Some New De Morgan Picture Operator Triples in Picture Fuzzy Logic
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DOI:
https://doi.org/10.15625/1813-9663/33/2/10706Keywords:
Key words, Picture fuzzy sets, , Picture fuzzy t-norms, Picture fuzzy t-conorm, De Morgan picture operator tripleAbstract
A new concept of picture fuzzy sets (PFS) were introduced in 2013, which are direct
extensions of the fuzzy sets and the intuitonistic fuzzy sets. Then some operations on PFS with
some properties are considered in [ 9,10 ]. Some basic operators of fuzzy logic as negation, tnorms
, t-conorms for picture fuzzy sets firstly are defined and studied in [13,14]. This paper is
devoted to some classes of representable picture fuzzy t-norms and representable picture fuzzy
t-conorms on PFS and a basic algebra structure of Picture Fuzzy Logic – De Morgan triples of
picture operators.
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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, Elsevier.
B.C. Cuong, Picture fuzzy sets - First results. Part 1, Seminar “Neuro-Fuzzy Systems with
Applications”, Preprint 03/2013, May 2013, Institute of Mathematics, Hanoi, Vietnam.
B.C. Cuong , Picture fuzzy sets - First results. Part 2, Seminar “Neuro-Fuzzy Systems with
Applications”, Preprint 04/2013, June 2013, Institute of Mathematics, Hanoi Vietnam.
B.C. Cuong and V. Kreinovich , Picture Fuzzy Sets - a new concept for computational
intelligence problems , in the Proceedings of the 3rd World Congress on Information and
Communication Technologies (WICT 2013), Hanoi, Vietnam, IEEE CS, 2013, p. 1-6, ISBN 918-1-
-3230-6.
B.C.Cuong, Picture Fuzzy Sets, Journal of Computer Science and Cybernetics, Vol.30, n.4,
, 409-420.
Glad Deschrijver, Chris Cornelis, Etienne E. Kerre, On the Representation of Intuitionistic
Fuzzy t-Norms and t-Conorms", IEEE Transactions on Fuzzy Systems, Vol. 12, No. 1, 2004, pp. 45-
J. Goguen , " L -fuzzy sets", J. Math. Anal. Appl., vol. 18, 1967, 145-174.
B.C. Cuong , P.V. Hai, Some fuzzy logic operators for picture fuzzy sets, in the Proceedings of
the 2015 IEEE International Conference on Knowledge Systems Engineering, KSE 2015, IEEE
Computer Society Publications and CPS, 2015, pp.132-137, Washington
B.C.Cuong, R.T. Ngan and B.D. Hai, An involutive picture fuzzy negation on picture fuzzy
sets and some De Morgan triples, in the Proceedings of the 2015 IEEE International Conference on
Knowledge Systems Engineering, KSE 2015, IEEE Computer Society Publications and CPS, 2015,
pp.126 -131, Washington.
B.C.Cuong, P.H.Phong and F. Smarandache, Standard Neutrosophic Soft Theory: Some First
Results, Neutrosophic Sets and Systems, vol.12, 2016, pp.80-91.
F.Smaranddache, A unifying field in logics. Neutrosophy: Neutrosophic probability, set and
logic, American Research Press, Rehoboth, 1999.
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, Symbolic computational models for intuitionistic linguistic
information, Journal of Computer Science an Cybernetics, Vol. 32 ,n.1, 30-44, 2016.
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, Generalized Picture Distance Measure and Applications to Picture Fuzzy
Clustering. Applied Soft Computing 46 (2016) 284–295.
L.H. Son, Measuring Analogousness in Picture Fuzzy Sets: From Picture Distance
Measures to Picture Association, Measures. Fuzzy Optimization and Decision Making
(2017) DOI: 10.1007/s10700-016-9249-5.
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.
G.Wei, Picture 2-Type linguistic Bonferroni mean operators and their application to
multiple attribute decision making, Int. J. Fuzzy Systems, DOI 10.1007/s40815-016-0266-x
C.Wang, X.Zhou, H.Tu, S.Tao, Some geometric aggregation operators based on picture
fuzzy sets and their application in multiple attribute decision making, Italian Journal of
Pure and Applied Mathematics, n.37, 2017, pp.477-492.
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, R.T.Ngan, L.C.Ngoc, Some Algebraic Properties of Picture Fuzzy t-Norms
and picture Fuzzy t – Conorms on Standard Neutrosophic Sets, Vixra.org/General
Mathematics, 2016.
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, Some New De Morgan Triples of Operators in the Picture Fuzzy
Sets Theory, Seminar “Neuro-Fuzzy Systems with Applications”, Preprint 08/2017,
June 2017, Institute of Mathematics, Hanoi, Vietnam.
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
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