Interval-valued intuitionistic fuzzy MADM method based on TOPSIS and grey correlation analysis

Fankang Bu; Jun He; Haorun Li; Qiang Fu; Fankang Bu; Jun He; Haorun Li; Qiang Fu

doi:10.3934/mbe.2020300

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5584-5603. doi: 10.3934/mbe.2020300

Previous Article Next Article

Research article Special Issues

Interval-valued intuitionistic fuzzy MADM method based on TOPSIS and grey correlation analysis

National Key Laboratory of Science and Technology on ATR, College of Electronic Science, National University of Defence Technology, Changsha 410000, China

Received: 26 May 2020 Accepted: 09 August 2020 Published: 18 August 2020

In this paper, we propose an interval-valued intuitionistic fuzzy Multi-Attribute Decision Making (MADM) method based on improved TOPSIS and Grey Correlation Analysis (GCA), in which the attribute values are interval-valued intuitionistic fuzzy numbers. So that we can deal with imprecise information in fuzzy and rough form in MADM problems by using interval-valued intuitionistic fuzzy numbers Firstly, the concept of interval intuitionistic fuzzy entropy is introduced to calculate the entropy weight of attributes. And the combined weight is calculated by combining the entropy weight with the subjective weight. Secondly, the reverse order phenomenon in the traditional TOPSIS method is eliminated by constructing absolute Positive Ideal Solution (PIS) and absolute Negative Ideal Solution (NIS) in the form of interval-valued intuitionistic fuzzy numbers. Furthermore, the improved TOPSIS method and grey correlation analysis method are combined to describe the degree of closeness for each alternative from the ideal solution, and then the ranking and selection of each alternative are made accordingly to this degree. Finally, the rationality and effectiveness of our method are verified by an example and its sensitivity analysis. The result shows that our method makes the solution of MADM problems more objective and reasonable.
- multi-attribute decision making (MADM),
- interval-valued intuitionistic fuzzy numbers,
- TOPSIS,
- grey correlation analysis (GCA)
Citation: Fankang Bu, Jun He, Haorun Li, Qiang Fu. Interval-valued intuitionistic fuzzy MADM method based on TOPSIS and grey correlation analysis[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5584-5603. doi: 10.3934/mbe.2020300

Related Papers:

Abstract

In this paper, we propose an interval-valued intuitionistic fuzzy Multi-Attribute Decision Making (MADM) method based on improved TOPSIS and Grey Correlation Analysis (GCA), in which the attribute values are interval-valued intuitionistic fuzzy numbers. So that we can deal with imprecise information in fuzzy and rough form in MADM problems by using interval-valued intuitionistic fuzzy numbers Firstly, the concept of interval intuitionistic fuzzy entropy is introduced to calculate the entropy weight of attributes. And the combined weight is calculated by combining the entropy weight with the subjective weight. Secondly, the reverse order phenomenon in the traditional TOPSIS method is eliminated by constructing absolute Positive Ideal Solution (PIS) and absolute Negative Ideal Solution (NIS) in the form of interval-valued intuitionistic fuzzy numbers. Furthermore, the improved TOPSIS method and grey correlation analysis method are combined to describe the degree of closeness for each alternative from the ideal solution, and then the ranking and selection of each alternative are made accordingly to this degree. Finally, the rationality and effectiveness of our method are verified by an example and its sensitivity analysis. The result shows that our method makes the solution of MADM problems more objective and reasonable.

