1. Home
  2. Issues
  3. Volume 29, Issue 3 (2018)
  4. Multi-Attribute Decision Making with Int ...

Informatica


Multi-Attribute Decision Making with Interval-Valued Hesitant Fuzzy Information, a Novel Synthetic Grey Relational Degree Method
Volume 29, Issue 3 (2018), pp. 517–537
Pub. online: 1 January 2018      Type: Research Article      Open accessOpen Access
Received
1 October 2017
Accepted
1 May 2018
Published
1 January 2018

Abstract

Quantitative and qualitative fuzzy information measures have been proposed to solve multi-attribute decision making (MADM) problems with interval–valued hesitant fuzzy information from different points. We analyse the existing fuzzy information measures of the interval-valued hesitant fuzzy sets (IVHFSs) in detail and classify them into two categories. One is based on the closeness of the data, such as the distance, and the other is based on the linear relationship or variation tendency, such as the correlation coefficient. These two kinds of information measures are actually partial measures which pay attention to only one factor of the data. Therefore, we construct a novel synthetic grey relational degree by considering both the closeness and the variation tendency factors of the data to improve the existing information measures and enhance the grey relational analysis (GRA) theory for IVHFSs. However, the notion of the synthetic grey relational degree is not only restricted to the IVHFSs but can be extended to other sets. Furthermore, we employ two practical MADM examples about emergency management evaluation and pattern recognition to validate and compare the proposed synthetic grey relational degree with other information measures, which demonstrate its superiorities in discrimination and accuracy.

References

 
Asan, U., Kadaifci, C., Bozdag, E., Soyer, A., Serdarasan, S. (2018). A New approach to DEMATEL based on interval-valued hesitant fuzzy sets. Applied Soft Computing, 66, 34–49.
 
Chen, N., Xu, Z.S. (2014). Properties of interval-valued hesitant fuzzy sets. Journal of Intelligent & Fuzzy Systems, 27, 143–158.
 
Chen, N., Xu, Z.S., Xia, M.M. (2013a). Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Applied Mathematical Modelling, 37, 2197–2211.
 
Chen, N., Xu, Z.S., Xia, M.M. (2013b). Interval-valued hesitant preference relations and their applications to group decision making. Knowledge-Based Systems, 37(1), 528–540.
 
Deng, J.L. (1989). Introduction to grey system theory. The Journal of Grey System, 1(1), 1–24.
 
Farhadinia, B. (2013). Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Information Sciences, 240, 129–144.
 
Farhadinia, B. (2015). Study on division and subtraction operations for hesitant fuzzy sets, interval-valued hesitant fuzzy sets and typical dual hesitant fuzzy sets. Journal of Intelligent & Fuzzy Systems, 28, 1393–1402.
 
Fernández, R.P., Alonso, P., Bustince, H., Díaz, I., Jurioc, A., Montes, S. (2015). Ordering finitely generated sets and finite interval-valued hesitant fuzzy sets. Information Sciences, 325, 375–392.
 
Gitinavard, H., Mousavi, S.M., Vahdani, B. (2016). A new multi-criteria weighting and ranking model for group decision-making analysis based on interval-valued hesitant fuzzy sets to selection problems. Neural Computing and Applications, 27(6), 1593–1605.
 
Gitinavard, H., Mousavi, S.M., Vahdani, B. (2017). Soft computing-based new interval-valued hesitant fuzzy multi-criteria group assessment method with last aggregation to industrial decision problems. Soft Computing, 21(12), 3247–3265.
 
Guan, X., Sun, G.D., Yi, X., Zhou, Z. (2018). Grey relational analysis for hesitant fuzzy sets and its applications to multi-attribute decision making. Mathematical Problems in Engineering. Article ID 7436054.
 
Guo, J. (2013). Hybrid multiattribute group decision making based on intuitionistic fuzzy information and GRA method. ISRN Applied Mathematics. Article ID 146026.
 
He, Y.D., He, Z., Shi, L.X., Meng, S.S. (2016). Multiple attribute group decision making based on IVHFPBMs and a new ranking method for interval-valued hesitant fuzzy information. Computers & Industrial Engineering, 99, 63–77.
 
