International Journal of Intelligent Systems and Applications(IJISA)
ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)
Published By: MECS Press
IJISA Vol.8, No.1, Jan. 2016
Operations and Ranking Methods for Intuitionistic Fuzzy Numbers, a Review and New Methods
Full Text (PDF, 857KB), PP.35-48
Intuitionistic Fuzzy Numbers (IFNs) transfer more information than fuzzy numbers do in uncertain situations. It is caused that many others tried to define methods for ranking of IFNs and arithmetic operations on them, which are used in practical applications of IFNs such as decision making. Arithmetic operators on IFNs changed membership and non-membership degrees. The resulted degrees have important interpretations in real application of IFNs. In this paper, we will first review the existing methods for ranking and arithmetic operations on several representations of IFNs. Then, we will propose a new method based on arithmetic mean and geometric mean to compute membership and non-membership degrees of resulted IFN from arithmetic operations on IFNs. It is caused that the resulted degrees don't change monotonousness and be closer to reality. Furthermore, a new method for ranking of IFNs will be proposed. Finally, the proposed methods are used in the numerical examples, compared to some other existing methods.
Cite This Paper
Abazar Keikha, Hassan Mishmast Nehi,"Operations and Ranking Methods for Intuitionistic Fuzzy Numbers, a Review and New Methods", International Journal of Intelligent Systems and Applications(IJISA), Vol.8, No.1, pp.35-48, 2016. DOI: 10.5815/ijisa.2016.01.05
K.T. Atanassov, Intuitionistic Fuzzy Sets, in: V. Sgurev, Ed., VII ITKR'S Session SO_a Jone 1983.
K. T. Atanassov, Intuitionistic Fuzzy Sets Past, Present and Future, in EUSFLAT Conf., M. Wagenknecht and R. Hampel, Eds. University of Applied Sciences at Zittau/G¨orlitz, Germany, 12-19, 2003.
K. T. Atanassov, Intuitionistic fuzzy sets and interval valued fuzzy sets, First Int. Workshop on IFSs, GNs, KE, London, 6-7 Sept., 1-7, 2006.
K. T. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31, 343-349, 1989.
K. T. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64, 159-174, 1994.
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96, 1986.
K. T. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, Springer-Verlag,1999.
A. I. Ban, D. A. Tuse, Trapezoidal/triangular intuitionistic fuzzy numbers versus interval-valued trapezoidal/triangular fuzzy numbers and applications to multicriteria decision making methods, 18th Int. Conf. on IFSs, Sofia, 10-11 May 2014.
I. Beg. T. Rashid, Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS, OPSEARCH, 51, 98-129, 2014.
H. Bustincee, P. Burillo, Vague sets are intuitionistic fuzzy sets, Fuzzy Sets Systems, 79,403-405, 1996.
Z. Chen, W. Yang, A new multiple attribute group decision making method in intuitionistic fuzzy setting, Applied Mathematical Modeling, 35, 4424-4437, 2011.
T. Y. Chen, H. P. Wang, Y. Y. Lu, A multicriteria group decision-making approach based on interval-valued intuitionistic fuzzy sets: A comparative perspective, Expert Systems with Applications, 38, 7647-7658, 2011.
P. K. De, D. Das, A study on ranking of trapezoidal intuitionistic fuzzy numbers, International Journal of Computer Information Systems and Industrial Management Applications, ISSN 2150-7988, 6, 437-444, 2014.
W. L. Gau, D. J. Buehrer, Vague Sets, IEEE Transaction on system, Man, and Cybernetics, 23, 2, 610-614, 1993.
A. Kumar, M. Kaur, A ranking approach for intuitionistic fuzzy numbers and its application, Journal of applied research and technology, 11, 3, 381-396, 2013.
D. F. Li, Multiattribute decision making method based on generalized OWA operators with intuitionistic fuzzy sets, Expert Systems with Applications, 37, 8673-8678, 2010.
D. F. Li, J. X. Nan, M. J. Zhang, Ranking method of triangular intuitionistic fuzzy numbers and application to decision making, International Journal of Computational Intelligence Systems, 3, 5, 522-530, 2010.
D. F. Li, A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems, Computers and Mathematics with Applications, 60, 1557-1570, 2010.
D. F. Li, A note on using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly, Microelectronics Reliability 48, 17-41, 2008.
F. Liu, X. H. Yuan, Fuzzy number intuitionistic fuzzy set, Fuzzy Systems and Mathematics, 21, 88-91, 2007.
J. X. Nan, D. F. Li, M. J. Zhang, A lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers, International Journal of Computational Intelligence Systems, 3, 280-289, 2010.