References

[1]	A. Mardani, E. K. Zavadskas, Z. Khalifah, N. Zakuan, A. Jusoh, K. M. Nor, et al., A review of multi-criteria decision-making applications to solve energy management problems: Two decades from 1995 to 2015, Renewable Sustainable Energy Rev., 71 (2017), 216-256.
[2]	X. Zeng, L. Shu, S. Yan, Y. Shi, F. He, A novel multivariate grey model for forecasting the sequence of ternary interval numbers, Appl. Math. Model, 69 (2019), 273-286.
[3]	H. Wang, S. He, C. Li, X. Pan, Pythagorean uncertain linguistic variable hamy mean operator and its application to multi-attribute group decision making, J. Autom. Sin., 6 (2019), 194-206.
[4]	P. Wang, P. Liu, Some Maclaurin symmetric mean aggregation operators based on Schweizer-Sklar operations for intuitionistic fuzzy numbers and their application to decision making, J. Intell. Fuzzy Syst., 36 (2019), 3801-3824.
[5]	L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338-353.
[6]	K. T. Atanassov, G. Pasi, R. R. Yager, Intuitionistic fuzzy interpretations of multi-measurement tool multi-criteria decision making, Int. J. Syst. Sci., 36 (2005), 859-868.
[7]	K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Set. Syst., 31 (1989), 343-349.
[8]	D. K. Joshi, S. Kumar, Entropy of interval-valued intuitionistic hesitant fuzzy set and its application to group decision making problems, Granular Comput., 1 (2018), 1-15.
[9]	D. Ye, D. Liang, P. Hu, Three-Way decisions with interval-valued intuitionistic fuzzy decision-theoretic rough sets in group decision-making, Symmetry, 10 (2018), 281.
[10]	L. Wu, G. Wei, H. Gao, Y. Wei, Some Interval-Valued Intuitionistic Fuzzy Dombi Hamy Mean Operators and Their Application for Evaluating the Elderly Tourism Service Quality in Tourism Destination, Mathematics, 6 (2018), 294.
[11]	K. Kumar, D. Pandey, Discussion on the switching between type-2 fuzzy sets and intuitionis-tic fuzzy sets: An application in medical diagnosis, J. Inf. Optim. Sci., 39 (2018), 427-444.
[12]	S. M. Chen, Z. C. Huang, Multiattribute decision making based on interval-valued intuitionistic fuzzy values and linear programming methodology, Inf. Sci., 381 (2017), 341-351.
[13]	H. C. J. Chao, C. T. Tung, C. H. Chu, Extension theorems for interval-valued intuitionistic fuzzy sets, J. Discrete Math. Sci. Cryptography, 3 (2018), 707-712.
[14]	M. Wei, Q. Dai, S. Sun, S. Ionita, Eva. Volná, A. Gavrilov, et al., A prediction model for traffic emission based on interval-valued intuitionistic fuzzy sets and case-based reasoning theory, J. Intell. Fuzzy. Syst., 31 (2016), 3039-3046.
[15]	H. Zhao, Z. Xu, Z. Yao, Interval-valued intuitionistic fuzzy derivative and differential operations, Int. J. Comput. Int. Syst., 9 (2016), 36-56.
[16]	F. Meng, X. Chen, Correlation Coefficient of Interval-Valued Intuitionistic Uncertain Linguistic Sets and Its Application, J. Cybern., 48 (2017), 114-135.
[17]	Y. Kang, S. Wu, D. Cao, W. Weng, New hesitation-based distance and similarity measures on intuitionistic fuzzy sets and their applications, Int. J. Syst. Sci., 49 (2018), 1-17.
[18]	D. F. Liu, X. H. Chen, D. Peng, Interval-valued intuitionistic fuzzy ordered weighted cosine similarity measure and its application in investment decision-making, Complexity, 2017, 1-11.
[19]	V. P. Ananthi, P. Balasubramaniam, T. Kalaiselvi, A new fuzzy clustering algorithm for the segmentation of brain tumor, Soft. Comput., 20 (2015), 1-21.
[20]	Q. Gao, D. L. Xu, An empirical study on the application of the evidential reasoning rule to decision making in financial investment, Knowl. Based Syst., 164 (2019), 226-234.
[21]	M. Nahangi, Y. Chen, B. Mccabe, Safety-based efficiency evaluation of construction sites using data envelopment analysis (DEA), Saf. Sci., 113 (2019), 382-388.
[22]	Y. Zhu, X. Wang, S. Deng, M. Zhao, X. Ao, Evaluation of Curtain Grouting Efficiency by Cloud Model - based Fuzzy Comprehensive Evaluation Method, KSCE. J. Civ. Eng., 23 (2019), 2852-2866.
