Some Aspects of Picture Fuzzy Set

Some Aspects of Picture Fuzzy Set

Palash Dutta Silpashree Ganju 

Dept. of Mathematics, Dibrugarh University-India 786001

Corresponding Author Email: 
palash.dtt@gmail.com, silpashree1993@gmail.com
Page: 
127-141
|
DOI: 
https://doi.org/10.18280/ama_a.540109
Received: 
15 March 2017
|
Accepted: 
15 April 2017
|
Published: 
30 March 2017
| Citation

OPEN ACCESS

Abstract: 

In this paper, decomposition theorems of picture fuzzy set (PFS) have been proved. (⍺,δ,β)-cut of picture fuzzy set have been defined and some of its properties are studied. Later on extension principle for PFS has been defined and studied some of its properties. Finally, picture fuzzy arithmetic based on extension principle has been performed.

Keywords: 

Fuzzy set, Fuzzy arithmetic, Extension principle, Picture fuzzy set

1. Introduction
2. Preliminaries
3. Proposition (Cuong and Kreinovich, 2013)
4. Decomposition Theorem for PFS
5. Properties of Picture Fuzzy Set
6. Extension Principle of PFS
7. Picture Fuzzy Arithmetic
8. Conclusion
  References

1. K.T. Atanassov, Intuitionistic fuzzy sets, 1986, Fuzzy Sets and Systems, vol. 20, pp. 87–96. 

2. B.C. Cuong, Picture Fuzzy Sets, 2014, Journal of Computer Science and Cybernetics, vol. 30, pp. 409–420. 

3. B.C. Cuong, P.V. Hai, Some fuzzy logic operators for picture fuzzy sets, 2015, Seventh International Conference on Knowledge and Systems Engineering, pp. 132-137. 

4. B.C. Cuong, R.T. Ngan, B.D. Hai, An involutive picture fuzzy negator on picture fuzzy sets and some De Morgan triples, 2015, Seventh International Conference on Knowledge and Systems Engineering, pp. 126-131. 

5. B.C. Cuong, V. Kreinovich, Picture Fuzzy Sets- a new concept for computational intelligence problems, 2013, In Proceedings of the Third World Congress on Information and Communication Technologies WIICT 2013, pp. 1-6. 

6. B.C. Cuong, V. Kreinovich, R.T. Ngan, A classification of representable t-norm operators for picture fuzzy sets, 2016, Departmental Technical Reports (CS). Paper 1047. http://digitalcommons.utep.edu/cs_techrep/1047 

7. P.H. Phong, D.T. Hieu, R.H. Ngan, P.T. Them, Some Compositions of Picture Fuzzy Relations, 2014, Kỷ yếu Hội nghị Quốc gia lần thứ … về Nghiên cứu cơ bản và ứng dụng Công Nghệ thông tin (FAIR); …, ngày …/…/… 

8. L.H. Son, Generalized picture distance measure and applications to picture fuzzy clustering, 2016, Appl. Soft Comput. J.

9. L.A. Zadeh, Fuzzy sets, 1965, Inform. Control. Vol. 8, pp. 338–356.