Operation properties and δ-equalities of complex fuzzy sets

International Journal of Approximate Reasoning

Volumn 50, Issue 8, 2009, Pages 1227-1249

  Zhang, Guangquan ^a   Dillon, Tharam Singh ^b   Cai, Kai Yuan ^c   Ma, Jun ^a   Lu, Jie ^a  

^a UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

^b CURTIN UNIVERSITY   (Australia)

^c BEIHANG UNIVERSITY   (China)

Author keywords

Equality; Complex fuzzy set; Distance measure; Fuzzy set; Operation

Indexed keywords

COMPLEX FUZZY SET; COMPLEX FUZZY SETS; COMPLEX PLANES; DISTANCE MEASURE; OPERATION; UNIT CIRCLES;

MEMBERSHIP FUNCTIONS;

FUZZY SETS;

EID: 70349972054     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2009.05.010     Document Type: Article

References (20)

1. J.J. Buckley, Fuzzy complex numbers, in: Proceedings of ISFK, Guangzhou, China, 1987, pp. 597-700.
2. Buckley J.J. Fuzzy complex numbers. Fuzzy Sets and Systems 33 3 (1989) 333-345
3. Buckley J.J. Fuzzy complex analysis I: Definition. Fuzzy Sets and Systems 41 2 (1991) 269-284
4. Buckley J.J. Fuzzy complex analysis II: Integration. Fuzzy Sets and Systems 49 2 (1992) 171-179
5. Cai K.Y. δ-Equalities of fuzzy sets. Fuzzy Sets and Systems 76 1 (1995) 97-112
6. Cai K.Y. Robustness of fuzzy reasoning and δ-equalities of fuzzy sets. IEEE Transaction on Fuzzy Systems 9 5 (2001) 738-750
7. Coupland S., and John R. New geometric inference techniques for type-2 fuzzy sets. International Journal of Approximate Reasoning 49 1 (2008) 198-211
8. Dalalah D.M. Piecewise parametric polynomial fuzzy sets, International Journal of Approximate Reasoning 50 7 (2009) 1081-1096
9. Georgescu I. A generalization of the CAI δ-equality of fuzzy sets. Proceedings of the International Conference on Fuzzy Information Processing: Theory and Applications vol. I (2003), Tsinghua University Press/Springer pp. 123-127
10. Hong D.H., and Hwang S.Y. A note on the value similarity of fuzzy systems variables. Fuzzy Sets and Systems 66 3 (1994) 383-386
11. Pappis C.P. Value approximation of fuzzy systems variables. Fuzzy Sets and Systems 39 1 (1991) 111-115
12. Ramot D., Milo R., Friedman M., and Kandel A. Complex fuzzy sets. IEEE Transaction on Fuzzy Systems 10 2 (2002) 171-186
13. Ramot D., Friedman M., Langholz G., and Kandel A. Complex fuzzy logic. IEEE Transaction on Fuzzy Systems 11 4 (2003) 450-461
14. Tóczy L., and Hirota K. Approximate reasoning by linear rule interpolation and general approximation. International Journal of Approximate Reasoning 9 3 (1993) 197-225
15. Virant J. Design Considerations of Time in Fuzzy Systems (2000), Kluwer Academic Publishers
16. Yeh C.-T. On improving trapezoidal and triangular approximations of fuzzy numbers. International Journal of Approximate Reasoning 48 1 (2008) 297-313
17. Zadeh L.A. Fuzzy sets. Information and Control 8 (1965) 338-353
18. Zhang G.Q. Fuzzy limit theory of fuzzy complex numbers. Fuzzy Sets and Systems 46 2 (1992) 227-235
19. Zhang G.Q. Fuzzy distance and limit of fuzzy numbers. Fuzzy Systems and Mathematics 6 1 (1992) 21-28
20. Zhang G.Q. Fuzzy continuous function and its properties. Fuzzy Sets and Systems 43 2 (1991) 159-175