1. Home
  2. Issues
  3. Volume 29, Issue 2 (2018)
  4. Interval-Valued 2-Tuple Linguistic Induc ...

Informatica


Interval-Valued 2-Tuple Linguistic Induced Continuous Ordered Weighted Distance Measure and Its Application to Multiple Attribute Group Decision Making
Volume 29, Issue 2 (2018), pp. 321–352
Pub. online: 1 January 2018      Type: Research Article      Open accessOpen Access
Received
1 January 2017
Accepted
1 May 2018
Published
1 January 2018

Abstract

This paper aims to propose a new distance measure, the interval-valued 2-tuple linguistic induced continuous ordered weighted distance (IT-ICOWD) measure, which consists of the interval-valued 2-tuple linguistic induced continuous ordered weighted averaging (IT-ICOWA) operator and the ordered weighted distance (OWD) measure. In these operators, we consider the risk attitude of decision maker. Furthermore, we discuss some desired properties and various special cases of the IT-ICOWD measure. Additionally, a method of multiple attribute group decision making (MAGDM) in interval-valued 2-tuple linguistic environment is developed on the basis of the IT-ICOWD measure. Through this method, we obtain three simple and exact formulae to determine the order-inducing variables of the IT-ICOWD measure, the weighting vector of decision makers and the weighting vector of attributes, respectively. At last, a numerical example is presented to illustrate the practicability and feasibility of proposed method.

References

 
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.
 
Atanassov, K.T. (2012). On Intuitionistic Fuzzy Sets Theory. Studies in Fuzziness and Soft Computing. Springer-Verlag, Berlin.
 
Bellman, R.E., Zadeh, L.A. (1970). Decision-making in fuzzy environment. Management Science, 17, 141–164.
 
Cabrerizo, F.J., Herrera-Viedma, E., Pedrycz, W. (2013). A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts. European Journal of Operational Research, 230, 624–633.
 
Chen, C.T., Tai, W.S. (2005). Measuring the intellectual capital performance based on 2-tuple fuzzy linguistic information. In: Proceedings of the 10th Annual Meeting of. Asia Pacific Region of Decision Sciences Institute, Taiwan.
 
Chen, S.M., Lee, L.W. (2010). A new method for fuzzy group decision-making based on interval linguistic labels. In: Proceedings of the 2010 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1–4.
 
Dong, Y.C., Zhang, H.J., Herrera-Viedma, E. (2016). Integrating experts’ weights generated dynamically into the consensus reaching process and its applications in managing non-cooperative behaviors. Decision Support Systems, 84, 1–15.
 
Dong, Y.C., Ding, Z.G., Chiclana, F., Herrera-Viedma, E. (2017). Dynamics of public opinions in an online and offline social network. IEEE Transactions on Big Data. https://doi.org/10.1109/TBDATA.2017.2676810. In press.
 
Herrera, F., Martinez, L. (2000). A 2-tuple linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8, 746–752.
 
Herrera, F., Herrera-Viedma, E., Martinez, L. (2008). A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Transactions on Fuzzy Systems, 16, 354–370.
 
Liao, H.C., Xu, Z.S., Zeng, X.J. (2014). Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Information Sciences, 271, 125–142.
 
Li, C.G., Zeng, S.Z., Pan, T.J., Zheng, L.N. (2014). A method based on induced aggregation operators and distance measure to multiple attribute decision making under 2-tuple linguistic environment. Journal of Computer and System Sciences, 80, 1339–1349.
 
Liu, X., Chen, H.Y., Zhou, L.G. (2011). A method based on the T-GOWA operator and the T-IGOWA operator to multiple attribute decision making under 2-tuple linguistic environment. Statistics & Decision, 21, 22–26 (in Chinese).
 
Liu, H.C., You, J.X., Lu, C., Shan, M.M. (2014a). Application of interval 2-tuple linguistic MULTIMOORA method for health-care waste treatment technology evaluation and selection. Waste Management, 34, 2355–2364.
 
Liu, H.C., You, J.X., You, X.Y. (2014b). Evaluating the risk of healthcare failure modes using interval 2-tuple hybrid weighted distance measure. Computers & Industrial Engineering, 78, 249–258.
 
Liu, W.Q., Dong, Y.C., Chiclana, F., Cabrerizo, F.J., Herrera-Viedma, E. (2017). Group decision-making based on heterogeneous preference relations with self-confidence. Fuzzy Optimization and Decision Making, 16, 429–447.
 
Massanet, S., Riera, J.V., Torrens, J., Herrera-Viedma, E. (2014). A new linguistic computational model based on discrete fuzzy numbers for computing with words. Information Sciences, 258, 277–290.
 
Mendel, J.M. (2007). Type-2 fuzzy sets and systems: an overview. IEEE Computational Intelligence Magazine, 2, 20–29.
 
Meng, F.Y., Zhu, M.X., Chen, X.H. (2016). Some generalized interval-valued 2-Tuple linguistic correlated aggregation operators and their application in decision making. Informatica, 27, 111–139.
 
Moore, R.E. (1966). Interval Analysis. Prentice-Hall, New Jersey.
 
Morente-Molinera, J.A., Mezei, J., Carlsson, C., Herrera-Viedma, E. (2017). Improving supervised learning classification methods using multigranular linguistic modeling and fuzzy entropy. IEEE Transactions on Fuzzy Systems, 25, 1078–1088.
 
Pérez, I.J., Cabrerizo, F.J., Herrera-Viedma, E. (2010). A mobile decision support system for dynamic group decision making problems. IEEE Transactions on Systems, Man and Cybernetics – Part A: Systems and Humans, 40, 1244–1256.
 
