1. Home
  2. Issues
  3. Volume 29, Issue 2 (2018)
  4. The PROMTHEE II Method Based on Probabil ...

Informatica


The PROMTHEE II Method Based on Probabilistic Linguistic Information and Their Application to Decision Making
Volume 29, Issue 2 (2018), pp. 303–320
Pub. online: 1 January 2018      Type: Research Article      Open accessOpen Access
Received
1 October 2017
Accepted
1 March 2018
Published
1 January 2018

Abstract

The probabilistic linguistic terms set (PLTS) can reflect different importance degrees or weights of all possible linguistic terms (LTs) given by the experts for a specific object. The PROMETHEE II method is an important ranking method which can comprise preferences as well as indifferences, and it has a unique characteristic that can provide different types of preference functions. Based on the advantages of the PLTS and the PROMETHEE II method, in this paper, we extend the PROMETHEE II method to process the probabilistic linguistic information (PLI), and propose the PL-PROMETHEE II method with an improved possibility degree formula which can avoid the weaknesses from the original formula. Then concerning the multi-attribute decision making (MADM) problems with totally unknown weight information, the maximum deviation method is used to get the objective weight vector of the attributes, and net flows of the alternatives from the PROMETHEE II method are used to rank the alternatives. Finally, a numerical example is given to illustrate the feasibility of the proposed method.

References

 
Bai, C.Z., Zhang, R., Qian, L.X., Wu, Y.N. (2017). Comparisons of probabilistic linguistic term sets for multi-criteria decision making. Knowledge-Based Systems, 119(C), 284–291.
 
Brans, J.P., Vincke, P.A. (1985). A preference ranking organization method: the PROMETHEE method for MCDM. Management Science, 31(6), 647–656.
 
Cabrerizo, F.J., Ureńa, M.R., Pedrycz, W., Herrera-Viedma, E. (2014). Building consensus in group decision making with an allocation of information granularity. Fuzzy Sets and Systems, 255, 115–127.
 
Cabrerizo, F.J., Al-Hmouz, R., Morfeq, A., Balamash, A.S., Martínez, M.A., Herrera-Viedma, E. (2017). Soft consensus measures in group decision making using unbalanced fuzzy linguistic information. Soft Computing, 21(11), 3037–3050.
 
Capuano, N., Chiclana, F., Fujita, H., Herrera-Viedma, E., Loiam, V. (2017). Fuzzy group decision making with incomplete information guided by social influence. IEEE Transactions on Fuzzy Systems. https://doi.org/10.1109/TFUZZ.2017.2744605. In press.
 
Chen, C.T., Hung, W.Z., Cheng, H.L. (2011). Applying linguistic PROMETHEE method in investment portfolio decision-making. International Journal of Electronic Business Management, 9(2), 139–148.
 
Chiclana, F., Tapia Garcia, J.M., Del Moral, M.J., Herrera-Viedma, E. (2013). A statistical comparative study of different similarity measures of consensus in group decision making. Information Sciences, 221(2), 110–123.
 
Del Moral, M.J., Chiclana, F., Tapia, J.M., Herrera-Viedma, E. (2017). A comparative study on consensus measures in group decision making. International Journal of Intelligent Systems. https://doi.org/10.1002/int.21954. In press.
 
Dong, Y.C., Li, C.C., Herrera, F. (2015). An optimization-based approach to adjusting unbalanced linguistic preference relations to obtain a required consistency level. Information Sciences, 292(5), 27–38.
 
Gomes, L.F.A.M., Lima, M.M.P.P. (1991). Todim: basic and application to multicriteria ranking of projects with environmental impacts. Paris, 16(1), 113–127.
 
Gou, X., Xu, Z. (2016). Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Information Sciences, 372, 407–427.
 
Greco, S., Kadziński, M., Mousseau, V., Słowiński, R. (2011). ELECTRE: robust ordinal regression for outranking methods. European Journal of Operational Research, 214(1), 118–135.
 
