A multi-criteria decision making procedure based on interval-valued intuitionistic fuzzy bonferroni means

Abstract

Inspired by the idea of Bonferroni mean, in this paper we develop an aggregation technique called the interval-valued intuitionistic fuzzy Bonferroni mean for aggregating interval-valued intuitionistic fuzzy information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define a weighted interval-valued intuitionistic fuzzy Bonferroni mean, based on which we give a procedure for multi-criteria decision making under interval-valued intuitionistic fuzzy environments.

Keywords

Bonferroni mean / interval-valued intuitionistic fuzzy number / multi-criteria decision making / interval-valued intuitionistic fuzzy Bonferroni mean / weighted interval-valued intuitionistic fuzzy Bonferroni mean

References

[1] Atanassov K., Gargov G.. Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1989, 31: 343-349.

[2] Beliakov G., James S., Mordelová J., Rückschlossová T., Yager R.R.. Generalized Bonferroni mean operators in multi-criteria aggregation. Fuzzy Sets and Systems, 2010, 161: 2227-2242.

[3] Beliakov G., Pradera A., Calvo T.. Aggregation Functions: A Guide for Practitioners, 2007, Heidelberg: Springer

[4] Bonferroni C.. Sulle medie multiple di potenze. Bolletino Matematica Italiana, 1950, 5: 267-270.

[5] Bullen P.S.. Handbook of Mean and Their Inequalties, 2003, Dordrecht: Kluwer

[6] Chen Q., Xu Z.S., Liu S.S., Yu X.H.. A method based on interval-valued intuitionistic fuzzy entropy for multiple attribute decision making. Information: An International Interdisciplinary Journal, 2010, 13: 67-77.

[7] Choquet G.. Theory of capacities. Annales de l’Institut Fourier, 1953, 5: 131-296.

[8] Dempster A.P.. Upper and lower probabilities induced by a multi-valued mapping. Annals of Mathematical Statistics, 1967, 38: 325-339.

[9] Dujmovic J.J.. Continuous preference logic for system evaluation. IEEE Transactions on Fuzzy Systems, 2007, 15: 1082-1099.

[10] Marichal J.L.. k-Intolerant capacities and Choquet integrals. European Journal of Operational Research, 2007, 177: 1453-1468.

[11] Shafer G.. Mathematical Theory of Evidence, 1976, Princeton, NJ: Princeton University Press.

[12] Sugeno M.. Theory of fuzzy integrals and its applications, 1974, Tokyo, Japan: Tokyo Institute of Technology

[13] Wang Z.J., Li K.W., Wang W.Z.. An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Information Sciences, 2009, 179: 3026-3040.

[14] Xu Z.S.. An overview of methods for determining OWA weights. International Journal of Intelligent Systems, 2005, 20: 843-865.

[15] Xu Z.S.. A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Information Sciences, 2010, 180: 181-190.

[16] Xu Z.S.. Uncertain Bonferroni mean operators. International Journal of Computational Intelligence Systems, 2010, 3: 761-769.

[17] Xu Z.S.. A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decision and Negotiation, 2010, 19: 57-76.

[18] Xu Z.S.. Choquet integrals of weighted intuitionistic fuzzy information. Information Sciences, 2010, 180: 726-736.

[19] Xu Z.S., Cai X.Q.. Incomplete interval-valued intuitionistic preference relations. International Journal of General Systems, 2009, 38: 871-886.

[20] Xu Z.S., Cai X.Q.. Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information. International Journal of Intelligent Systems, 2010, 25: 489-513.

[21] Xu Z.S., Chen J., Wu J.J.. Clustering algorithm for intuitionistic fuzzy sets. Information Sciences, 2008, 178: 3775-3790.

[22] Xu Z.S., Yager R.R.. Dynamic intuitionistic fuzzy multi-attribute decision making. International Journal of Approximate Reasoning, 2008, 48: 246-262.

[23] Xu Z.S., Yager R.R.. Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optimization and Decision Making, 2009, 8: 123-139.

[24] Xu Z.S., Yager R.R.. Intuitionistic fuzzy Bonferroni means. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 2011, 41: 568-578.

[25] Yager R.R.. On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 1988, 18: 183-190.

[26] Yager R.R.. On generalized Bonferroni mean operators for multi-criteria aggregation. International Journal of Approximate Reasoning, 2009, 50: 1279-1286.

[27] Yager R., Beliakov G., James S.. On generalized Bonferroni means. Proceedings of the Eurofuse Workshop Preference Modelling and Decision Analysis, 2009, Spain: Pamplona 1-6.

[28] Yoon K.. The propagation of errors in multiple-attribute decision analysis: a practical approach. Journal of Operational Research Society, 1989, 40: 681-686.

[29] Zhao H., Xu Z.S., Ni M.F., Liu S.S.. Generalized aggregation operators for intuitionistic fuzzy sets. International Journal of Intelligent Systems, 2010, 25: 1-30.