Rodriguez, R.M., Martinez, L., Herrera, F. (2011). Hesitant fuzzy linguistic term sets. In: Wang, Y., Li, T. (Eds.), Foundations of Intelligent Systems, (Vol. 122), pp. 287–295.
 
Sengupta, A., Pal, T.K. (2009). Fuzzy Preference Ordering of Interval Numbers in Decision Problems, Studies in Fuzziness and Soft Computing. Springer-Verlag, Berlin.
 
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25, 529–539.
 
Xu, Z.S. (2004). Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Information Sciences, 168(1–4), 171–184.
 
Xu, Z.S. (2005). An approach to pure linguistic multiple attribute decision making under uncertainty. International Journal of Information Technology and Decision Making, 4, 197–206.
 
Xu, Z.S., Chen, J. (2008). Ordered weighted distance measure. Journal of Systems Science and Systems Engineering, 17, 432–445.
 
Xu, Y.J., Wang, H.M. (2011). Distance measure for linguistic decision making. Systems Engineering Procedia, 1, 450–456.
 
Yager, R.R. (1988). On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Systems, Man and Cybernetics B, 18, 183–190.
 
Yager, R.R. (1993). Families of OWA operators. Fuzzy Sets and Systems, 59, 125–148.
 
Yager, R.R. (2004a). Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making, 393–107.
 
Yager, R.R. (2004b). OWA aggregation over a continuous interval argument with applications to decision making. IEEE Transactions on Systems, Man and Cybernetics B, 34, 1952–1963.
 
Yager, R.R., Filev, D.P. (1999). Induced ordered weighted averaging operators. IEEE Transactions on Systems, Man and Cybernetics B, 29, 141–150.
 
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8, 338–353.
 
Zadeh, L.A. (1975a). The concept of a linguistic variable and its application to approximate reasoning, Part 1. Information Sciences, 8, 199–249.
 
Zadeh, L.A. (1975b). The concept of a linguistic variable and its application to approximate reasoning, Part 2. Information Sciences, 8, 301–357.
 
Zadeh, L.A. (1975c). The concept of a linguistic variable and its application to approximate reasoning, Part 3. Information Sciences, 8, 43–80.
 
Zhang, H.M. (2012). The multiattribute group decision making method based on aggregation operators with interval-valued 2-tuple linguistic information. Mathematical and Computer Modelling, 56, 27–35.
 
Zhang, H.M. (2013). Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making. Applied Mathematical Modelling, 37, 4269–4282.
 
Zhou, L.G., Chen, H.Y., Wang, X., Ding, Z.Q. (2010). Induced continuous ordered weighted averaging operators and their applications in interval group decision making. Control and Decision, 25, 179–184.
 
Zhou, L.G., Chen, H.Y., Liu, J.P. (2013). Continuous ordered weighted distance measure and its application to multiple attribute group decision making. Group Decision and Negotiation, 22, 739–758.
 
Zhou, L.G., He, Y.D., Chen, H.Y., Liu, J.P. (2014a). Compatibility of interval fuzzy preference relations with the COWA operator and its application to group decision making. Soft Computing, 18, 2283–2295.
 
Zhou, L.G., Wu, J.X., Chen, H.Y. (2014b). Linguistic continuous ordered weighted distance measure and its application to multiple attributes group decision making. Applied Soft Computing, 25, 266–276.
 
Zhou, L.G., Jin, F.F., Chen, H.Y., Liu, J.P. (2016). Continuous intuitionistic fuzzy ordered weighted distance measure and its application to group decision making. Technological and Economic Development of Economy, 22, 75–99.

Biographies

Liu Xi
liuxi5137@126.com

X. Liu is a lecturer of School of Mathematics and Statistics, Hefei Normal University, China. She received a PhD degree in School of Mathematical Sciences from Anhui University. She has contributed several journal articles to professional journals. Her current research interests include decision making theory, forecasting, information fusion, fuzzy statistics and fuzzy mathematics.

Han Bing
ice05013861001@163.com

B. Han is a lecturer of School of Mathematical Sciences, Anhui University, China. She received a PhD degree in School of Mathematical Sciences from Anhui University. She has contributed over 10 journal articles to professional journals such as Knowledge-Based Systems and Expert Systems with Applications. Her current research interests include aggregation operators, group decision making and combined forecasting.

Chen Huayou
huayouc@126.com

H. Chen is a professor of School of Mathematical Sciences, Anhui University, China. He received a PhD degree in operational research from University of Science Technology of China in 2002. He graduated from Nanjing University for 2 years postdoctoral research work in 2005. He has published a book: The Efficient Theory of Combined Forecasting and Applications (Science Press, Beijing, 2008) and has contributed over 120 journal articles to professional journals, such as Fuzzy Sets and Systems, Information Sciences, Group Decision and Negotiation, etc. His current research interests include information fusion, multi-criteria decision making, aggregation operators and combined forecasting.

Zhou Ligang
shuiqiaozlg@126.com

L. Zhou is a professor of School of Mathematical Sciences, Anhui University. He received a PhD degree in operations research from Anhui University in 2013. He has contributed over 40 journal articles to professional journals, such as Fuzzy Sets and Systems, Applied Mathematical Modelling, Applied Soft Computing, Group Decision and Negotiation, Expert Systems with Applications, etc. His current research interests include group decision making, aggregation operators and combined forecasting.


Full article Cited by PDF XML
Full article Cited by PDF XML

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

Keywords
group decision making, distance measure interval-valued 2-tuple linguistic information IOWA operator COWA operator

Metrics
since January 2020
1040

Article info
views

 626

Full article
views
498

PDF
downloads

 232

XML
downloads


Share


RSS