V. L. G. Nayagam, G. Venkateshwari, G. Sivaraman, Rank ing of intuitionistic fuzzy numbers, Applied Soft Computing, 11, 3368-3372, 2011.
V. L. G. Nayagam, S. Muralikrishnan, G. Sivaraman, Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets, Expert Systems with Applications 38, 1464-1467, 2011.
V. L. G. Nayagam, S. Muralikrishnan, G. Sivaraman, Ranking of interval-valued intuitionistic fuzzy sets, Applied Soft Computing 11, 3368-3372, 2011.
R. Parvathi , C. Malathi, Arithmetic operations on symmetric trapezoidal intuitionistic fuzzy numbers, International Journal of Soft Computing and Engineering (IJSCE), ISSN: 2231-2307, 2, 2, 2012.
Z. Peng, Q. Chen, A new method for ranking canonical intuitionistic fuzzy numbers, Proceedings of the International Conference on Information Engineering and Applications (IEA) 2012, Lecture Notes in Electrical Engineering, 216, 609-616, 2013.
W. J. Qiang, Z. Zhong, Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems, Journal of Systems Engineering and Electronics, 20, 2, 321-326, 2009.
W. J. Qiang, Z. Zhong, Programming method of multicriteria decision-making based on intuitionistic fuzzy number with incomplete certain information, Control and decision, 23 , 10, 1145-1148, 2008.
S. S. Roseline, E. C. H. Amirtharaj, A new ranking of intuitionistic fuzzy numbers with distance method based on the circumcenter of centroids, International Journal of Applied Mathematics & Statistical Sciences (IJAMSS) 2, 4, 37-44, 2013.
A. Solairaju, P. J. Robinson, S. R. Kumar, Interval valued intuitionistic fuzzy MAGDM problems with OWA entropy weights, International Journal of Mathematics Trends and Technology, 9, 2, 2014.
E. Szmidt and J. Kacprzyk, Concept of distances and entropy for intuitionistic fuzzy sets and their applications in group decision making, Sixth Int. Conf. on IFSs, Varna, 13-14 Sept. 2002, NIFS, 8, 3, 11-25, 2002.
C. Tan, X. Chen, Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making, Expert Systems with Applications, 37, 149-157, 2010.
S. P. Wan, Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making, Applied Mathematical Modeling 37, 4112-4126, 2013.
J. Q. Wang, R. Nie, H. Y. Zhang, X. H. Chen, New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis, Information Sciences, 251, 79-95, 2013.
Y. M. Wang, J.B Yanga, D. L. Xua, K. S. Chinc, On the centroids of fuzzy numbers, Fuzzy Sets and Systems 157, 919-926, 2006.
C. P. Wei, A new method for ranking intuitionistic fuzzy numbers, International Journal of Knowledge and Systems Science, 2, 43-49, 2011.
Z. Xu, X. Cai, Intuitionistic Fuzzy Information Aggregation: Theory and Applications, Science Press Beijing and Springer-Verlag Berlin Heidelberg 2012, ISBN 978-7-03-033321-6 Science Press Beijing.
Z. Xu, Intuitionistic Fuzzy Aggregation Operators, IEEE Transactions on Fuzzy Systems, 15, 6, 2007.
Z. Xu, Intuitionistic preference relations and their application in group decision making, Information Sciences, 177 , 2363-2379, 2007.
Z. Xu, M. Xia, Induced generalized intuitionistic fuzzy operators, Knowledge-Based Systems 24, 197-209, 2011.
Z. Xu, Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control and Decision, 22, 215-219, 2007.
J. Ye, Prioritized aggregation operators of trapezoidal intuitionistic fuzzy sets and their application to multicriteria decision-making, Journal of Neural Computing and Applications, 25, 6, 1447-1454, 2014.
D. Yu, Intuitionistic trapezoidal fuzzy information aggregation methods and their applications to teaching quality evaluation, Journal of Information & Computational Science 10:6, 1861-1869, 2013.
V. F. Yu, L. Q. Dat, N. H. Quang, T. A. Son, S.Y. Chou, A. C. Lin, An extension of fuzzy TOPSIS approach based on centroid-index ranking method, Scientific Research and Essays, 7, 14, 1485-1493, 2012.
L. A. Zadeh, Fuzzy sets, Information and Control, 8, 338-353, 1965.
M. J. Zhang, J. X. NAN, A compromise ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems, Iranian Journal of Fuzzy Systems, 10, 6, 21-37, 2013.