Symmetric Intuitionistic Fuzzy Weighted Mean Operators Based on Weighted Archimedean t-Norms and t-Conorms for Multi-Criteria Decision Making

Ma, Zhen Ming; Yang, Wei

doi:10.15388/20-INFOR390

Informatica

Symmetric Intuitionistic Fuzzy Weighted Mean Operators Based on Weighted Archimedean t-Norms and t-Conorms for Multi-Criteria Decision Making

Volume 31, Issue 1 (2020), pp. 89–112

Zhen Ming Ma Wei Yang

https://doi.org/10.15388/20-INFOR390

Pub. online: 23 March 2020 Type: Research Article

Open Access

Received
1 February 2019

Accepted
1 September 2019

Published
23 March 2020

Abstract

Using different operational laws on membership and non-membership information, various intuitionistic fuzzy aggregation operators based on Archimedean t-norm and t-conorm or their special cases have been extensively investigated for multi-criteria decision making. In spite of this, they are not suitable for some practical cases. In this paper, symmetric intuitionistic fuzzy weighted mean operators w.r.t. general weighted Archimedean t-norms and t-conorms are introduced to deal neutrally or fairly with membership and non-membership information to meet the need of decision makers in some cases. The relationship among the proposed operators and the existing ones is discussed. Particularly, using the parameters in the aggregation operators, the attitude whether the decision maker is optimistic, pessimistic or impartial is reflected. At last, an example is given to show the behaviour of the proposed operators for multi-criteria decision making under intuitionistic fuzzy environment.

References

Atanassov, K. (1986). Intuitionistic fuzzy set. Fuzzy Sets and Systems, 20, 87–96.

Alghamdi, M.A., Alshehri, N.O., Akram, M. (2018). Multi-criteria decision-making methods in bipolar fuzzy environment. International Journal of Fuzzy Systems, 20, 2057–2064.

Alonso, S., Perez, I.J., Cabrerizo, F.J., Herrera-Viedma, E. (2013). A linguistic consensus model for Web 2.0 communities. Applied Soft Computing, 13, 149–157.

Beliakov, G., James, S. (2013). On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts. Fuzzy Sets and Systems, 211, 84–98.

Beliakov, G., Pradera, A., Calvo, T. (2007). Aggregation Functions: A Guide for Practitioners. Springer, Heidelberg, Berlin, New York.

Beliakov, G., Bustince, H., Goswami, D.P., Mukherjee, U.K., Pal, N.R. (2011). On averaging operators for Atanassov’s intuitionistic fuzzy sets. Information Sciences, 181, 1116–1124.

Bonferroni, C. (1950). Sulle medie multiple di potenze. Bolletino Matematica Italiana, 5, 267–270.

Calvo, T., Mesiar, R. (2003). Weighted triangular norms-based aggregation operators. Fuzzy Sets and Systems, 137, 3–10.

Chen, T.Y. (2011). Bivariate models of optimism and pessimism in multi-criteria decision-making based on intuitionistic fuzzy sets. Information Sciences, 181, 2139–2165.

Chen, S.M., Tan, J.M. (1994). Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 67, 163–172.

Del Moral, M.J., Chiclana, F., Tapia, J.M., Herrera-Viedma, E. (2018). A comparative study on consensus measures in group decision making. International Journal of Intelligent Systems, 33, 1624–1638.

Deng, J.L. (1989). Introduction to grey system theory. Journal of Grey Systems, 1, 1–24.

Deschrijver, G., Kerre, E.E. (2003). On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems, 133, 227–235.

Deschrijver, G., Kerre, E.E. (2007). On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision. Information Sciences, 177, 1860–1866.

Deschrijver, G., Kerre, E.E. (2008). Aggregation operators in interval-valued fuzzy and Atanassov’s intuitionistic fuzzy set sheory. In: Bustince, H., Herrera, F., Montero, J. (Eds.), Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Springer, Heidelberg, New York, pp. 183–203.

Dong, Y., Zhao, S., Zhang, H., Chiclana, F., Herrera-Viedma, E. (2018). A self-management mechanism for non-cooperative behaviors in large-scale group consensus reaching processes. IEEE Transactions on Fuzzy Systems, 26, 3276–3288.

Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., Prade, H. (2005). Terminological difficulties in fuzzy set theory – the case of intuitionistic fuzzy sets. Fuzzy Sets and Systems, 156, 485–491.

Gau, W.L., Buehrer, D.J. (1993). Vague sets. IEEE Transactions on Systems Man and Cybernetics, 23, 610–614.

Hardy, G.H., Littlewood, Pólya G, J.E. (1934). Inequalities. Cambridge University Press, Cambridge.

Hong, D.H., Choi, C.H. (2000). Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 114, 103–113.

Klement, E.P., Mesiar, R., Pap, E. (2000). Triangular Norms. Kluwer Academic Publishers, Boston, London, Dordrecht.

