Extension of the fuzzy integral for general fuzzy set-valued information

IEEE Transactions on Fuzzy Systems

Volumn 22, Issue 6, 2014, Pages 1625-1639

  Anderson, Derek T ^a   Havens, Timothy C ^b   Wagner, Christian ^c   Keller, James M ^d   Anderson, Melissa F ^e   Wescott, Daniel J ^f  

^a MISSISSIPPI STATE UNIVERSITY   (United States)

^b Michigan Technological University   (United States)

^c UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^d Department of Electrical Engineering and Computer Science   (United States)

^e Department of Anthropology Texas State University ^*  (United States)

^f TEXAS STATE UNIVERSITY   (United States)

Author keywords

Discontinuous interval; fuzzy integral (FI); nonconvex fuzzy set; sensor data fusion; skeletal age at death estimation; subnormal fuzzy set

Indexed keywords

ALGORITHMS; DATA FUSION; DECISION MAKING; FUZZY SETS; IMAGE PROCESSING; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS;

DISCONTINUOUS INTERVAL; FLEXIBLE AGGREGATION; FORENSIC ANTHROPOLOGIES; FUZZY INTEGRAL; MULTI CRITERIA DECISION MAKING; NONCONVEX; UNCERTAIN INFORMATIONS; ZADEH'S EXTENSION PRINCIPLES;

SENSOR DATA FUSION;

EID: 84906250605     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2014.2302479     Document Type: Article

References (29)