Jin, F.F., Ni, Z.W., Chen, H.Y. (2016a). Interval-valued hesitant fuzzy Einstein prioritized aggregation operators and their applications to multi-attribute group decision making. Soft Computing, 20(5), 1863–1878.
 
Jin, F.F., Ni, Z.W., Chen, H.Y., Li, Y.P., Zhou, L.G. (2016b). Multiple attribute group decision making based on interval-valued hesitant fuzzy information measures. Computers & Industrial Engineering, 101, 103–115.
 
Kong, Z., Wang, L.F., Wu, Z.X. (2011). Application of fuzzy soft set in decision making problems based on grey theory. Journal of Computational and Applied Mathematics, 236, 1521–1530.
 
Kuo, M.S., Liang, G.S. (2011). Combining VIKOR with GRA techniques to evaluate service quality of airports under fuzzy environment. Expert Systems with Applications, 38, 1304–1312.
 
Li, X.Y., Wei, G.W. (2014). GRA method for multiple criteria group decision making with incomplete weight information under hesitant fuzzy setting. Journal of Intelligent & Fuzzy Systems, 27, 1095–1105.
 
Li, Z.W., Wen, G.Q., Xie, N.X. (2015). An approach to fuzzy soft sets in decision making based on grey relational analysis and Dempster–Shafer theory of evidence: an application in medical diagnosis. Artificial Intelligence in Medicine, 64, 161–171.
 
Liou, J.J.H., Tamošaitienė, J., Zavadskas, Tzeng G. H, E.K. (2016). New hybrid COPRAS-G MADM model for improving and selecting suppliers in green supply chain management. International Journal of Production Research, 54(1), 114–134.
 
Liu, Y., Liu, J., Hong, Z.Y. (2018). A multiple attribute decision making approach based on new similarity measures of interval-valued hesitant fuzzy sets. International Journal of Computational Intelligence Systems, 11, 15–32.
 
Meng, F.Y., Chen, X.H. (2014). An approach to interval-valued hesitant fuzzy multi-attribute decision making with incomplete weight information based on hybrid Shapley operators. Informatica, 25(4), 617–642.
 
Meng, F.Y., Chen, X.H., Zhang, Q. (2016). Correlation coefficients of interval-valued hesitant fuzzy sets and their application based on the Shapley function. International Journal of Intelligent Systems, 31(1), 17–43.
 
Mu, Z.M., Zeng, S.Z., Baležentis, T. (2015). A novel aggregation principle for hesitant fuzzy elements. Knowledge-Based Systems, 84, 134–143.
 
Peng, D.H., Wang, T.D., Gao, C.Y., Wang, H. (2017). Enhancing relative ratio method for MCDM via attitudinal distance measures of interval-valued hesitant fuzzy sets. Internal Journal of Machine Learning & Cybernetics, 8(4), 1347–1368.
 
Quirós, P., Alonso, P., Bustince, H., Díaz, I., Montes, S. (2015). An entropy measure definition for finite interval-valued hesitant fuzzy sets. Knowledge-Based Systems, 84, 121–133.
 
Rostamzadeh, R., Esmaeili, A., Nia, A.S., Saparauskas, J., Ghorabaee, M.K. (2017). A fuzzy ARAS method for supply chain management performance measurement in SMES under uncertainty. Transformations in Business & Economics, 16(2A), 319–348.
 
Sun, G.D., Guan, X., Yi, X., Zhou, Z. (2018). Grey relational analysis between hesitant fuzzy sets with applications to pattern recognition. Expert Systems with Applications, 92, 521–532.
 
Tang, H.X. (2015). A novel fuzzy soft set approach in decision making based on grey relational analysis and Dempster–Shafer theory of evidence. Applied Soft Computing, 31, 317–325.
 
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25, 529–539.
 
Turskis, Z., Zavadskas, E.K. (2010). A novel method for multiple criteria analysis: grey additive ratio assessment (ARAS-G) method. Informatica, 21(4), 597–610.
 
Verma, R. (2017). Hesitant interval-valued fuzzy sets: some new results. International Journal of Machine Learning and Cybernetics, 8(3), 865–876.
 
Wei, G.W. (2011a). Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making. Expert Systems with Applications, 38, 11671–11677.
 
Wei, G.W. (2011b). Grey relational analysis method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information. Expert Systems with Applications, 38, 4824–4828.
 
