Notes on Extension of Fuzzy Complex Sets
Main Article Content
Abstract
The aim of this paper is to modify and improve the corresponding weakness results of multi-fuzzy complex numbers as an extension of fuzzy complex numbers, next we introduce and study the generalized multi-fuzzy complex numbers and get some results. Lastly, we discuss the derivative of functions mapping complex numbers into as an extension of fuzzy complex derivatives.
Article Details

This work is licensed under a Creative Commons Attribution 4.0 International License.
Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.
References
1. Rejun, L., Shaoqing, Y., Baowen, L., and Weihai,
F., Fuzzy complex numbers, BUSEFAL, 25 (1985)
79-86.
2. Buckley, J.J., Fuzzy complex numbers, Fuzzy
Sets and Systems 33 (1989) 333–345.
3. Quan, M.S., Fuzzy complex numbers and some
operational properties, J. of Lanzhou University,
NSE, 32 (1996) 643-645.
4. Buckley, J.J. and Qu, Y., Fuzzy complex analysis
I: Differentiation, Fuzzy Sets and Systems 41 (1991)
269–284.
5. Dubois, D. and Prade, H., Towards fuzzy
differential calculus, Part 3: Differentiation, Fuzzy
Sets and Systems 8 (1982) 225-233.
6. Cai, Q.P., The continuity of complex fuzzy
function, Adv. in Int. and Soft Computing 2 (2009)
695-704.
7. Chun, C. and Ma, S., The differentiation of
complex fuzzy functions, Proc. of the 9th NCFMFS,
Baoding, Hebei U. Press, (1998) 162-166.
8. Data, S.k., Biswas T., Tamang S., Some
inequalities involving fuzzy complex numbers,
Theory and Applications of Mathematics &
Computer Science 4 (1) (2014) 106–113.
9. Dianjun, Y., On the complex fuzzy derivative,
BUSEFAL, 81 (2000) 90-92.
10. Guangquan, Z., Fuzzy continuous function and its
properties, Fuzzy Sets and Systems 43 (1991) 159–
171.
11. Ousmane, M. and Congxin, W., Semi continuity
of complex fuzzy functions, Tsinghua Science and
Technology, 8 (2003) 65-70.
12. Qiu, D. and Shu, L., Notes on “On the restudy of
fuzzy complex analysis: Part I and Part II”, Fuzzy
Sets and Systems 159 (2008) 2185–2189.
13. Qiu, D., Shu, L. and Mo, Z.W., Notes on fuzzy
complex analysis, Fuzzy Sets and Systems 160
(2009) 1578-1589.
14. Qiu, J., Wu, C. and Li, F., On the restudy of fuzzy
complex analysis: Part II. The continuity and
differentiation of fuzzy complex functions, Fuzzy
Sets and Systems 120 (2001) 517–521.
15. Wu, C. and Qiu, J., Some remarks for fuzzy
complex analysis, Fuzzy Sets and Systems 106
(1999) 231–238.
16. Zengtai, G. and Shengquan, M., The research
advances in fuzzy complex analysis, Math. in Prac.
and Theory 36 (2006) 200-211.
17. Zheng, L. and Ha, M., Further discussions on
rectangular fuzzy complex numbers, Proc. of the 8th
ICMLC, Baoding, (2009) 642-646.
18. Zadeh, L.A., Fuzzy sets, Inform. & Control 8
(1965) 338–353.
19. Zadeh, L.A., The Concept of a Linguistic Variable
and its Application to Approximate Reasoning.
Memorandum ERL-M 411, Berkeley, Ca., (1973).
20. Zadeh, L.A., The concept of a linguistic variable
and its application to approximate reasoning (I), (II),
and (III), Inf. Sci. 8 (1975) 199–249, 301–357, 9
(1975) 43–80.
21. Yager, R.R., On the theory of bags, Int. J. General
Systems, 13 (1985) 23-37.
22. Sebastian, S. and Ramakrishnan, T.V., Multifuzzy
sets: An extension of fuzzy sets, Fuzzy inf.
Eng., 3 (2011) 35-43.
23. Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy
Sets and Systems 20 (1986) 87–96.
24. Dey, A. and Pal, M., Multi-fuzzy complex
numbers and multi-fuzzy complex sets, Int. J. of
Fuzzy System Applications, 4 (2015) 15-27.
25. Dey, A. and Pal, M., Multi-fuzzy complex
nilpotent matrices, Int. J. of Fuzzy System
Applications, 5 (2016) 52-76.
26. Chang, S.S.L. and Zadeh, L.A., Fuzzy mappings
and control, IEEE Trans. Syst., Man and Cyber.,
SMC-2, (1972) 30-34.