A Straightforward Approach for Determining the Weights of Decision Makers Based on Angle Cosine and Projection Method
Group decision making with multiple attribute has
attracted intensive concern in the decision analysis area. This paper
assumes that the contributions of all the decision makers (DMs) are not
equal to the decision process based on different knowledge and
experience in group setting. The aim of this paper is to develop a novel
approach to determine weights of DMs in the group decision making
problems. In this paper, the weights of DMs are determined in the
group decision environment via angle cosine and projection method.
First of all, the average decision of all individual decisions is defined
as the ideal decision. After that, we define the weight of each decision
maker (DM) by aggregating the angle cosine and projection between
individual decision and ideal decision with associated direction
indicator μ. By using the weights of DMs, all individual decisions are
aggregated into a collective decision. Further, the preference order of
alternatives is ranked in accordance with the overall row value of
collective decision. Finally, an example in a chemical company is
provided to illustrate the developed approach.
[1] S.-J. Chen and C.-L. Hwang, Fuzzy Multiple Attribute Decision Making:
Methods and Applications, New York: Springer-Verlag, 1992, pp. 16-41.
[2] C.-L. Hwang and K. Yoon, Multiple Attribute Decision Making: Methods
and Applications, Berlin: Springer-Verlag, 1981, pp. 16-57.
[3] Z. Yue, “Group decision making with multi-attribute interval data”,
Information Fusion, vol. 14, pp. 551-561, 2013.
[4] X. Chen, H.J. Zhang, Y.C. Dong, “The fusion process with heterogeneous
preference structures in group decision making: a survey, Information
Fusion”, vol. 24, pp. 72-83, 2015.
[5] P.D. Liu, J. Fang, “Methods for aggregating intuitionistic uncertain
linguistic variables and their application to group decision making”,
Information Sciences, vol. 205, pp. 58-71, 2012.
[6] Agell, Núria, Sánchez, Mónica, Prats, Francesc, Roselló, Llorenç,
“Ranking multi-attribute alternatives on the basis of linguistic labels in
group decisions”, Information Sciences, vol. 209, pp. 49–60, 2012.
[7] S.E. Bodily, “Note—A Delegation Process for Combining Individual
Utility Functions”, Management Science, vol. 25, pp. 1035-1041, 1979.
[8] B.G. Mirkin, P.C. Fishburn, Group Choice, Halsted Press, 1979, pp.
62-90.
[9] R. Ramanathan, L.S. Ganesh, “Group preference aggregation methods
employed in AHP: An evaluation and an intrinsic process for deriving
members' weightages”, European Journal of Operational Research, vol.
79, pp. 249-265, 1994.
[10] H. Hsi-Mei, C. Chen-Tung, “Aggregation of fuzzy opinions under group
decision making”, Fuzzy Sets and Systems, vol. 79, pp. 279-285, 1996
[11] S. Ben Khèlifa, J.-M. Martel, “Deux propositions d’aide multicritère à la
décision de groupe, in: Ben Abdelaziz, Haouari et Mellouli (Eds.),
Optimisation et Décision”, Centre de Publication Universitaire, Tunis, vol.
1, pp. 213–228, 2000.
[12] R. Van den Honert, “Decisional Power in Group Decision Making: A
Note on the Allocation of Group Members’ Weights in the Multiplicative
AHP and SMART”, Group Decision and Negociation, vol. 10, pp.
275-286, 2001.
[13] M.J. Beynon, “A method of aggregation in DS/AHP for group
decision-making with the non-equivalent importance of individuals in the
group”, Computers & Operations Research, vol. 32, pp. 1881-1896, 2005.
[14] Z. Xu, “Group decision making based on multiple types of linguistic
preference relations”, Information Sciences, vol. 178, pp. 452-467, 2008.
[15] C. Fu, S.-L. Yang, “The group consensus based evidential reasoning
approach for multiple attributive group decision analysis”, European
Journal of Operational Research, vol. 206, pp. 601-608, 2010.