[23]	A. Kumar, R. N. Rai, Evaluation of Wear Properties of Stir Cast AA7050-10% B4C Ex Situ Composite through Fuzzy-TOPSIS MCDM Method, Solid State Phenom., 291 (2019), 1-12.
[24]	M. Akram, N. Waseem, P. Liu, Novel approach in decision making with m-Polar fuzzy ELECTRE-I, Int. J. Fuzzy Syst., 21 (2019), 1-13.
[25]	W. Yunlong, L. Kai, G. Guan, Y. Yanyun, L. Fei, Evaluation method for Green jack-up drilling platform design scheme based on improved grey correlation analysis, Appl. Ocean. Res., 85 (2019), 119-127.
[26]	S. J. Zhou, B. Liu, J. Meng, Quality evaluation of raw moutan cortex using the AHP and gray correlation-TOPSIS method, Pharmacognosy. Mag., 13 (2017), 528-533.
[27]	P. P. Das, S. Chakraborty, A grey correlation-based TOPSIS approach for optimization of surface roughness and micro hardness of Nitinol during WEDM operation, Mater. Today Proceedings, 2019.
[28]	Y. Zhou, X. Liu, F. Li, W. Jiang, Railway route selection based on entropy weight method-gray correlation improvement TOPSIS, IOP Conference Series Earth and Environmental Science, 2019. Available from: https://iopscience.iop.org/journal/1755-1315.
[29]	S. H. Zyoud, D. Fuchs-Hanusch, A bibliometric-based survey on AHP and TOPSIS techniques. Expert. Syst. Appl, 78 (2017), 158-181.
[30]	C. T. Chen, Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy. Set. Syst, 114 (2000), 1-9.
[31]	S. S. Yang, N. Nasr, S. K. Ong, A. Y. C. Nee, Designing automotive products for remanufacturing from material selection perspective. J. Clean. Prod, 153 (2017), 570-579.
[32]	S. F. Liu, Y. Lin, Grey information theory and practical applications, London: Springer-Verlag, 2011,10-30.
[33]	K. T. Atanassov, Intuitionistic fuzzy sets. Fuzzy. Set. Syst, 20 (1986), 87-96.
[34]	J. J. Peng, J. Q. Wang, J. Wang, X. H. Chen, Multicriteria decision-making approach with hesitant interval-valued intuitionistic fuzzy sets, Sci. World Journal, 2014 (2014), 1-22.
[35]	Y. Song, X. Wang, L. Lei, A. Xue, Combination of interval-valued belief structures based on intuitionistic fuzzy set, Knowl. Based. Syst., 67 (2014), 61-70.
[36]	T. Y. Chen, The extended linear assignment method for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets, Appl. Math. Model, 38 (2014), 2101-2117.
[37]	Z. Xu, Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control Decis., 22 (2007).
[38]	E. Szmidt, J. Kacprzyk, Distances between intuitionistic fuzzy sets, Fuzzy. Set. Syst., 114 (2000), 505-518.
[39]	H. Liao, Z. Xu, X. J. Zeng, Novel correlation coefficients between hesitant fuzzy sets and their application in decision making, Knowl. Based. Syst., 82(2015), 115-127.
[40]	P. Burillo, H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy. Set. Syst., 78 (1996), 305-316.
[41]	J. Ye, Two effective measures of intuitionistic fuzzy entropy, Computing, 87 (2010), 55-62.
[42]	W. Zeng, H. Li, Relationship between similarity measure and entropy of interval valued fuzzy sets, Fuzzy. Set. Syst, 157 (2006), 1477-1484.
[43]	Q. S. Zhang, S. Y. Jiang, A note on information entropy measures for vague sets and its applications, Inf. Sci., 178 (2008), 4184-4191.
[44]	P. Wang, C. P. Wei, Constructing method of interval-valued intuitionistic fuzzy entropy, Comput. Eng. Appl., 47 (2011), 43-45.
[45]	C. Lin, G. Kou, Y. Peng, F. E. Alsaadi, Aggregation of the nearest consistency matrices with the acceptable consensus in AHP-GDM, Ann. Oper. Res. (2020), 1-17.
[46]	C. Y. Xie, Z. Q. Luo, N. Jia, W. Wang, Goafs' risk discrimination based on improved topsis coupled with ga-bp, J. Northeast. Univer., 3 (2016), 440-445.
[47]	Z. S. Xu, R. R. Yager, Dynamic intuitionistic fuzzy multi-attribute decison making, Int. J. Approx. Reason, 48 (2008), 246-262.
[48]	Z. S. Xu, J. Chen, Approach to Group Decision Making Based on Interval-Valued Intuitionistic Judgment Matrices, Syst. Eng. Theory Pract., 27 (2007),126-133.

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)