Document Type : Research Paper
Authors
Abstract
In this paper, a novel intuitionist fuzzy TOPSIS method for group
decision making will be presented. In this method the preference
values for an alternative on criteria and the weight values of criteria
are given by experts, using linguistic values of trapezoidal intuitionist
fuzzy numbers, and weights of decision makers’ opinions are
unknown. In proposed method, expected values and weighted
averaging operator for trapezoidal intuitionist fuzzy numbers are used
to induce the weight values of criteria and decision makers’ opinions.
Then an algorithm for ranking alternatives is presented under
trapezoidal intuitionist fuzzy environment. Finally, using a numerical
example, the efficiency of new extended TOPSIS method is
investigated.
Keywords
1. S. Abbasbandy, T. Hajjari, A new approach for ranking of
trapezoidal fuzzy number, Comput. Math. Appl. 57 (2009) 413-419.
2. B. Asady, A. Zendehnam, Ranking fuzzy numbers by distance
minimization, Appl. Math. Model. 31 (2007) 2589-2598.
3. B. Ashtiani, F. Haghighirad, G.A. Montazer, Extension of fuzzy
TOPSIS method based on interval-valued fuzzy sets. Appl. Soft
Comput. 9 (2009) 457 461.
4. K. Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20 (1986) 87
96.
5. A. Awasthi, S.S. Chauhan, S.K. Goyal, A multi-criteria decision
making approach for location planning for urban distribution centers
under uncertainty, Math. Comput. Model. 53 (2011) 98 109.
6. F.E. Boran, S. Genç, M. Kurt, D. Akay, A multi-criteria intuitionistic
fuzzy group decision making for supplier selection with TOPSIS
method, Expert Syst. Appl. 36 (2009) 11363-11368.
7. C.T. Chen, Extensions of the TOPSIS for group decision-making
under fuzzy environment, Fuzzy Sets Syst. 114 (2000) 1 9.
8. S.M. Chen, L.W. Lee, Fuzzy multiple attributes group decisionmaking
based on the interval type-2 TOPSIS method, Expert Syst.
Appl. 37 (2010) 2790-2798.
9. T.Y. Chen, C.Y. Tsao, The interval-valued fuzzy TOPSIS method
and experimental analysis, Fuzzy Sets Syst. 159 (2008) 1410 1428.
10. Z. Chen, W. Yang, A new multiple attribute group decision making
method in intuitionistic fuzzy setting, Appl. Math. Model. (2011) doi:
10. 1016 / j. apm. 2011. 03.015.
11. T-C. Chu, Y-C. Lin, An interval arithmetic based fuzzy TOPSIS
model, Expert Syst. Appl. 36 (2009) 10870 10876.
12. T-C. Chu, Y-C. Lin, A fuzzy TOPSIS method for robot selection,
Int. J. Adv. Manuf. Tech. 21 (2003) 284 290.
13. D. Dubois, H. Prade, The mean value of a fuzzy number, Fuzzy Sets
Syst. 24 (1978) 279-300.
14. P. Grzegrorzewski, The hamming distance between intuitionistic
fuzzy sets, In Proceedings of the 10th IFSA world congress, Istanbul,
Turkey, 2003.
15. C. L., Hwang, K. Yoon, Multiple attributes decision making methods
and applications, Springer, Berlin, Heidelberg, 1981.
16. G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, & M. Izadikhah,
تصمیم گیری گروهی بر پایه یک روش تاپسیس فازی... 33
Extension of the TOPSIS method for decision-making problems with
fuzzy data, Appl. Math. Comput. 181 (2006) 1544 1551.
17. M. S. Kuo, G. H. Tzeng, W. C. Huang, Group decision-making
based on concepts of ideal and anti-ideal points in a fuzzy
environment, Math. Comput. Model. 45 (2007) 324 339.
18. I. Mahdavi, N. Mahdavi-Amiri, A. Heidarzade, R. Nourifar,
Designing a model of fuzzy topsis in multiple criteria decision making.
Appl. Math. Comput. 206 (2008) 607 617.
19. H. M. Nehi, H. R. Maleki, optimization problem, In Proceedings of
the 9th WSEAS international conference on systems, Athens,
Greece, 2005.
20. 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, Appl. Math. Model. 35 (2011) 2544
2556.