[16] J. Xu, Z. Wu, “A discrete consensus support model for multiple attribute
group decision making”, Knowledge-Based Systems, vol. 24, pp.
1196-1202, 2011.
[17] L. Zhou, H. Chen, J. Liu, “Generalized logarithmic proportional
averaging operators and their applications to group decision making”,
Knowledge-Based Systems, vol. 36, pp. 268-279, 2012.
[18] Z. Zhang, “Generalized Atanassov’s intuitionistic fuzzy power geometric
operators and their application to multiple attribute group decision
making”, Information Fusion, vol. 14, pp. 460-486, 2013.
[19] T. Tsabadze, “A method for aggregation of trapezoidal fuzzy estimates
under group decision-making”, Fuzzy Sets and Systems, vol. 266, pp.
114-130, 2014. [20] Z. Yue, “A method for group decision-making based on determining
weights of decision makers using TOPSIS”, Appl. Math. Model., vol. 35,
pp. 1926-1936, 2011.
[21] Z.S. Xu, Uncertain Multiple Attribute Decision Making: Methods and
Applications, Beijing: Tsinghua University Press, 2004, ch. 3.
[22] G. Zheng, Y. Jing, H. Huang, Y. Gao, “Application of improved grey
relational projection method to evaluate sustainable building envelope
performance”, Applied Energy, vol. 87, pp. 710-720, 2010.
[23] Z. Yue, “Approach to group decision making based on determining the
weights of experts by using projection method”, Appl. Math. Model., vol.
36, pp. 2900-2910, 2012.
[24] H.-S. Shih, H.-J. Shyur, E.S. Lee, “An extension of TOPSIS for group
decision making”, Mathematical and Computer Modelling, vol. 45, pp.
801-813, 2007.
[1] S.-J. Chen and C.-L. Hwang, Fuzzy Multiple Attribute Decision Making:
Methods and Applications, New York: Springer-Verlag, 1992, pp. 16-41.
[2] C.-L. Hwang and K. Yoon, Multiple Attribute Decision Making: Methods
and Applications, Berlin: Springer-Verlag, 1981, pp. 16-57.
[3] Z. Yue, “Group decision making with multi-attribute interval data”,
Information Fusion, vol. 14, pp. 551-561, 2013.
[4] X. Chen, H.J. Zhang, Y.C. Dong, “The fusion process with heterogeneous
preference structures in group decision making: a survey, Information
Fusion”, vol. 24, pp. 72-83, 2015.
[5] P.D. Liu, J. Fang, “Methods for aggregating intuitionistic uncertain
linguistic variables and their application to group decision making”,
Information Sciences, vol. 205, pp. 58-71, 2012.
[6] Agell, Núria, Sánchez, Mónica, Prats, Francesc, Roselló, Llorenç,
“Ranking multi-attribute alternatives on the basis of linguistic labels in
group decisions”, Information Sciences, vol. 209, pp. 49–60, 2012.
[7] S.E. Bodily, “Note—A Delegation Process for Combining Individual
Utility Functions”, Management Science, vol. 25, pp. 1035-1041, 1979.
[8] B.G. Mirkin, P.C. Fishburn, Group Choice, Halsted Press, 1979, pp.
62-90.
[9] R. Ramanathan, L.S. Ganesh, “Group preference aggregation methods
employed in AHP: An evaluation and an intrinsic process for deriving
members' weightages”, European Journal of Operational Research, vol.
79, pp. 249-265, 1994.
[10] H. Hsi-Mei, C. Chen-Tung, “Aggregation of fuzzy opinions under group
decision making”, Fuzzy Sets and Systems, vol. 79, pp. 279-285, 1996
[11] S. Ben Khèlifa, J.-M. Martel, “Deux propositions d’aide multicritère à la
décision de groupe, in: Ben Abdelaziz, Haouari et Mellouli (Eds.),
Optimisation et Décision”, Centre de Publication Universitaire, Tunis, vol.