Wei, G.W. (2011c). Grey relational analysis model for dynamic hybrid multiple attribute decision making. Knowledge-Based Systems, 24, 672–679.
 
Wei, G.W., Zhao, X.F., Lin, R. (2013). Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making. Knowledge-Based Systems, 46, 43–53.
 
Wei, G.W., Lin, R., Wang, H.J. (2014a). Distance and similarity measures for hesitant interval-valued fuzzy sets. Journal of Intelligent & Fuzzy Systems, 27, 19–36.
 
Wei, G.W., Zhao, X.F., Lin, R., Wang, H.J. (2014b). Models for hesitant interval-valued fuzzy multiple attribute decision making based on the correlation coefficient with incomplete weight information. Journal of Intelligent & Fuzzy Systems, 26, 1631–1644.
 
Yang, Y., Lang, L., Lu, L.L., Sun, Y.M. (2017). A new method of multiattribute decision-making based on interval-valued hesitant fuzzy soft sets and its application. Mathematical Problems in Engineering. Article ID 9376531.
 
Yu, D.J. (2017). Hesitant fuzzy multi-criteria decision making methods based on Heronian mean. Technological and Economic Development of Economy, 23(2), 296–315.
 
Zang, Y.Q., Sun, W., Han, S.Y. (2017). Grey relational projection method for multiple attribute decision making with interval-valued dual hesitant fuzzy information. Journal of Intelligent & Fuzzy Systems, 33, 1053–1066.
 
Zhang, Z.M. (2016). Multi-criteria decision-making using interval-valued hesitant fuzzy QUALIFLEX methods based on a likelihood-based comparison approach. Neural Computing and Applications, 28(7), 1–20.
 
Zhang, X.L., Xu, Z.S. (2013). Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowledge-Based Systems, 52, 53–64.
 
Zhang, X.L., Xu, Z.S. (2014). The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowledge-Based Systems, 61, 48–58.
 
Zhang, S.F., Liu, S.Y., Zhai, R.H. (2011). An extended GRA method for MCDM with interval-valued triangular fuzzy assessments and unknown weights. Computers & Industrial Engineering, 61, 1336–1341.
 
Zhang, X., Jin, F., Liu, P.D. (2013). A grey relational projection method for multi-attribute decision making based on intuitionistic trapezoidal fuzzy number. Applied Mathematical Modelling, 37, 3467–3477.
 
Zhang, Z.M., Wang, C., Tian, D.Z., Li, K. (2014). Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making. Computers & Industrial Engineering, 67, 116–138.

Biographies

Sun Guidong
dwhsgd@163.com

G. Sun is currently pursuing the PhD degree at Naval Aviation University. He has authored and co-authored over 15 research papers and published some papers in leading international journals, such as Expert Systems with Applications, Applied Soft Computing, and the International Journal of Fuzzy Systems. His research interests include fuzzy multi criteria decision-making, information fusion, and pattern recognition. He also serves as a reviewer of the several distinguished journals as KBS and IEEE TKDE.

Guan Xin
gxtongwin@163.com

X. Guan is currently a full-time professor and a doctor tutor at Naval Aviation University. She is an author of four books, over 100 articles, and over 10 inventions. Her research interests include evidence reasoning, signal processing, and target recognition. She received the award in the Program for New Century Excellent Talents by the Minister of Education in 2011 and was awarded the Taishan Scholar in 2017. She is an active journal reviewer of journals such as Chinese Journal of Aeronautics, The Chinese Journal of Electronics, Science China, and so on.

Yi Xiao

X. Yi is currently a full-time professor and a doctor tutor in Naval Aviation University. He has published over 50 papers and three academic monographs. His major is wireless sensor network and intelligent information processing.

Zhou Zheng

Z. Zhou is currently an associate professor in Naval Aviation University. His research interests include cyberspace countermeasures and computer networks.


Full article Related articles Cited by PDF XML
Full article Related articles Cited by PDF XML

Copyright
© 2018 Vilnius University
Open access article under the CC BY license.

Keywords
multi-attribute decision making (MADM) interval-valued hesitant fuzzy sets (IVHFSs) synthetic grey relational degree information measures

Metrics
since January 2020
1084

Article info
views

645

Full article
views

550

PDF
downloads

197

XML
downloads


Share


RSS