Li, D.F. (2010). Multiattribute decision making method based on generalized OWA operators with intuitionistic fuzzy sets. Expert Systems with Applications, 37, 8673–8678.

Liao, H., Xu, Z.S. (2014). Intuitionistic fuzzy hybrid weighted aggregation operators. International Journal of Intelligent Systems, 29, 971–993.

Liao, H., Xu, Z.S. (2015). Consistency of the fused intuitionistic fuzzy preference relation in group intuitionistic fuzzy analytic hierarchy process. Applied Soft Computing, 35, 812–826.

Ma, Z.M., Xu, Z.S. (2016). Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. International Journal of Intelligent Systems, 31, 1198–1219.

Ma, Z.M., Xu, Z.S. (2018). Hyperbolic scales involving appetites-based intuitionistic multiplicative preference relations for group decision making. Information Sciences, 451–452, 310–325.

Sambuc, R. (1975). Fonctions ϕ-floues. Application l’aide au diagnostic en pathologie thyroidienne. Ph.D. Thesis, Univ. Marseille, France.

Tan, C., Jiang, Z., Chen, X. (2013). Some issues on quasi-arithmetic intuitionistic fuzzy OWA operators. Applied Mathematics & Information Sciences, 7, 955–961.

Urena, R., Kou, G., Dong, Y., Chiclana, F., Herrera-Viedma, E. (2019). A review on trust propagation and opinion dynamics in social networks and group decision making frameworks. Information Sciences, 478, 461–475.

Wang, W., Liu, X. (2011). Intuitionistic fuzzy geometric aggregation operators based on Einstein operations. International Journal of Intelligent Systems, 26, 1049–1075.

Wang, W., Liu, X. (2012). Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Transactions on Fuzzy Systems, 20, 923–938.

Xu, Z.S. (2007). Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15, 1179–1187.

Xu, Z.S., Yager, R.R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of Intelligent Systems, 35, 417–433.

Xu, Z.S., Yager, R.R. (2011). Intuitionistic fuzzy Bonferroni means. IEEE Transactions on Systems, Man, and Cybernetics–Part B: Cybernetics, 41, 568–578.

Xu, C.Y., Ma, Z.M. (2019). Symmetric intuitionistic multiplicative aggregation operator for group decision making in intuitionistic multiplicative environments. Journal of Intelligent & Fuzzy Systems, 36, 5909–5918.

Xia, M., Xu, Z.S. (2012). Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Information Fusion, 13, 31–47.

Xia, M., Xu, Z.S., Zhu, B. (2012). Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm. Knowledge-Based Systems, 31, 78–88.

Yager, R.R. (1988). On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Systems Man and Cybernetics, 18, 183–190.

Yager, R.R. (2004a). Weighted triangular norms using generating functions. International Journal of Intelligent Systems, 19, 217–231.

Yager, R.R. (2004b). Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making, 3, 93–107.

Yager, R.R. (2009). On generalized Bonferroni mean operators for multi-criteria aggregation. International Journal of Approximate Reasoning, 50, 1279–1286.

Yager, R.R., Filev, D.P. (1999). Induced ordered weighted averaging operators. IEEE Transactions on Systems Man and Cybernetics, 29, 141–150.

Yang, W., Chen, Z.P. (2012). The quasi-arithmetic intuitionistic fuzzy OWA operators. Knowledge-Based Systems, 27, 219–233.

Yang, W., Jhang, S.T., Fu, Z.W., Ma, Z.M. (2019). Aggregating intuitionistic fuzzy preference relations with symmetrical intuitionistic fuzzy Bonferroni mean operators in group decision making. Information Sciences.

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

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

Zhao, H., Xu, Z.S., Ni, M.F., Liu, S.S. (2010). Generalized aggregation operators for intuitionistic fuzzy sets. International Journal of Intelligent Systems, 25, 1–30.

Biographies

Ma Zhen Ming

dmgywto@126.com

Z.M. Ma is an associate professor at School of Mathematics and Statistics, Linyi University. He has received his MS degree in systems theory and PhD in computational mathematics from the School of Mathematics and Statistics, Wuhan University. His current research is focused on decision-making theory and intelligent decision support systems.

Yang Wei

wyoeng@126.com

W. Yang is a lecturer at School of Mathematics and Statistics, Linyi University. She has received her MS degree in applied mathematics from the School of Scineces, University of Science and Technology, Beijing. Her current research is focused on decision-making theory.

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Keywords

multi-criteria decision making intuitionistic fuzzy set weighted Archimedean t-norm and t-conorm symmetric intuitionistic fuzzy weighted mean operator

Funding

This research was supported by the NSF of Shandong Province (No. ZR2017MG027) and AMEP (DYSP) of Linyi University (No. LYDX2014BS017).

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