Li, A.J., Quan, X.C., Wang, Y., Tao, K., Guo, L.Y. (2012). Selection of contaminated site soil remediation technology based on PROMETHEE II. Chinese Journal of Environmental Engineering, 6(10), 3767–3773.
 
Li, Y.H., Liu, P., Chen, Y. (2014). Some single valued neutrosophic number heronian mean operators and their application in multiple attribute group decision making. Informatica, 27(1), 85–110.
 
Li, C.C., Dong, Y., Herrera, F., Herrera-Viedma, E., Martínez, L. (2017). Personalized individual semantics in computing with words for supporting linguistic group decision making, an application on consensus reaching. Information Fusion, 33(1), 29–40.
 
Lin, M.W., Xu, Z.S. (2017). Probabilistic linguistic distance measures and their applications in multi-criteria group decision making. Soft Computing Applications for Group Decision-Making and Consensus Modeling, 357, 411–440.
 
Liu, P. (2013). Some Hamacher aggregation operators based interval valued intuitionistic fuzzy numbers and their application to group decision making. Application Math Model, 37(4), 2430–2444.
 
Liu, P. (2017). Multiple attribute group decision making method based on interval-valued intuitionistic fuzzy power Heronian aggregation operators. Computers & Industrial Engineering, 108, 199–212.
 
Liu, P., Chen, S.M. (2017). Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers. IEEE Transactions on Cybernetics, 47(9), 2514–2530.
 
Liu, P., Jin, F. (2012). Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making. Information Sciences, 205(1), 58–71.
 
Liu, P., Li, H. (2017). Interval-valued intuitionistic fuzzy power Bonferroni aggregation operators and their application to group decision making. Cognitive Computation, 9(4), 494–512.
 
Liu, P., Shi, L. (2017). Some Neutrosophic uncertain linguistic number Heronian mean operators and their application to multi-attribute group decision making. Neural Computing and Applications, 28(5), 1079–1093.
 
Liu, P., Su, Y. (2012). Multiple attribute decision making method based on the trapezoid fuzzy linguistic hybrid harmonic averaging operator. Informatica, 36(1), 83–90.
 
Liu, P., Tang, G. (2016). Multi-criteria group decision-making based on interval neutrosophic uncertain linguistic variables and Choquet integral. Cognitive Computation, 8(6), 1036–1056.
 
Liu, P., Teng, F. (2016). An extended TODIM method for multiple attribute group decision-making based on 2-dimension uncertain linguistic variable. Complexity, 21(5), 20–30.
 
Liu, P., Wang, P. (2017). Some improved linguistic intuitionistic fuzzy aggregation operators and their applications to multiple-attribute decision making. International Journal of Information Technology & Decision Making, 16(3), 817–850.
 
Liu, P., He, L., Yu, X.C. (2016a). Generalized hybrid aggregation operators based on the 2-dimension uncertain linguistic information for multiple attribute group decision making. Group Decision and Negotiation, 25(1), 103–126.
 
Liu, P., Zhang, L., Liu, X., Wang, P. (2016b). Multi-valued Neutrosophic number Bonferroni mean operators and their application in multiple attribute group decision making. International Journal of Information Technology & Decision Making, 15(5), 1181–1210.
 
Liu, P., Chen, S.M., Liu, J. (2017a). Some intuitionistic fuzzy interaction partitioned Bonferroni mean operators and their application to multi-attribute group decision making. Information Sciences, 411, 98–121.
 
Liu, W., Dong, Y., Chiclana, F., Cabrerizo, F.J., Herrera-Viedma, E. (2017b). Group decision-making based on heterogeneous preference relations with self-confidence. Fuzzy Optimization and Decision Making, 16(4), 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.
 
Milica, L., Milena, J. (2016). The comparison of the energy performance of hotel buildings using PROMETHEE decision-making method. Thermal Science, 20(1), 197–208.
 
Morente-Molinera, J.A., Mezei, J., Carlsson, C., Herrera-Viedma, E. (2017). Improving supervised learning classification methods using multi-granular linguistic modelling and fuzzy entropy. IEEE Transactions on Fuzzy Systems, 25(5), 1078–1089.
 