1. M. Sugeno, "Theory of fuzzy integrals and its applications," Ph.D. dissertation, Tokyo Institute of Technology, Yokohama, Japan, 1974.
2. H. Tahani and J. Keller, "Information fusion in computer vision using the fuzzy integral," IEEE Trans. Syst. Man Cybern., vol. 20, no. 3, pp. 733-741, May/Jun. 1990.
3. M. Grabisch. (1995). Fuzzy integral in multicriteria decision making. Fuzzy Sets Syst. [Online]. 69(3), pp. 279-298. Available: http://dx.doi.org/ 10.1016/0165-0114(94)00174-6
4. M. Anderson, D. T. Anderson, and D.Wescott, "Estimation of adult skeletal age-at-death using the sugeno fuzzy integral," J. Phys. Anthropol., vol. 142, pp. 30-41, 2010.
5. D. T. Anderson, M. Anderson, J. M. Keller, and D. Wescott, "Linguistic description of adult skeletal age-at-death estimations from fuzzy integral acquired fuzzy sets," in Proc. IEEE Int. Conf. Fuzzy Systems, 2011, pp. 2274-2281.
6. D. T. Anderson, T. C. Havens, C. Wagner, J. M. Keller, M. F. Anderson, and D. J. Wescott, "Sugeno fuzzy integral generalizations for sub-normal fuzzy set-valued inputs," in Proc. IEEE Int. Conf. Fuzzy Syst., Jun. 2012, pp. 1-8.
7. S. Auephanwiriyakul, J. Keller, and P. Gader, "Generalized Choquet fuzzy integral fusion," Inf. Fus., vol. 3, pp. 69-85, 2002.
8. A. Mendez-Vazquez, P. Gader, J. Keller, and K. Chamberlin, "Minimum classification error training for Choquet integrals with applications to landmine detection," IEEE Trans. Fuzzy Syst., vol. 16, no. 1, pp. 225-238, Feb. 2008.
9. J. Bolton, P. Gader, and J. N. Wilson, "Discrete Choquet integral as a distance metric," IEEE Trans. Fuzzy Syst., vol. 16, no. 4, pp. 1107-1110, Aug. 2008.
10. M. Grabisch and J.-M. Nicolas. (1994). Classification by fuzzy integral: Performance and tests. Fuzzy Sets Syst. [Online]. 65(23), pp. 255-271, Fuzzy Methods for Computer Vision and Pattern Recognition. Available: http://www.sciencedirect.com/science/article/pii/016501149490023X
11. L. Hu, D. T. Anderson, and T. C. Havens, "Fuzzy integral for multiple kernel aggregation," in Proc. IEEE Int. Conf. Fuzzy Syst., 2013, pp. 1-7, doi: 10.1109/FUZZ-IEEE.2013.6622312.
12. M. A. Mohamed and P. D. Gader, "Generalized hiddenmarkovmodels - I: Theoretical frameworks," IEEE Trans. Fuzzy Syst., vol. 8, no. 1, pp. 67-81, Feb. 2000.
13. D. Marr, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. New York, NY, USA: Henry Holt, 1982.
14. M. Grabisch, T.Murofushi, and M. Sugeno, Fuzzy Measures and Integrals: Theory and Applications. Heidelberg, Germany: Physica-Verlag, 2000.
15. M. Grabisch, H. Nguyen, and E. Walker, Fundamentals of Uncertainty Calculi, With Applications to Fuzzy Inference. Dordrecht, Germany: Kluwer, 1995.
16. C. Wagner, D. T. Anderson, and T. C. Havens, "Generalization of the fuzzy integral for discontinuous interval-and non-convex interval fuzzy set-valued inputs," in Proc. IEEE Int. Conf. Fuzzy Syst., 2013, pp. 1-8, doi: 10.1109/FUZZ-IEEE.2013.6622507.
17. C. Guo, D. Zhang, and C. Wu. (1998). Generalized fuzzy integrals of fuzzy-valued functions. Fuzzy Sets Syst. [Online]. 97(1), pp. 123-128. Available: http://www.sciencedirect.com/science/article/pii/ S0165011495003401
18. T. C. Havens, D. T. Anderson, and J. M. Keller, "A fuzzy Choquet integral with an interval type-2 fuzzy number-valued integrand," in Proc. IEEE Int. Conf. Fuzzy Syst., Jul. 2010, pp. 1-8.
19. O. Mendoza and P. Melin, "Extension of the Sugeno integral with interval type-2 fuzzy logic," in Proc. Fuzzy Inf. Process. Soc., Annu. Meet. North Amer., May 2008, pp. 1-6.
20. H. Liu, "Type 2 generalized intuitionistic fuzzy choquet integral operator for multi-criteria decision making," in Proc. Int. Symp. Parallel Distrib. Process. Appl., Sep. 2010, pp. 605-611.
21. C. Guo, D. Zhang, and C. Wu, "Fuzzy-valued measures and generalized fuzzy integrals," Fuzzy Sets Syst., vol. 97, pp. 255-260, 1998.
22. G. Wang and X. Li. (2002). Generalized Lebesgue integrals of fuzzy complex valued functions. Fuzzy Sets Syst. [Online]. 127(3), pp. 363-370. Available: http://www.sciencedirect.com/science/article/pii/ S0165011401000689
23. L. Zadeh. (1975). The concept of a linguistic variable and its application to approximate reasoningI. Inf. Sci. [Online]. 8(3), pp. 199-249. Available: http://dx.doi.org/10.1016/0020-0255(75)90036-5
24. C. Wagner and D. T. Anderson, "Extracting meta-measures from data for fuzzy aggregation of crowd sourced information," in Proc. IEEE Int. Conf. Fuzzy Syst., 2012, pp. 1-8, doi: 10.1109/FUZZ-IEEE.2012.6251281.
25. T. C. Havens, D. T. Anderson, C. Wagner, H. Deilamsalehy, and D. Wonnacott, "Fuzzy integrals of crowd-sourced intervals using a measure of generalized accord," in Proc. IEEE Int. Conf. Fuzzy Syst., 2013, pp. 1-8, doi: 10.1109/FUZZ-IEEE.2013.6622343.
26. D. T. Anderson, J. M. Keller, and T. C. Havens, "Learning fuzzy-valued fuzzy measures for the fuzzy-valued Sugeno fuzzy integral," in Proc. Int. Conf. Inf. Process. Manag. Uncertainty, 2010, pp. 502-511.
27. D. Dubois and H. Prade, "Fuzzy numbers: An overview," in Analysis of Fuzzy Information, Vol.I: Mathematics and Logic, J. Bezdek, Ed. Boca Raton, FL, USA: CRC, 1987, pp. 3-39.
28. D. T. Anderson, K. E. Stone, J. M. Keller, and C. J. Spain, "Combination of anomaly algorithms and image features for explosive hazard detection in forward looking infrared imagery," IEEE J. Sel. Topics Appl. Earth Observat. Remote Sens., vol. 5, no. 1, pp. 313-323, Feb. 2012.
29. T. C. Havens, K. Stone, D. T. Anderson, J. M. Keller, K. C. Ho, T. T. Ton, D. C.Wong, andM. Soumekh. (2012).Multiple kernel learning for explosive hazard detection in forward-looking ground-penetrating radar. SPIE Detect. Sens.Mines, Explos. Objects, Obscured Targets XVII, [Online], pp. 83 571D-83 571D-15. Available: http://dx.doi.org/10.1117/12.920482