Operations on type-2 fuzzy sets based on the set of pseudo-highest intersection points of convex fuzzy sets

Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS

Volumn , Issue , 2010, Pages

  Tahayori, Hooman ^a   Sadeghian, Alireza ^a   Visconti, Andrea ^b  

^a RYERSON UNIVERSITY   (Canada)

^b UNIVERSITY OF MILAN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BASIC OPERATION; CONVEX FUZZY SETS; INTERSECTION OPERATION; INTERSECTION POINTS; T - NORM; T-CONORMS; TYPE-2 FUZZY SET;

DATA PROCESSING; MATHEMATICAL OPERATORS;

FUZZY SETS;

EID: 77956594369     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/NAFIPS.2010.5548213     Document Type: Conference Paper

References (26)

1. L.A. Zadeh, "Fuzzy Sets," Information and Control, vol. 8, pp. 338- 353, 1965.
2. G.J. Klir, T.A. Folger. Fuzzy Sets, Uncertainty, and Information, Prentice-Hall, 1988.
3. W. Pedrycz, "Shadowed sets: representing and processing fuzzy sets," IEEE Trans. on Systems, Man, and Cybernetics, part B, vol. 28, pp. 103-109, 1998.
4. IEC-ISO, Guide to the Expression of Uncertainty in Measurement, October 1993.
5. A. Mencattini, M. Salmeri, R. Lojacono, "Type-2 Fuzzy Sets for Modeling Uncertainty in Measurement," AMUEM 2006 - International Workshop on Advanced Methods for Uncertainty Estimation in Measurement Sardagna, Trento, Italy, 20-21 April 2006.
6. M. Gehrke, C. L. Walker, E. A. Walker. "Some comments on interval valued fuzzy sets," Intl. Journal of Intelligent Systems, vol.11, pp.751- 759, 1996.
7. M. Mizumoto. K. Tanaka, "Some properties of fuzzy sets of type-2," Inform. Control, vol. 31, pp. 312-340, 1976.
8. L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-1," Inform. Sci., vol. 8, pp. 199-249, 1975.
9. J.M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions, Prentice-Hall, Upper-Saddle River, NJ, 2001.
10. R.I. John, S. Coupland," Extensions to Type-1 Fuzzy: Type-2 Fuzzy Logic and Uncertainty," Computational Intelligence: Principles and Practice, pp. 89-102, IEEE, 2006.
11. J.M. Mendel, "Advances in type-2 fuzzy sets and systems," Information Sciences, vol. 177, pp. 84-110, 2007.
12. J.M. Mendel, R.I. John, "Type-2 Fuzzy Sets Made Simple," IEEE Trans. on Fuzzy Systems, vol. 10, no. 2, pp. 117-127, 2002.
13. W. Blewitt, M.Z. Shang, S. Coupland, "A Novel Approach to Type-2 Fuzzy Addition," in Proc. of FUZZ-IEEE 2007, pp. 1-6, 2007.
14. S. Coupland, R.I. John, "Geometric Type-1 and Type-2 Fuzzy Logic Systems," IEEE Trans. on Fuzzy Systems, vol. 15, no. 1, pp. 3-15, 2007.
15. S. Coupland, R.I. John, "A Fast Geometric Method for Defuzzification of Type-2 Fuzzy Sets," IEEE Trans. on Fuzzy Systems, vol. 16, no. 4, pp. 929-941 2008.
16. Z. Gera and J. Dombi, "Exact calculations of extended logical operations on fuzzy truth values," Fuzzy Sets and Systems, vol. 159, pp. 1309-1326, 2008.
17. N.N. Karnik, J.M. Mendel, "Operations on type-2 fuzzy sets," Fuzzy Sets and Systems, vol. 122, pp. 327-348, 2001.
18. H. Tahayori, G. Degli Antoni, "A Simple Method for Performing Type-2 Fuzzy Set Operations Based on Highest Degree of Intersection Hyperplane," in Proc. of NAFIPS'07, pp. 404-409, San Diego, USA, 2007.
19. H. Tahayori, A.G.B. Tettamanzi, G. Degli Antoni, "Approximated Type-2 Fuzzy Set Operations," in Proc. of IEEE World Congress on Computational Intelligence, pp. 1910-1917, Vancouver, 2006.
20. H. Tahayori, A.G.B. Tettamanzi, G. Degli Antoni, A. Visconti, "On the Calculation of Extended Max and Min Operations between Convex Fuzzy Sets of the Real Line," Fuzzy Sets and Systems, vol. 160, no. 21, pp. 3103-3114, 2009.
21. H. Tahayori, A.G.B. Tettamanzi, G. Degli Antoni, A. Visconti, M. Moharrer, "Concave Type-2 Fuzzy Sets: Properties and Operations," Soft Computing Journal, vol. 14, no. 7, pp.749-756, 2010.
22. C. L. Walker, E. A. Walker, "The Algebra of Fuzzy Truth Values," Fuzzy Sets and Systems, vol. 149, pp. 309-347, 2005.
23. H. Bustince, P. Burillo, "Mathematical analysis of interval-valued fuzzy relations: Application to approximate reasoning," Fuzzy Sets and Systems, vol. 113, pp. 205-219, 2000.
24. Q. Liang, J. M. Mendel, "Interval type-2 fuzzy logic systems: Theory and design," IEEE Trans. Fuzzy Syst., vol. 8, pp. 535-550, 2000.
25. J. M. Mendel, R. I. John, F. Liu, "Interval Type-2 fuzzy logic systems made simple", IEEE Trans. on Fuzzy Systems, vol. 14, no 6, pp. 808- 821, 2006.
26. B. I. Turksen, "Interval valued fuzzy sets based on normal forms," Fuzzy Sets and Systems, vol. 20, pp. 191-210, 1986.