Monotone centroid flow algorithm for type reduction of general type-2 fuzzy sets

IEEE Transactions on Fuzzy Systems

Volumn 20, Issue 5, 2012, Pages 805-819

  Linda, Ondrej ^a   Manic, Milos ^a  

^a University of Idaho   (United States)

Author keywords

plane representationow; Centroid; General type 2 fuzzy sets (GT2 FSs); Type reduction

Indexed keywords

BENCH-MARK PROBLEMS; CENTROID; COMPLEX NATURE; COMPUTATIONAL INTENSITY; DYNAMIC UNCERTAINTY; ENGINEERING APPLICATIONS; FAST ALGORITHMS; FAST INFERENCE; FLOW ALGORITHM; INFERENCE PROCESS; ITERATIVE ALGORITHM; ITERATIVE PROCEDURES; MONOTONE PROPERTIES; TYPE REDUCTION; TYPE-2 FUZZY LOGIC SYSTEM; TYPE-2 FUZZY SET;

ALGORITHMS; BENCHMARKING; FUZZY LOGIC; FUZZY SETS;

ITERATIVE METHODS;

EID: 84867357760     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2012.2185502     Document Type: Article

References (35)

1. J. M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Upper Saddle River, NJ: Prentice-Hall, 2001.
2. J. M. Mendel, "Advances in type-2 fuzzy sets and systems," Inf. Sci., vol. 177, pp. 84-110, 2007. (Pubitemid 44566500)
3. H. Hagras, "Type-2 FLCs: A new generation of fuzzy controllers," IEEE Comput. Intell. Mag., vol. 2, no. 1, pp. 30-43, Feb. 2007. (Pubitemid 46718756)
4. N. N. Karnik and J. M. Mendel, "Type-2 fuzzy logic systems," IEEE Trans. Fuzzy Syst., vol. 7, no. 6, pp. 643-658, Dec. 1999. (Pubitemid 32212156)
5. S. Coupland and R. John, "Geometric type-1 and type-2 fuzzy logic systems," IEEE Trans. Fuzzy Syst., vol. 15, no. 1, pp. 3-15, Feb. 2007. (Pubitemid 46444300)
6. L. A. Zadeh, "The concept of a linguistic variable and its approximate reasoning - II," Inf. Sci., vol. 8, pp. 301-357, 1975.
7. H. A. Hagras, "A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots," IEEE Trans. Fuzzy Syst., vol. 12, no. 4, pp. 524-539, Aug. 2004.
8. J. Figueroa, J. Posada, J. Soriano, M. Melgarejo, and S. Rojas, "A type-2 fuzzy logic controller for tracking mobile objects in the context of robotic soccer games," in Proc. IEEE Int. Conf. Fuzzy Syst., 2005, pp. 359-364. (Pubitemid 41189533)
9. Ch. Lynch and H. Hagras, "Using uncertainty bounds in the design of an embedded real-time type-2 neuro-fuzzy speed controller for marine diesel engines," in Proc. IEEE Int. Conf. Fuzzy Syst., Vancouver, BC, Canada, 2006, pp. 1446-1453. (Pubitemid 46948942)
10. O. Linda and M. Manic, "Uncertainty-robust design of interval type-2 fuzzy logic controller for delta parallel robot," IEEE Trans. Ind. Informat., vol. 7, no. 4, pp. 661-671, Nov. 2011.
11. O. Linda and M. Manic, "Interval type-2 fuzzy voter design for fault tolerant systems," Inf. Sci., vol. 181, no. 14, pp. 2933-2950, Jul. 2011.
12. A. Niewiadomski, "On finity, countability, cardinalities, and cylindric extensions of type-2 fuzzy sets in linguistic summarization of databases," IEEE Trans. Fuzzy Syst., vol. 18, no. 3, pp. 532-545, Jun. 2010.
13. D. Wu and J. M. Mendel, "On the continuity of type-1 and interval type-2 fuzzy logic systems," IEEE Trans. Fuzzy Syst., vol. 19, no. 1, pp. 179-192, Feb. 2011.
14. N. Karnik and J. M. Mendel, "Centroid of a type-2 fuzzy set," Inf. Sci., vol. 132, pp. 195-220, 2001. (Pubitemid 32273094)
15. J. M. Mendel, R. John, and F. Liu, "Interval type-2 fuzzy logic systems made simple," IEEE Trans. Fuzzy Syst., vol. 14, no. 6, pp. 808-821, Dec. 2006. (Pubitemid 46432460)
