New Generalized Interval Valued Intuitionistic Fuzzy Numbers

Subject Areas : Applied Mathematics

Ezzatallah Baloui Jamkhaneh ¹ (Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran)
A. Saeidifar ² (Department of Statistics, Arak Branch, Islamic Azad University, Arak, Iran)

Received: 2017-03-12 Accepted : 2018-01-09 Published : 2018-05-01

Keywords: Generalized interval valued intuitionistic fuzzy sets, generalized interval valued intuitionistic fuzzy numbers, cut set, value index, ambiguity index,

Abstract :

The aim of this paper is investigate the notion of a generalized interval valuedintuitionistic fuzzy number (GIVIFN), which extends the interval valuedintuitionistic fuzzy number. Firstly, the concept of GIVIFNBs is introduced.Arithmetic operations and cut sets over GIVIFNBBs are investigated. Thenthe values and ambiguities of the membership degree and the non-membershipdegree and the value index and ambiguity index for GIVIFNs are dened.Finally, we develop a value and ambiguity-based ranking method.

References:

[1]L. Abdullah, L. Najib, A new preference scale MCDM method based on
interval-valued intuitionistic fuzzy sets and the analytic hierarchy process,
Soft Computing, 2016, 20(2), P.511-523.

[2]A. K. Adak, M. Bhowmik, Interval cut-set of interval-valued intuitionistic
fuzzy sets, African Journal of Mathematics and Computer Science
Research, 2011, 4(4), P.192-200.

[3]K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 1986,
20, P.87-96.

[4]K. T. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy
Sets and Systems, 1989, 31(3), P.343-349.

[5]E. Baloui Jamkhaneh, S. Nadarajah, A New generalized intuitionistic
fuzzy sets, Hacettepe Journal of Mathematics and Statistics, 2015, 44 (6),
P.1537-1551.

[6]E. Baloui Jamkhaneh, New generalized interval value intuitionistic fuzzy
sets, Research and Communications in Mathematics and Mathematical
Sciences, 2015, 5(1), P.33-46.

[7]E. Baloui Jamkhaneh, A value and ambiguity-based ranking method of
generalized intuitionistic fuzzy numbers, Research and Communications
in Mathematics and Mathematical Sciences, 2016, 6(2), P.89-103.

[8]P. Burillo, H. Bustince, V. Mohedano, Some denition of intuitionistic
fuzzy number, Fuzzy based expert systems, fuzzy Bulgarian enthusiasts,
September 28-30, 199), Soa, Bulgaria.

[9]S. S. L. Chang, L.A. Zadeh, On fuzzy mapping and control, IEEE
Transaction on Systems, Man and Cybernetics, 1972, 2(1), P.30-34.

[10]D. Dubois, H. Prade, Operations on fuzzy numbers, International Journal
of Systems Science, 1978, 9, P.613-626.

[11]H. Garg, A new generalized improved score function of interval valued
intuitionistic fuzzy sets and applications in expert systems, Applied Soft
Computing, 2016, 38, P.988-999.

[12]G. Intepe, E. Bozdag, T. Koc, The selection of technology forecasting
method using a multi-criteria interval-valued intuitionistic fuzzy group
decision making approach, Computers and Industrial Engineering, 2013,
65, P.277-285.

[13]J. Li, M. J. Lin, H. Chen, ELECTRE method based on interval valued
intuitionistic fuzzy number, Applied Mechanics and Materials, 2012, Vols.
220-223, P.2308-2312.

[14]G. S. Mahapatra, T. K. Roy, Reliability evaluation using triangular
intuitionistic fuzzy numbers arithmetic operations, Proceedings of World
Academy of Science, Engineering and Technology, Malaysia, 2009, 38,
P.587-585.

[15]G. S. Mahapatra, B. S. Mahapatra, Intuitionistic fuzzy fault tree analysis
using intuitionistic fuzzy numbers, International Mathematical Forum,
2010, 5(21), P.1015{1024.

[16]J. H. Park, I. Y. Park, Y. C. Kwun, X. Tan, Extension of the TOPSIS
method for decision making problems under interval-valued intuitionistic
fuzzy environment, Applied Mathematical Modeling, 2011, 35, P.2544-
2556.

[17]R. Parvathi, C. Malathi, Arithmetic operations on symmetric trapezoidal
intuitionistic fuzzy numbers, International Journal of Soft Computing and
Engineering, 2012, 02(2), P.268-273.

[18]A. Shabani, E. Baloui Jamkhaneh, A new generalized intuitionistic fuzzy
number, Journal of Fuzzy Set Valued Analysis, 2014, 4, P.1-10.

[19]S. Sudha, J. Rachel, I. Jeba, Crop production using interval-valued
intuitionistic fuzzy TOPSIS method, International Journal of Emerging
Research in Management and Technology, 2015, 4(11), P.435-466.

[20]S. Veeramachaneni, H. Kandikonda, An ELECTRE approach for
multicriteria interval-valued intuitionistic trapezoidal fuzzy group decision
making problems, Advances in Fuzzy Systems, 2016, vol. 2016, Article
ID 1956303, 17 pages, doi:10.1155/2016/1956303.

[21]J. Q. Wang, Z. Zhang, Aggregation operators on intuitionistic trapezoidal
fuzzy number and its application to multi-criteria decision making
problems, Journal of Systems Engineering and Electronics, 2009, 20,
P.321-326.

[22]J. Q. Wang, Z. Zhang, Multi-criteria decision making method with
incomplete certain information based on intuitionistic fuzzy number,
Control and Decision, 2009, 24, P.226-230.

[23]Z. S. Xu, Intuitionist fuzzy aggregation operators, IEEE Transactions on
Fuzzy Systems, 2007, 15(6), P.1179-1187.

[24]Z. S. Xu, Methods for aggregating interval valued intuitionistic fuzzy
information and their application to decision making, Control and
Decision, 2007, 22(2), P.215-219.

[25]J. Ye, Multicriteria fuzzy decision making method based on a novel
accuracy function under interval valued intuitionistic fuzzy environment,
Expert Systems with Applications, 2009, 36, P.6899-6902.

[26]X. H. Yuan, H. X. Li, Cut sets on interval valued intuitionistic fuzzy
sets, Sixth International Conference on Fuzzy Systems and Knowledge
Discovery, 2009, 6, P.167-171.

[27]L. A. Zadeh, Fuzzy sets, Information and Control, 1965, 8(3), P.338-356.