2-Tuple Linguistic Hesitant Fuzzy Aggregation Operators and Its Application to Multi-Attribute Decision Making

Tan, Chunqiao; Jia, Yuan; Chen, Xiaohong

doi:10.15388/Informatica.2017.132

Informatica

2-Tuple Linguistic Hesitant Fuzzy Aggregation Operators and Its Application to Multi-Attribute Decision Making

Volume 28, Issue 2 (2017), pp. 329–358

Chunqiao Tan Yuan Jia Xiaohong Chen

https://doi.org/10.15388/Informatica.2017.132

Pub. online: 1 January 2017 Type: Research Article

Open Access

Received
1 October 2015

Accepted
1 December 2016

Published
1 January 2017

Abstract

In this paper, a new class of uncertain linguistic variables called 2-tuple linguistic hesitant fuzzy sets (2-TLHFSs) is defined, which can express complex multi-attribute decision-making problems as well as reflect decision makers’ hesitancy, uncertainty and inconsistency. Besides, it can avoid information and precision losing in aggregation process. Firstly, several new closed operational laws based on Einstein t-norm and t-conorm are defined over 2-TLHFSs, which can overcome granularity and logical problems of existing operational laws. Based on the new operational laws, 2-tuple linguistic hesitant fuzzy Einstein weighted averaging (2-TLHFEWA) operator and 2-tuple linguistic hesitant fuzzy Einstein weighted geometric (2-TLHFEWG) operator are proposed, and some of their properties are investigated. Then, a new model method based on similarity to ideal solution is proposed to determine weights of attribute, which takes both subjective and objective factors into consideration. Finally, a linguistic hesitant fuzzy multi-attribute decision making procedure is developed by means of 2-TLHFEWA and 2-TLHFEWG operators. An example is given to illustrate the practicality and efficiency of the proposed approach.

References

Atanassov, K.T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets & Systems, 20, 87–96.

Atanassov, K.T., Gargov, G. (1989). Interval valued intuitionistic fuzzy sets. Fuzzy Sets & Systems, 31, 343–349.

Beg, I., Rashid, T. (2016). Hesitant 2-tuple linguistic information in multiple attributes group decision making. Journal of Intelligent & Fuzzy Systems, 30, 143–150.

Beliakov, G., Pradera, A., Calvo, T. (2007). Aggregation Functions: A Guide for Practitioners. Studies in Fuzziness and Soft Computing.

Bryson, N., Mobolurin, A. (1997). An action learning evaluation procedure for multiple criteria decision making problems. European Journal of Operational Research, 96, 379–386.

Cavus, N. (2011). The application of a multi-attribute decision-making algorithm to learning management systems evaluation. British Journal of Educational Technology, 42, 19–30.

Chen, N., Xu, Z.S., Xia, M.M. (2013). Interval-valued hesitant preference relations and their applications to group decision making. Knowledge-Based Systems, 37, 528–540.

Chen, S.M., Lee, L.W. (2010). A new method for fuzzy group decision-making based on interval linguistic labels. In: IEEE Transactions on Systems Man and Cybernetics, Istanbul, Turkey, pp. 1–4.

Chou, J.R. (2012). A linguistic evaluation approach for universal design. Information Sciences, 190, 76–94.

Deng, H., Yeh, C.H., Willis, R.J. (2000). Inter-company comparison using modified TOPSIS with objective weights. Computers & Operations Research, 27, 963–973.

Deng, Y., Chan, F.T.S., Wu, Y., Wang, D. (2011). A new linguistic MCDM method based on multiple-criterion data fusion. Expert Systems with Applications, 38, 6985–6993.

Diakoulaki, D., Mavrotas, G., Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: the critic method. Computers & Operations Research, 22, 763–770.

Dong, Y., Zhang, G., Hong, W.C. (2013). Linguistic computational model based on 2-tuples and intervals. IEEE Transactions on Fuzzy Systems, 21, 1006–1018.

Edwards, W., Barron, F.H. (1994). SMARTS and SMARTER: improved simple methods for multiattribute utility measurement. Organizational Behavior & Human Decision Processes, 60, 306–325.

Figueira, J.R., Roy, B. (2002). Determining the weights of criteria in the ELECTRE type methods with a revised Simos’ procedure. European Journal of Operational Research, 139, 317–326.