16. F. Liu, "An efficient centroid type-reduction strategy for general type-2 fuzzy logic system," Inf. Sci., vol. 178, pp. 2224-2236, 2008.
17. J. M. Mendel, F. Liu, and D. Zhai, "α-plane representation for type-2 fuzzy sets: Theory and applications," IEEE Trans. Fuzzy Syst., vol. 17, no. 5, pp. 1189-1207, Oct. 2009.
18. Ch. Wagner and H. Hagras, "Toward general type-2 fuzzy logic systems based on zSlices," IEEE Trans. Fuzzy Syst., vol. 18, no. 4, pp. 637-660, Aug. 2010.
19. J. M. Mendel, "Comments on α-plane representation for type-2 fuzzy sets: Theory and applications," IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 229-230, Feb. 2010.
20. X. Liu and J. M. Mendel, "Connect Karnik-Mendel algorithms to rootfinding for computing the centroid of an interval type-2 fuzzy set," IEEE Trans. Fuzzy Syst., vol. 19, no. 4, pp. 652-665, Aug. 2011.
21. D. Zhai and J. M. Mendel, "Centroid of a general type-2 fuzzy set computed by means of the centroid-flow algorithm," in Proc. World Congress Comput. Intell. 2010, Barcelona, Spain, Jul. 2010, pp. 895-902.
22. D. Zhai and J. M. Mendel, "Computing the centroid of a general type-2 fuzzy set by means of the centroid-flow algorithm," IEEE Trans. Fuzzy Syst., vol. 19, no. 3, pp. 401-422, Jun. 2011.
23. J. M. Mendel and R. I. John, "A fundamental decomposition of type-2 fuzzy sets," in Proc. IFSAWorld Congr. 20th NAFIPS Int. Conf., Jul. 2001, pp. 1896-1901.
24. H. Tahayori, A. G. B. Tettamanzi, and G. D. Antoni, "Approximated type-2 fuzzy set operations," in Proc. IEEE Int. Conf. Fuzzy Syst., 2006, pp. 1910-1917. (Pubitemid 46949008)
25. D. Wu and J. M. Mendel, "Enhanced Karnik-Mendel algorithms," IEEE Trans. Fuzzy Syst., vol. 17, no. 4, pp. 923-934, Aug. 2009.
26. S. Greenfield, R John, and S. Coupland, "A novel sampling method for type-2 defuzzification," in Proc. U.K. Workshop Comput. Intell., 2005, pp. 120-127.
27. S. Greenfield, F. Chiclana, S. Coupland, and R. John, "Type-2 defuzzification: Two contrasting approaches," in Proc. IEEE World Congr. Comput. Intell., Barcelona, Spain, Jun. 2010, pp. 3183-3189.
28. S. Greenfield, F. Chiclana, S. Coupland, and R. John, "The collapsing method of defuzzification for discretized interval type-2 fuzzy sets," Inf. Sci., vol. 179, no. 13, pp. 2055-2069, Jun. 2009.
29. C. Y. Yeh, W. H. Jeng, and S. J. Lee, "An enhanced type-reduction algorithm for type-2 fuzzy sets," IEEE Trans. Fuzzy Syst., vol. 19, no. 2, pp. 227-240, Apr. 2011.
30. N. N. Karnik and J.M. Mendel, "Operations on type-2 fuzzy sets," Fuzzy Sets Syst., vol. 122, no. 2, pp. 327-348, Sep. 2001.
31. H. Hamrawi and S. Coupland, "Non-specificity measures for type-2 fuzzy sets," in Proc. IEEE Int. Conf. Fuzzy Systems, Aug. 2009, pp. 732-737.
32. G. Klir andB. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications. Upper Saddle River, NJ: Prentice-Hall, 1995.
33. K. Duran, H. Bernal, and M. Melgarejo, "Improved iterative algorithm for computing the generalized centroid of an interval type-2 fuzzy set," in Proc. Annu. Meet. North Amer. Fuzzy Inf. Process. Soc., May 2008, pp. 1-5.
34. P. Jaccard, "Nouvelles recherches sur la distribution florale," Bulletin Soc. Vaud des Sci. Naturelles, vol. 44, pp. 223-270, 1908.
35. J. M. Mendel and F. Liu, "Super-exponential convergence of the Karnik- Mendel algorithms for computing the centroid of an interval type-2 fuzzy set," IEEE Trans. Fuzzy Syst., vol. 15, no. 2, pp. 309-320, Apr. 2007. (Pubitemid 46563430)