2) FSs; 3) reviews how the centroid of a T2 FS can be computed using alpha-plane computations that are also very simple because they can be performed using existing Karnik Mendel algorithms that are applied to each alpha-plane; 4) shows how many theoretically based geometrical properties can be obtained about the centroid, even before the centroid is computed; 5) provides examples that show that the mean value (defuzzified value) of the centroid can often be approximated by using the centroids of only 0 and 1 alpha-planes of a T2 FS; 6) examines a triangle quasi-T2 fuzzy logic system (Q-T2 FLS) whose secondary membership functions are triangles and for which all calculations use existing T1 or IT2 FS mathematics, and hence, they may be a good next step in the hierarchy of FLSs, from T1 to IT2 to T2; and 7) compares T1, IT2, and triangle Q-T2 FLSs to forecast noise-corrupted measurements of a chaotic Mackey-Glass time series. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1109/TFUZZ.2009.2024411 | IEEE TRANSACTIONS ON FUZZY SYSTEMS |
Keywords | Field | DocType |
alpha-Plane, centroid, Mackey-Glass time series, quasi-type-2 fuzzy logic systems (Q-T2 FLSs), set theoretic operations, type-2 fuzzy sets (T2 FSs) | Defuzzification,Fuzzy classification,Fuzzy set operations,Fuzzy logic,Algorithm,Fuzzy set,Artificial intelligence,Fuzzy number,Membership function,Machine learning,Centroid,Mathematics | Journal |
Volume | Issue | ISSN |
17 | 5 | 1063-6706 |
Citations | PageRank | References |
136 | 3.92 | 37 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mendel, J.M. | 1 | 10926 | 1042.42 |
| Feilong Liu | 2 | 429 | 15.52 |
| Daoyuan Zhai | 3 | 287 | 9.85 |