The Intuitionistic Fuzzy Ordered Weighted Averaging-Weighted Average Operator and its Application in Financial Decision Making
We present a new intuitionistic fuzzy aggregation
operator called the intuitionistic fuzzy ordered weighted
averaging-weighted average (IFOWAWA) operator. The main
advantage of the IFOWAWA operator is that it unifies the OWA
operator with the WA in the same formulation considering the degree
of importance that each concept has in the aggregation. Moreover, it is
able to deal with an uncertain environment that can be assessed with
intuitionistic fuzzy numbers. We study some of its main properties and
we see that it has a lot of particular cases such as the intuitionistic
fuzzy weighted average (IFWA) and the intuitionistic fuzzy OWA
(IFOWA) operator. Finally, we study the applicability of the new
approach on a financial decision making problem concerning the
selection of financial strategies.
[1] G. Beliakov, A. Pradera, and T. Calvo, Aggregation Functions: A guide
for practitioners, Springer-Verlag, Berlin, 2007.
[2] T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New Trends
and applications, Physica-Verlag, New York, 2002.
[3] Z.S. Xu, and Q.L. Da, "An Overview of Operators for Aggregating
Information", International Journal of Intelligent Systems, vol. 18, pp.
953-969, 2003.
[4] R.R. Yager, "On Ordered Weighted Averaging Aggregation Operators in
Multi-Criteria Decision Making", IEEE Transactions on Systems, Man
and Cybernetics, vol. 18, pp. 183-190, 1988.
[5] N. Karayiannis, "Soft Learning Vector Quantization and Clustering
Algorithms Based on Ordered Weighted Aggregation Operators", IEEE
Transaction Neural Networks, vol. 11, 1093-1105, 2000.
[6] R.R. Yager, "Generalized OWA Aggregation Operators", Fuzzy
Optimization and Decision Making, vol. 3, pp.93-107, 2004.
[7] G. Beliakov, "Learning Weights in the Generalized OWA Operators",
Fuzzy Optimization and Decision Making, vol. 4, pp. 119-130, 2005.
[8] P. Liu. A weighted aggregation operators multi-attribute group decision
making method based on interval-valued trapezoidal fuzzy numbers.
Expert Systems with Applications, vol. 38, pp. 1053-1060, 2011.
[9] B.S. Ahn, and H. Park, "Least-squared ordered weighted averaging
operator weights", International Journal of Intelligent Systems, vol. 23,
pp. 33-49, 2008.
[10] X.W. Liu, "The solution equivalence of minimax disparity and minimum
variance problems for OWA operators", International Journal of
Approximate Reasoning, vol. 45, pp. 68-81, 2007.
[11] J.M. Merig├│, "The induced generalized hybrid averaging operator and its
application in financial decision making", International Journal of
Human and Social Sciences, vol. 4, pp. 1014-1019, 2009
[12] J.M. Merig├│, "Fuzzy decision making with immediate probabilities",
Computers & Industrial Engineering, vol. 58, pp. 651-657, 2010.
[13] J.M. Merig├│, "A unified model between the weighted average and the
induced OWA operator", Expert Systems with Applications, vol.38, pp.
11560-11572, 2011.
[14] J.M. Merig├│, "The probabilistic weighted average and its application in
multiperson decision making", International Journal of Intelligent
Systems, vol. 27, pp. 457-476, 2012
[15] J.M. Merig├│, and M. Casanovas, "Decision making with distance
measures and induced aggregation operators", Computers & Industrial
Engineering, vol. 60, pp. 66-76, 2011.
[16] J.M. Merig├│, and A.M. Gil-Lafuente, "The induced generalized OWA
operator", Information Sciences, vol. 179, pp. 729-741, 2009.
[17] J.M. Merig├│, and A.M. Gil-Lafuente, "New decision-making techniques
and their application in the selection of financial products", Information
Sciences, vol. 180, pp. 2085-2094, 2010.
[18] J.M. Merig├│, and A.M. Gil-Lafuente, "OWA operators in human resource
management", Economic Computation and Economic Cybernetics
Studies and Research, vol. 45, pp. 153-168, 2011.
[19] G.W. Wei, "FIOWHM operator and its application to group decision
making", Expert Systems with Applications, vol. 38, pp. 2984-2989,
2011.
[20] Y.J. Xu, and H.M. Wang, "Approaches based on 2-tuple linguistic power
aggregation operators for multiple attribute group decision making under
linguistic environment", Applied Soft Computing, vol. 11, pp.
3988-3997, 2011.
[21] Z.S. Xu, and M.M. Xia, "Induced generalized intuitionistic fuzzy
operators", Knowledge-Based Systems, vol. 24, pp. 197-209, 2011.
[22] L.G. Zhou, and H.Y. Chen, "Continuous generalized OWA operator and
its application to decision making", Fuzzy Sets and Systems, vol. 16, pp.
18-34, 2011.
[23] V. Torra, "The weighted OWA operator", International Journal of
Intelligent Systems, vol. 12, pp. 153-166, 1997.
[24] K.T. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, vol.
20, pp. 87-96, 1986.
[25] G.W. Wei, "Maximizing deviation method for multiple attribute decision
making in intuitionistic fuzzy setting", Knowledge-Based Systems,
vol.21, pp. 833-836, 2008.
[26] G.W. Wei, "Some induced geometric aggregation operators with
intuitionistic fuzzy information and their application to group decision
making", Applied Soft Computing, vol. 10, pp. 423-431, 2010.