Herrera, F., Herrera-Viedma, E. (2000). Choice functions and mechanisms for linguistic preference relations. European Journal of Operational Research, 120, 144–161.

Herrera, F., Martinez, L. (2001). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8, 746–752.

Jahan, A., Mustapha, F., Sapuan, S.M., Ismail M, Y., Bahraminasab, M. (2012). A framework for weighting of criteria in ranking stage of material selection process. International Journal of Advanced Manufacturing Technology, 58, 411–420.

James, G., Dolan, M.D. (2010). Multi-criteria clinical decision support a primer on the use of multiple criteria decision making methods to promote evidence-based, patient-centered healthcare. Patient: Patient-Centered Outcomes Research, 3, 229–248.

Kersuliene, V., Turskis, Z. (2010). Selection of rational dispute resolution method by applying new step-wise weight assessment ratio analysis (SWARA). Journal of Business Economics & Management, 11, 243–258.

Krylovas, A., Zavadskas, E.K., Kosareva, N., Dadelo, S. (2014). New KEMIRA method for determining criteria priority and weights in solving MCDM problem. International Journal of Information Technology & Decision Making, 13, 1119–1133.

Lennon, E., Farr, J., Besser, R. (2013). Evaluation of multi-attribute decision making systems applied during the concept design of new microplasma devices. Expert Systems with Applications, 40, 6321–6329.

Lin, R., Zhao, X., Wei, G. (2014). Models for selecting an ERP system with hesitant fuzzy linguistic information. Journal of Intelligent and Fuzzy Systems Applications in Engineering and Technology, 26, 2155–2165.

Liu, P.D., Jin, F. (2012). Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making. Information Sciences, 205, 58–71.

Liu, P., Liu, C., Rong, L. (2014a). Intuitionistic fuzzy linguistic numbers geometric aggregation operators and their application to group decision making. Economic Computation & Economic Cybernetics Studies & Research, 48, 95–113.

Liu, Z.B., Lu, L.L., Zhang, Z.Y., Chen, Y.S. (2014b). Synthetic evaluation of oilfield development plans based on a cloud model. Energy Technology and Policy an Open Access Journal, 1, 1–7.

Marti, L., Herrera, F. (2012). An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges. Information Sciences, 207, 1–18.

Martinez, L. (2007). Sensory evaluation based on linguistic decision analysis. International Journal of Approximate Reasoning, 44, 148–164.

Meng, F.Y., Chen, X., Zhang, Q. (2014). Multi-attribute decision analysis under a linguistic hesitant fuzzy environment. Information Sciences, 267, 287–305.

Merigo, J.M., Gil, A.M. (2013). Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making. Information Sciences, 236, 1–16.

Mu, Z., Zeng, S., Balezentis, T. (2015). A novel aggregation principle for hesitant fuzzy elements. Knowledge-Based Systems, 84, 134–143.

Poyhonen, M., Hamalainen, R.P. (2001). On the convergence of multiattribute weighting methods. European Journal of Operational Research, 129, 569–585.

Robert, D., Swezey, W. (1979). An application of a multi-attribute utilities model to training analysis. Human Factors, 21, 183–189.

Rodriguez, R.M., Martinez, L., Herrera, F. (2014a). A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Information Sciences, 241, 28–42.

Rodriguez, R.M., Martinez, L., Torra, V., Xu, Z.S., Herrera, F. (2014b). Hesitant fuzzy sets: state of the art and future directions. International Journal of Intelligent Systems, 29, 495–524.

Rybarczyk, G., Wu, C. (2010). Bicycle facility planning using GIS and multi-criteria decision analysis. Applied Geography, 30, 282–293.

Tao, Z., Chen, H., Zhou, L., Liu, J. (2014). On new operational laws of 2-tuple linguistic information using Archimedean t-norm and s-norm. Knowledge-Based Systems, 66, 156–165.

Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25, 529–539.

Vaidogas, E.R., Sakenaite, J. (2011). Multi-attribute decision-making in economics of fire protection. Inzinerine Ekonomika Engineering Economics, 22, 262–270.

Wan, S.P. (2013). Some hybrid geometric aggregation operators with 2-tuple linguistic information and their applications to multi-attribute group decision making. International Journal of Computational Intelligence Systems, 6, 750–763.