1, pp. 213–228, 2000.
[12] R. Van den Honert, “Decisional Power in Group Decision Making: A
Note on the Allocation of Group Members’ Weights in the Multiplicative
AHP and SMART”, Group Decision and Negociation, vol. 10, pp.
275-286, 2001.
[13] M.J. Beynon, “A method of aggregation in DS/AHP for group
decision-making with the non-equivalent importance of individuals in the
group”, Computers & Operations Research, vol. 32, pp. 1881-1896, 2005.
[14] Z. Xu, “Group decision making based on multiple types of linguistic
preference relations”, Information Sciences, vol. 178, pp. 452-467, 2008.
[15] C. Fu, S.-L. Yang, “The group consensus based evidential reasoning
approach for multiple attributive group decision analysis”, European
Journal of Operational Research, vol. 206, pp. 601-608, 2010.
[16] J. Xu, Z. Wu, “A discrete consensus support model for multiple attribute
group decision making”, Knowledge-Based Systems, vol. 24, pp.
1196-1202, 2011.
[17] L. Zhou, H. Chen, J. Liu, “Generalized logarithmic proportional
averaging operators and their applications to group decision making”,
Knowledge-Based Systems, vol. 36, pp. 268-279, 2012.
[18] Z. Zhang, “Generalized Atanassov’s intuitionistic fuzzy power geometric
operators and their application to multiple attribute group decision
making”, Information Fusion, vol. 14, pp. 460-486, 2013.
[19] T. Tsabadze, “A method for aggregation of trapezoidal fuzzy estimates
under group decision-making”, Fuzzy Sets and Systems, vol. 266, pp.
114-130, 2014. [20] Z. Yue, “A method for group decision-making based on determining
weights of decision makers using TOPSIS”, Appl. Math. Model., vol. 35,
pp. 1926-1936, 2011.
[21] Z.S. Xu, Uncertain Multiple Attribute Decision Making: Methods and
Applications, Beijing: Tsinghua University Press, 2004, ch. 3.
[22] G. Zheng, Y. Jing, H. Huang, Y. Gao, “Application of improved grey
relational projection method to evaluate sustainable building envelope
performance”, Applied Energy, vol. 87, pp. 710-720, 2010.
[23] Z. Yue, “Approach to group decision making based on determining the
weights of experts by using projection method”, Appl. Math. Model., vol.
36, pp. 2900-2910, 2012.
[24] H.-S. Shih, H.-J. Shyur, E.S. Lee, “An extension of TOPSIS for group
decision making”, Mathematical and Computer Modelling, vol. 45, pp.
801-813, 2007.
@article{"International Journal of Business, Human and Social Sciences:70942", author = "Qiang Yang and Ping-An Du", title = "A Straightforward Approach for Determining the Weights of Decision Makers Based on Angle Cosine and Projection Method", abstract = "Group decision making with multiple attribute has
attracted intensive concern in the decision analysis area. This paper
assumes that the contributions of all the decision makers (DMs) are not
equal to the decision process based on different knowledge and
experience in group setting. The aim of this paper is to develop a novel
approach to determine weights of DMs in the group decision making
problems. In this paper, the weights of DMs are determined in the
group decision environment via angle cosine and projection method.
First of all, the average decision of all individual decisions is defined
as the ideal decision. After that, we define the weight of each decision
maker (DM) by aggregating the angle cosine and projection between
individual decision and ideal decision with associated direction
indicator μ. By using the weights of DMs, all individual decisions are
aggregated into a collective decision. Further, the preference order of
alternatives is ranked in accordance with the overall row value of
collective decision. Finally, an example in a chemical company is
provided to illustrate the developed approach.", keywords = "Angel cosine, ideal decision, projection method,
weights of decision makers.", volume = "9", number = "10", pages = "3335-7", }
