IJPAM: Volume 112, No. 4 (2017)

Title

CUT SETS ON TRAPEZOIDAL FUZZY NUMBER AND
INTUITIONISTIC FUZZY NUMBER: A NEW PERSPECTIVE

Authors

M. Clement Joe Anand$^1$, Janani Bharatraj$^2$
$^{1,2}$Department of Mathematics
School of Science and Humanities
Hindustan University
Padur, Chennai, 603103, INDIA

Abstract

The human cognition and interaction with the outside world involves structure with no sharp boundaries in which the transition of membership to non-membership function is gradual rather than abrupt. The concept of cut sets and fuzzy numbers were developed and intensive research has been taking place and applied in human cognition. In this paper, we have introduced matrix-cut for trapezoidal fuzzy number by studying its properties, arithmetic operations and decomposition theorems. Finally, the Trapezoidal Intuitionistic Fuzzy number (TFN) and its arithmetic properties using matrix cut have also been proposed.

History

Received: October 4, 2016
Revised: December 23, 2016
Published: February 19, 2017

AMS Classification, Key Words

AMS Subject Classification: 03E72
Key Words and Phrases: fuzzy sets, trapezoidal fuzzy numbers, decomposition theorems, intuitionistic fuzzy sets, trapezoidal intuitionistic fuzzy numbers

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Bibliography

1
K.T. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag Heidelberg, Germany, 1999.

2
K.T. Atanassov, On Intuitionistic Fuzzy Sets Theory, Springer Verlag, Berlin Heidelberg, 2012.

3
T. Beaula, M. Priyadharsini, Operations on intuitionistic trapezoidal fuzzy numbers using interval arithmetic, International Journal of Fuzzy Mathematical Archive, 9, No. 1 (2015), 125-133.

4
J.J. Buckley, E. Eslami, An Introduction to Fuzzy Logic and Fuzzy Sets, Physica-Verlag Heidelberg, New York, 2002.

5
P. Dutta, H. Boruah, T. Ali, Fuzzy arithmetic with and without using $\alpha$-cut method: A comparative study, International Journal of Latest Trends in Computing , 2, No. 1 (2011), 99-107.

6
P.A. Ejegwa, S.O. Akowe, P.M. Otene, J.M. Ikyule, An overview on intuitionistic fuzzy sets, International Journal of Scientific and Technology Research, 3, No. 3 (2014), 142-144.

7
S. Gao, Z. Zhang, C. Cao, Multiplication operation on fuzzy numbers, Journal of Software, 4 No.4 (2009), 331-338, doi: https://doi.org/10.4304/jsw.4.4.331-338.

8
J.Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18, No. 1 (1967), 145-174.

9
A. Kaufmann, Introduction to the Theory of Fuzzy Subsets, Academic Press, London, 1975.

10
A. Kaufmann, M.M. Gupta, Introduction to Fuzzy Arithmetic Theory and Applications, International Thomson Computer Press, USA, 1991.

11
X. Li, X. Yuan, E.S. Lee, The three-dimensional fuzzy sets and their cut sets, Journal of Computers and Mathematics, 58, No. 7 (2009), 1349-1359, doi: https://doi.org/10.1016/j.camwa.2009.02.031.

12
G.S. Mahapatra, T.K. Roy, Intuitionistic fuzzy number and its arithmetic operation with application on system failure, Journal of Uncertain Systems, 7, No. 2 (2013), 92-107.

13
R. Parvathi, C. Malathi, Arithmetic operations on symmetric trapezoidal intuitionistic fuzzy numbers, International Journal of Soft Computing and Engineering, 2, No. 2 (2012), 268-273, doi: https://doi.org/10.1.1.498.8900.

14
Z. Sun, J. Han, Inverse alpha-cuts and interval $[a,b)$-cuts, IEEE Xplore, 1, No. 1 (2006), 441-444, doi: https://doi.org/10.1109/ICICIC.2006.105.

15
J. Vahidi, S. Rezvani, Arithmetic operations on trapezoidal fuzzy numbers, Journal Non-Linear Analysis and Application (2013), 1-8, doi: https://doi.org/10.5899/2013/jnaa-00111.

16
S. Veeramachaneni, H. Kandikonda, An ELECTRE approach for multicriteria interval-valued intuitionistic trapezoidal fuzzy group decision making problems, Advances in Fuzzy systems, 2016 (2016), 17 pages, doi: https://doi.org/org/10.1155/2016/1956303.

17
X.H. Yuan, H.X. Li, K.B. Sun, The cut sets decomposition theorems and representation theorems on Intuitionistic fuzzy sets and interval valued fuzzy sets, Science China Information Sciences, 54, No. 1 (2011), 91-110, doi: https://doi.org/10.1007/s11432-010-4078-6.

How to Cite?

DOI: 10.12732/ijpam.v112i4.7 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 112
Issue: 4
Pages: 749 - 762


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