Wang, H.L. (2008). Grey cloud model and its application in intelligent decision support system supporting complex decision. International Colloquium on Computing, Communication, Control and Management.

Wang, J.Q., Wu, J.T. (2014). Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Information Sciences, 288, 55–72.

Wang, J., Wang, J.Q., Zhang, H., Chen, X.H. (2016). Multi-criteria group decision-making approach based on 2-tuple linguistic aggregation operators with multi-hesitant fuzzy linguistic information. International Journal of Fuzzy Systems, 18, 81–97.

Xu, Z. (2006). Induced uncertain linguistic OWA operators applied to group decision making. Information Fusion, 7, 231–238.

Xu, J.P., Shen, F. (2014). A new outranking choice method for group decision making under Atanassov’s interval-valued intuitionistic fuzzy environment. Knowledge-Based Systems, 70, 177–188.

Yu, D.J. (2014). Some hesitant fuzzy information aggregation operators based on Einstein operational laws. International Journal of Intelligent Systems, 29, 320–340.

Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8, 338–353.

Zadeh, L.A. (1973). Outline of a new approach to the analysis of complex systems and decision processes interval-valued fuzzy sets. IEEE Transactions on Systems Man and Cybernetics, 3, 28–44.

Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Part I. Information Sciences, 8, 199–249.

Zardari, N.H., Ahmed, K., Shirazi, S.M., Yusop, Z.B. (2015). Weighting Methods and Their Effects on Multi-Criteria Decision Making Model Outcomes in Water Resources Management. Springer International Publishing.

Zavadskas, E.K., Podvezko, V. (2016). Integrated determination of objective criteria weights in MCDM. International Journal of Information Technology & Decision Making, 15, 267–283.

Zeng, S.Z., Chen, S. (2015). Extended VIKOR method based on induced aggregation operators for intuitionistic fuzzy financial decision making. Economic Computation and Economic Cybernetics Studies and Research, 49, 289–303.

Zeng, S.Z., Gonzalez, J., Lobato, C. (2015). The effect of organizational learning and Web 2.0 on innovation. Management Decision, 53, 1906–1920.

Zhang, Z., Guo, C. (2015). New operations of hesitant fuzzy linguistic term sets with applications in multi-attribute group decision making. IEEE International Conference on Fuzzy Systems, 1–8.

Zhao, H., Xu, Z., Liu, S. (2015). Dual hesitant fuzzy information aggregation with Einstein t-conorm and t-norm. Journal of Systems Science & Systems Engineering, 1–25.

Zhou, L.G., Chen, H.Y. (2013). The induced linguistic continuous ordered weighted geometric operator and its application to group decision making. Computers & Industrial Engineering, 66, 222–232.

Zhou, L.G., Tao, Z.F., Chen, H.Y., Liu, J.P. (2014a). Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making. Applied Mathematical Modelling, 38, 2190–2205.

Zhou, L.G., Tao, Z.F., Chen, H.Y., Liu, J.P. (2014b). Intuitionistic fuzzy ordered weighted cosine similarity measure. Group Decision and Negotiation, 23, 879–900.

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

Tan Chunqiao

chungqiaot@mail.csu.edu.cn

chunqiao@sina.com

C. Tan received his PhD degree in management science and engineering from Beijing Institute of Technology in 2006. He is a professor in Nanjing Audit University. He has contributed over 30 journal articles to professional journals such as IEEE Transactions on Fuzzy Systems, Fuzzy Sets and Systems, Journal of the Operational Research Society, Knowledge-Based Systems, Fuzzy Optimization and Decision Making, Applied Soft Computing, International Journal of Fuzzy Systems, International Journal of Intelligent and Fuzzy Systems. His current research interests include decision analysis and game theory.

Jia Yuan

Y. Jia is a master degree candidate in management science and engineering at the business school of Central South University. Her research interest is decision-making theory and application.

Chen Xiaohong

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Keywords

multi-attribute decision making aggregation operator 2-tuple linguistic hesitant fuzzy sets 2-tuple linguistic hesitant fuzzy Einstein weighted averaging operators 2-tuple linguistic hesitant fuzzy Einstein weighted geometric operator

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