A new approach to similarity and inclusion measures between general type-2 fuzzy sets

Soft Computing

Volumn 18, Issue 4, 2014, Pages 809-823

  Zhao, Tao ^a   Xiao, Jian ^a   Li, YiXing ^a   Deng, XueSong ^a  

^a SOUTHWEST JIAOTONG UNIVERSITY   (China)

Author keywords

General type 2 fuzzy sets; Inclusion measure; Similarity measure; Plane theory

Indexed keywords

FUZZY LOGIC;

AXIOMATIC DEFINITIONS; GENERAL TYPE-2 FUZZY; GENERAL TYPE-2 FUZZY SETS; INCLUSION MEASURE; INTERVAL TYPE-2 FUZZY; REPRESENTATION THEORY; SIMILARITY MEASURE; TYPE-1 FUZZY SETS;

FUZZY SETS;

EID: 84897579805     PISSN: 14327643     EISSN: 14337479     Source Type: Journal    
DOI: 10.1007/s00500-013-1101-z     Document Type: Article

References (31)

1. Coupland S, John RI (2004a) Fuzzy logic and computational geometry. In: Proceedings of the International Conference on Recent Advances in Soft Computing. Nottingham, pp 3-8.
2. Coupland S, John RI (2004b) A new and efficient method for the Type-2 meet operation. In: Proceedings of the IEEE International Conference on Fuzzy Systems, pp 959-964.
3. Coupland S, John RI (2007) Geometric type-1 and type-2 fuzzy logic system. IEEE Trans Fuzzy Syst 15(1): 3-15.
4. Hamrawi H, Coupland S (2010) Measures of uncertainty for type-2 fuzzy sets. In: Proceedings of the computational intelligence (UKCI), 2010 UK workshop on digital object identifier, pp 1-6.
5. Hwang CM, Yang MS, Hung WL, Lee ES (2011) Similarity, inclusion and entropy measures between type-2 fuzzy sets based on the Sugeno integral. Math Comput Model 53: 1788-1797.
6. John RI, Coupland S (2007) Type-2 fuzzy logic: a historical view. IEEE Comput Intell Mag 2(1): 57-62.
7. Kosko B (1990) Fuzziness vs. probability. Int J Gen Syst 17: 211-240.
8. Karnik NN, Mendel JM, Liang Q (1999) Type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 7(6): 643-658.
9. Liang Q, Mendel JM (2000) Interval type-2 fuzzy logic systems: theory and design. IEEE Trans Fuzzy Syst 18: 535-550.
10. Liu YH, Xiong FL (2002) Subsethood on intuitionistic fuzzy sets. In: Proceedings of the international conference on machine learning and cybernetics, pp 1336-1339.
11. Liu F (2008) An efficient centroid type-reduction strategy for general type-2 fuzzy logic system. Inform Sci 178(9): 2224-2236.
12. Mendel JM (2001) Uncertain rule-based fuzzy logic systems: introduction and new directions. Prentice Hall, Upper Saddle River.
13. Mitchell HB (2005) Pattern recognition using type-II fuzzy sets. Inform Sci 170(2): 409-418.
14. Mendel JM, John RI, Liu F (2006) Interval type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 14(6): 808-821.
15. Mendel JM, Liu F, Zhai DY (2009) Alpha-plane representation for type-2 fuzzy sets: theory and applications. IEEE Trans Fuzzy Syst 17(5): 1189-1207.
16. Mendel JM (2010) Comments on alpha-plane representation for type-2 fuzzy sets: theory and applications. IEEE Trans Fuzzy Syst 18(1): 229-230.
17. Mendel JM, Wu DR (2010) Perceptual computing: aiding people in making subjective judgments. Wiley-IEEE Press, Hoboken.
18. Rickard JT, Aisbett J, Gibbon G (2009) Fuzzy subsethood for fuzzy sets of type-2 and generalized type-n. IEEE Trans Fuzzy Syst 17(1): 50-60.
19. Wu DR, Mendel JM (2007) Uncertainty measures for interval type-2 fuzzy sets. Inform Sci 177(23): 5378-5393.
20. Wagner C, Hagras H (2008) z-Slices-towards bridging the gap between interval and general type-2 fuzzy logic. In: Proceedings of the IEEE international conference on fuzzy systems, pp 489-497.
21. Wu DR, Mendel JM (2008) A vector similarity measure for linguistic approximation: Interval type-2 and type-1 fuzzy sets. Inform Sci 178(2): 381-402.
22. Wagner C, Hagras H (2009) z-Slices based general type-2 FLC for the control of autonomous mobile robots in real world environments. In: Proceedings of the IEEE international conference on fuzzy systems, pp 718-725.
23. Wu DR, Mendel JM (2009) A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets. Inform Sci 179(8): 1169-1192.
24. Wagner C, Hagras H (2010) Towards general type-2 fuzzy logic systems based on z-Slices. IEEE Trans Fuzzy Syst 18(4): 637-660.
25. Yang MS, Lin DC (2009) On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering. Comput Math Appl 57: 896-907.
26. Zadeh LA (1965) Fuzzy sets. Inform Control 8: 338-356.
27. Zadeh LA (1975) The concept of linguistic variable and its application to approximate reasoning. Inform Sci 8(2): 199-249.
28. Zeng WY, Li HX (2006) Relationship between similarity measure and entropy of interval valued fuzzy sets. Fuzzy Sets Syst 157(11): 1477-1484.
29. Zeng WY, Guo P (2008) Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship. Inform Sci 178(5): 1334-1342.
30. Zhang HY, Zhang WX, Mei CL (2009) Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure. Knowl Based Syst 22(6): 449-454.
31. Zhai DY, Mendel JM (2011) Uncertainty measures for general type-2 fuzzy sets. Inform Sci 181(3): 503-518.