Pang, Q., Xu, Z.S., Wang, H. (2016). Probabilistic linguistic term sets in multi-attribute group decision making. Information Sciences, 369, 128–143.
 
Rodriguez, R.M., Martinez, L., Herrera, F. (2012). Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on Fuzzy Systems, 20(1), 109–119.
 
Senvar, O., Tuzkaya, G., Kahraman, C. (2014). Multi criteria supplier selection using fuzzy PROMETHEE method. Supply Chain Management Under Fuzziness, 313, 21–34.
 
Tan, Q.Y., Feng, X.Q., Zhang, H.R. (2016). Hesitant fuzzy language based on possibility degree PROMETHEE. Statistics Methods and Decision Making, 9, 82–85.
 
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.
 
Wang, J.Q., Li, J.J. (2009). The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Science & Technology Information, 33, 8–9.
 
Wang, S., Liu, J. (2017). Extension of the TODIM method to intuitionistic linguistic multiple attribute decision making. Symmetry, 9(6), 95. https://doi.org/10.3390/sym9060095.
 
Wu, J., Chiclana, F., Herrera-Viedma, E. (2015). Trust based consensus model for social network in an incomplete linguistic information context. Applied Soft Computing, 35, 827–839.
 
Ye, J. (2017). Multiple attribute decision-making method using correlation coefficients of normal neutrosophic sets. Symmetry, 9(6), 80. https://doi.org/10.3390/sym9060080.
 
You, X., Chen, T., Yang, Q. (2016). Approach to multi-criteria group decision-making problems based on the best-worst-method and ELECTRE method. Symmetry, 8(9), 95. https://doi.org/10.3390/sym8090095.
 
Zadeh, L.A. (1975a). The concept of a linguistic variable and its application to approximate reasoning – I. Information Science, 8(3), 199–249.
 
Zadeh, L.A. (1975b). The concept of a linguistic variable and its application to approximate reasoning – II. Information Science, 8, 301–353.
 
Zadeh, L.A. (1975c). The concept of a linguistic variable and its application to approximate reasoning – III. Information Science, 9, 43–80.
 
Zhang, X.L., Xing, X.M. (2017). Probabilistic linguistic VIKOR method to evaluate green supply chain initiatives. Sustainability, 9(7), 1231.
 
Zhang, H.J., Dong, Y., Herrera-Viedma, E. (2017). Consensus building for the heterogeneous large-scale GDM with the individual concerns and satisfactions. IEEE Transaction on Fuzzy Systems. https://doi.org/10.1109/TFUZZ.2017.2697403.
 
Zhao, J., You, X.Y., Liu, H.C., Wu, S.M. (2017). An extended VIKOR method using intuitionistic fuzzy sets and combination weights for supplier selection. Symmetry, 9(9), 169. https://doi.org/10.3390/sym9090169.

Biographies

Liu Peide
Peide.liu@gmail.com

P. Liu received the BS and MS degrees in signal and information processing from Southeast University, Nanjing, China, in 1988 and 1991, respectively, and the PhD degree in information management from Beijing Jiaotong University, Beijing, China, in 2010. He is currently a professor with the School of Management Science and Engineering, Shandong University of Finance and Economics, Shandong, China. He is an associate editor of the Journal of Intelligent and Fuzzy Systems, the editorial board of the journal Technological and Economic Development of Economy, and the members of editorial board of the other 12 journals. He has authored or coauthored more than 200 publications. His research interests include aggregation operators, fuzzy logic, fuzzy decision making, and their applications.

Li Ying

Y. Li received the BS degrees in logistics management from Shandong University of Finance and Economics, Jinan, China, in 2015. She is studying for her master in management science and engineering from Shandong University of Finance and Economics. Her research interests include aggregation operators, fuzzy logic, fuzzy decision making, and their applications.


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
probabilistic linguistic term PROMETHEE II MADM

Metrics
since January 2020
1455

Article info
views

 654

Full article
views
612

PDF
downloads

 240

XML
downloads


Share


RSS