21. S. Sadi-Nezhad, K. K. Damghani, Application of a fuzzy TOPSIS
method base on modified preference ratio and fuzzy distance
measurement in assessment of traffic police centers performance,
Appl. Soft Comput. 10 (2010) 1028-1039.
22. C.C. Sun, A performance evaluation model by integrating fuzzy AHP
and fuzzy TOPSIS methods, Expert Syst. Appl. 37 (2010) 7745
7754.
23. C. Tan, A multi-criteria interval-valued intuitionistic fuzzy group
decision making with Choquet integral-based TOPSIS, Expert Syst.
Appl. 38 (2011) 3023-3033.
24. G. Torlak, M. Sevkli, M. Sanal, S. Zaim, Analyzing business
competition by using fuzzy TOPSIS method: An example of Turkish
domestic airline industry, Expert Syst. Appl. 38 (2011) 3396-3406.
25. B. Vahdani et al., Group decision making based on novel fuzzy
modified TOPSIS method, Appl. Math. Model. (2011)
doi:10.1016/j.apm.2011.02.040.
26. A.H. Vencheh, M. Allame, On the relation between a fuzzy number
and its centroid, Comput. Math. Appl. 59 (2010) 3578-3582.
27. J. Q. Wang, Z. Zhang, Aggregation operators on intuitionistic
trapezoidal fuzzy number and its application to multicriteria decision
making problems, J. Syst. Eng. Electron. 20 (2009) 321 326.
28. T.-C. Wang, H.-D. Lee, Developing a fuzzy TOPSIS approach based
on subjective weights and objective weights, Expert Syst. Appl. 36
(2009) 8980 8985.
32 مطالعات مدیریت صنعتی، سال دهم، شماره 82 ، پاییز 19
29. Y. J. Wang, H. S. Lee, Generalizing TOPSIS for fuzzy multiplecriteria
group decision-making, Comput. Math. Appl. 53 (2007)
1762 1772.
30. J.Z. Wu, Q. Zhang, Multicriteria decision making method based on
intuitionistic fuzzy weighted entropy, Expert Systems with
Applications, (2010).
31. F. Ye, An extended TOPSIS method with interval-valued
intuitionistic fuzzy numbers for virtual enterprise partner selection,
Expert Syst. Appl. 37 (2010) 7050-7055.
32. J. Ye, Expected value method for intuitionistic trapezoidal fuzzy
multicriteria decision-making problems, Expert Syst. Appl. (2011)
doi: 10.1016 /j.eswa. 2011.03.059.
33. L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338 356
trapezoidal fuzzy number, Comput. Math. Appl. 57 (2009) 413-419.
2. B. Asady, A. Zendehnam, Ranking fuzzy numbers by distance
minimization, Appl. Math. Model. 31 (2007) 2589-2598.
3. B. Ashtiani, F. Haghighirad, G.A. Montazer, Extension of fuzzy
TOPSIS method based on interval-valued fuzzy sets. Appl. Soft
Comput. 9 (2009) 457 461.
4. K. Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20 (1986) 87
96.
5. A. Awasthi, S.S. Chauhan, S.K. Goyal, A multi-criteria decision
making approach for location planning for urban distribution centers
under uncertainty, Math. Comput. Model. 53 (2011) 98 109.
6. F.E. Boran, S. Genç, M. Kurt, D. Akay, A multi-criteria intuitionistic
fuzzy group decision making for supplier selection with TOPSIS
method, Expert Syst. Appl. 36 (2009) 11363-11368.
7. C.T. Chen, Extensions of the TOPSIS for group decision-making
under fuzzy environment, Fuzzy Sets Syst. 114 (2000) 1 9.
8. S.M. Chen, L.W. Lee, Fuzzy multiple attributes group decisionmaking
based on the interval type-2 TOPSIS method, Expert Syst.
Appl. 37 (2010) 2790-2798.
9. T.Y. Chen, C.Y. Tsao, The interval-valued fuzzy TOPSIS method
and experimental analysis, Fuzzy Sets Syst. 159 (2008) 1410 1428.
10. Z. Chen, W. Yang, A new multiple attribute group decision making
method in intuitionistic fuzzy setting, Appl. Math. Model. (2011) doi:
10. 1016 / j. apm. 2011. 03.015.
