Pythagorean Picture Fuzzy Sets, Part 1- basic notions

Bui Cong Cuong
Author affiliations

Authors

  • Bui Cong Cuong Institute of Mathematics, VAST

DOI:

https://doi.org/10.15625/1813-9663/35/4/13898

Keywords:

Keywords. Picture Fuzzy Set, Pythagorean Picture Fuzzy Set

Abstract

Picture fuzzy set (2013) is a generalization of the Zadeh‟ fuzzy set (1965) and the Antanassov‟
intuitionistic fuzzy set. The new concept could be useful for many computational intelligent
problems. Basic operators of the picture fuzzy logic were studied by Cuong, Ngan [10,11 ].New
concept –Pythagorean picture fuzzy set ( PPFS) is a combination of Picture fuzzy set with the
Yager‟s Pythagorean fuzzy set [12-14].First, in the Part 1 of this paper, we consider basic notions
on PPFS as set operators of PPFS‟s , Pythagorean picture relation, Pythagorean picture fuzzy soft
set. Next, the Part 2 of the paper is devoted to main operators in fuzzy logic on PPFS: picture
negation operator, picture t-norm, picture t-conorm, picture implication operators on PPFS.As a
result we will have a new branch of the picture fuzzy set theory.

Metrics

Metrics Loading ...

References

L.A. Zadeh, Fuzzy Sets, Information and Control , 8, (1965) 338-353.

L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning ,

Information Sciences, vol. 8, (1975) 199-249.

K.Atanassov , Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.20 (1986) 87-96.

K.Atanassov, On Intuitionistic Fuzzy Sets Theory, Springer, 2012, Berlin.

T.H.Nguyen and E.Walker, A first course in fuzzy logic , Second Edition, Chapman& Hall /

CRC, 2000, Boca Raton,

E.P.Klement and R.Mesiar , Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular

Norms, 1st Edition, 2005.

J.Fodor and M. Roubens, Fuzzy preference modeling and multicriteria decision support, Kluwer

Academic Pub. London, 1994.

B.C.Cuong and V.Krenovitch, Picture Fuzzy Sets- a new concept for computational intelligence problems, in the Proceedings of the 3rd World Congress on Information and Communication Technology, WICT 2013,Hanoi,IEEE CS, pp 1-6,2013.

B.C. Cuong , Picture fuzzy sets , Journal Computer science and Cybernetics, V. 30(4) ,419-430, 2014.

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

B.C.Cuong, R.T.Ngan, L.B. Long, Some new de morgan picture operator triples in picture fuzzy logic, Journal of computer science and Cybernetics, V. 33(2),143-164,2017.

A.A.Yager, Pythagorean fuzzy subsets, in the Proceedings of Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, 57-61, 2013.

A.A.Yager, A.M. Abbasov, Pythagorean membership grades, complex numbers, and decision making, Int. J. Intell. Syst., 28(5), 436-452, 2013.

A.A. Yager, Pythagorean membership grades in multicriteria decision making, IEEE Trans. Fuzzy Syst., 22(4), 958-965,2014.

D. Molodtsov , Soft set theory – First results, Computer & Mathematics with Applications 37 (4-5), 19-31,1999

P.K.Maji, R.Bismas, A.R.Roy, Soft set theory, Computer & Mathematics with Applications 45 555-562,2003

P.H. Phong, B.C. Cuong, Some intuitionistic linguistic aggregation operators, Journal of

Computer Science and Cybernetics, vol. 30, n.3, 216-226, 2014.

P.H.Phong, B.C.Cuong, Multi-criteria group decision making with Picture Linguistic

Numbers, VNU Journal of Science : Computer Science and Communication Engineering,

vol.32 ,n.3, 38-51, 2016.

L.H.Son., Thong, P.H.: Some Novel Hybrid Forecast Methods Based On Picture Fuzzy

Clustering for Weather Nowcasting from Satellite Image Sequences. Applied Intelligence

(1) (2017) 1-15.

L.H.Son, Viet, P.V., Hai, P.V. Picture Inference System: A New Fuzzy Inference System

on Picture Fuzzy Set. Applied Intelligence (2017) DOI: 10.1007/s10489-016-0856-1.

L.H.Son, L DPFCM: A novel distributed picture fuzzy clustering method on picture fuzzy

sets. Expert systems with applications 42 (2015) 51-66.

P.H.Thong and L.H.Son, Picture Fuzzy Clustering : A New Computational Intelligence

Method, Soft Computing, v.20 (9) 3544-3562, 2016.

G.Wei, Picture fuzzy cross-entropy for multiple attribute decision making problems,

Journal of Business Economics and Management, vol. 17(4),491-502,2016.

S.V.Aruna Kumar, B.S. Harish, V.N.M.Aradhya, A picture fuzzy clustering approach for

brain tumor segmentation, in the Proceedings of the IEEE Second International Conference

On Cognitive Computing and Information Processing, CCIP, 2016.

B.C.Cuong, A new direction of fuzzy logic,in the Proceedings of the 8th National

Conference on Funamental and Applied Information Technology Research (FAIR‟8),

Hanoi, 9-10/7/2015, pp. 1-7, Natural Science and Technology Pub., Hanoi, 2015

B.C.Cuong, Pythagorean Picture Fuzzy Set: Basic notions and Main operators in fuzzy

logic, Preprint Seminar “ Neuro-Fuzzy Systems with Application,” N3/2019, Institute of

Mathematics ,March 2019

Downloads

Published

31-10-2019

How to Cite

[1]
B. C. Cuong, “Pythagorean Picture Fuzzy Sets, Part 1- basic notions”, JCC, vol. 35, no. 4, p. 293–304, Oct. 2019.

Issue

Section

Articles