11. T-C. Chu, Y-C. Lin, An interval arithmetic based fuzzy TOPSIS
model, Expert Syst. Appl. 36 (2009) 10870 10876.
12. T-C. Chu, Y-C. Lin, A fuzzy TOPSIS method for robot selection,
Int. J. Adv. Manuf. Tech. 21 (2003) 284 290.
13. D. Dubois, H. Prade, The mean value of a fuzzy number, Fuzzy Sets
Syst. 24 (1978) 279-300.
14. P. Grzegrorzewski, The hamming distance between intuitionistic
fuzzy sets, In Proceedings of the 10th IFSA world congress, Istanbul,
Turkey, 2003.
15. C. L., Hwang, K. Yoon, Multiple attributes decision making methods
and applications, Springer, Berlin, Heidelberg, 1981.
16. G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, & M. Izadikhah,
تصمیم گیری گروهی بر پایه یک روش تاپسیس فازی... 33
Extension of the TOPSIS method for decision-making problems with
fuzzy data, Appl. Math. Comput. 181 (2006) 1544 1551.
17. M. S. Kuo, G. H. Tzeng, W. C. Huang, Group decision-making
based on concepts of ideal and anti-ideal points in a fuzzy
environment, Math. Comput. Model. 45 (2007) 324 339.
18. I. Mahdavi, N. Mahdavi-Amiri, A. Heidarzade, R. Nourifar,
Designing a model of fuzzy topsis in multiple criteria decision making.
Appl. Math. Comput. 206 (2008) 607 617.
19. H. M. Nehi, H. R. Maleki, optimization problem, In Proceedings of
the 9th WSEAS international conference on systems, Athens,
Greece, 2005.
20. 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, Appl. Math. Model. 35 (2011) 2544
2556.
21. S. Sadi-Nezhad, K. K. Damghani, Application of a fuzzy TOPSIS
method base on modified preference ratio and fuzzy distance
measurement in assessment of traffic police centers performance,
Appl. Soft Comput. 10 (2010) 1028-1039.
22. C.C. Sun, A performance evaluation model by integrating fuzzy AHP
and fuzzy TOPSIS methods, Expert Syst. Appl. 37 (2010) 7745
7754.
23. C. Tan, A multi-criteria interval-valued intuitionistic fuzzy group
decision making with Choquet integral-based TOPSIS, Expert Syst.
Appl. 38 (2011) 3023-3033.
24. G. Torlak, M. Sevkli, M. Sanal, S. Zaim, Analyzing business
competition by using fuzzy TOPSIS method: An example of Turkish
domestic airline industry, Expert Syst. Appl. 38 (2011) 3396-3406.
25. B. Vahdani et al., Group decision making based on novel fuzzy
modified TOPSIS method, Appl. Math. Model. (2011)
doi:10.1016/j.apm.2011.02.040.
26. A.H. Vencheh, M. Allame, On the relation between a fuzzy number
and its centroid, Comput. Math. Appl. 59 (2010) 3578-3582.
27. J. Q. Wang, Z. Zhang, Aggregation operators on intuitionistic
trapezoidal fuzzy number and its application to multicriteria decision
making problems, J. Syst. Eng. Electron. 20 (2009) 321 326.
28. T.-C. Wang, H.-D. Lee, Developing a fuzzy TOPSIS approach based
on subjective weights and objective weights, Expert Syst. Appl. 36
(2009) 8980 8985.
32 مطالعات مدیریت صنعتی، سال دهم، شماره 82 ، پاییز 19
29. Y. J. Wang, H. S. Lee, Generalizing TOPSIS for fuzzy multiplecriteria
group decision-making, Comput. Math. Appl. 53 (2007)
1762 1772.
30. J.Z. Wu, Q. Zhang, Multicriteria decision making method based on
intuitionistic fuzzy weighted entropy, Expert Systems with
Applications, (2010).
31. F. Ye, An extended TOPSIS method with interval-valued
intuitionistic fuzzy numbers for virtual enterprise partner selection,
Expert Syst. Appl. 37 (2010) 7050-7055.
32. J. Ye, Expected value method for intuitionistic trapezoidal fuzzy
multicriteria decision-making problems, Expert Syst. Appl. (2011)
doi: 10.1016 /j.eswa. 2011.03.059.
33. L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338 356
)