[27] Z.S. Xu, "Intuitionistic fuzzy aggregation operators", IEEE Transactions
on Fuzzy Systems, vol. 15, pp. 1179-1187, 2007.
[28] J. Ye, "Fuzzy decision-making method based on the weighted correlation
coefficient under intuitionistic fuzzy environment", European Journal of
Operational Research, vol. 205, pp. 202-204, 2010.
[29] Z.S. Xu, and R.R. Yager, "Some geometric aggregation operators based
on intuitionistic fuzzy sets", International Journal of General Systems,
vol. 35,pp. 417-433, 2006.
[30] Y.J. Xu, and H.M. Wang, "The induced generalized aggregation
operators for intuitionistic fuzzy sets and their application in group
decision making", Applied Soft Computing, vol. 2012, pp. 1168-1179,
2012.
[31] S.Z. Zeng, and W.H. Su, "Intuitionistic fuzzy ordered weighted distance
operator" , Knowledge-Based Systems, vol. 24, pp. 1224-1232, 2011.
[32] S.Z. Zeng, "Some intuitionistic fuzzy weighted distance measures and
their application to group decision making", Group Decision and
Negotiation, in press. DOI:10.1007/s10726-011-9262-6.
[1] G. Beliakov, A. Pradera, and T. Calvo, Aggregation Functions: A guide
for practitioners, Springer-Verlag, Berlin, 2007.
[2] T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New Trends
and applications, Physica-Verlag, New York, 2002.
[3] Z.S. Xu, and Q.L. Da, "An Overview of Operators for Aggregating
Information", International Journal of Intelligent Systems, vol. 18, pp.
953-969, 2003.
[4] R.R. Yager, "On Ordered Weighted Averaging Aggregation Operators in
Multi-Criteria Decision Making", IEEE Transactions on Systems, Man
and Cybernetics, vol. 18, pp. 183-190, 1988.
[5] N. Karayiannis, "Soft Learning Vector Quantization and Clustering
Algorithms Based on Ordered Weighted Aggregation Operators", IEEE
Transaction Neural Networks, vol. 11, 1093-1105, 2000.
[6] R.R. Yager, "Generalized OWA Aggregation Operators", Fuzzy
Optimization and Decision Making, vol. 3, pp.93-107, 2004.
[7] G. Beliakov, "Learning Weights in the Generalized OWA Operators",
Fuzzy Optimization and Decision Making, vol. 4, pp. 119-130, 2005.
[8] P. Liu. A weighted aggregation operators multi-attribute group decision
making method based on interval-valued trapezoidal fuzzy numbers.
Expert Systems with Applications, vol. 38, pp. 1053-1060, 2011.
[9] B.S. Ahn, and H. Park, "Least-squared ordered weighted averaging
operator weights", International Journal of Intelligent Systems, vol. 23,
pp. 33-49, 2008.
[10] X.W. Liu, "The solution equivalence of minimax disparity and minimum
variance problems for OWA operators", International Journal of
Approximate Reasoning, vol. 45, pp. 68-81, 2007.
[11] J.M. Merig├│, "The induced generalized hybrid averaging operator and its
application in financial decision making", International Journal of
Human and Social Sciences, vol. 4, pp. 1014-1019, 2009
[12] J.M. Merig├│, "Fuzzy decision making with immediate probabilities",
Computers & Industrial Engineering, vol. 58, pp. 651-657, 2010.
[13] J.M. Merig├│, "A unified model between the weighted average and the
induced OWA operator", Expert Systems with Applications, vol.38, pp.
11560-11572, 2011.
[14] J.M. Merig├│, "The probabilistic weighted average and its application in
multiperson decision making", International Journal of Intelligent
Systems, vol. 27, pp. 457-476, 2012
[15] J.M. Merig├│, and M. Casanovas, "Decision making with distance
measures and induced aggregation operators", Computers & Industrial
Engineering, vol. 60, pp. 66-76, 2011.
[16] J.M. Merig├│, and A.M. Gil-Lafuente, "The induced generalized OWA
operator", Information Sciences, vol. 179, pp. 729-741, 2009.
[17] J.M. Merig├│, and A.M. Gil-Lafuente, "New decision-making techniques
and their application in the selection of financial products", Information
Sciences, vol. 180, pp. 2085-2094, 2010.
[18] J.M. Merig├│, and A.M. Gil-Lafuente, "OWA operators in human resource
management", Economic Computation and Economic Cybernetics
Studies and Research, vol. 45, pp. 153-168, 2011.
[19] G.W. Wei, "FIOWHM operator and its application to group decision
making", Expert Systems with Applications, vol. 38, pp. 2984-2989,
2011.
[20] Y.J. Xu, and H.M. Wang, "Approaches based on 2-tuple linguistic power
aggregation operators for multiple attribute group decision making under
linguistic environment", Applied Soft Computing, vol. 11, pp.
3988-3997, 2011.
[21] Z.S. Xu, and M.M. Xia, "Induced generalized intuitionistic fuzzy
operators", Knowledge-Based Systems, vol. 24, pp. 197-209, 2011.
[22] L.G. Zhou, and H.Y. Chen, "Continuous generalized OWA operator and
its application to decision making", Fuzzy Sets and Systems, vol. 16, pp.
18-34, 2011.
[23] V. Torra, "The weighted OWA operator", International Journal of
Intelligent Systems, vol. 12, pp. 153-166, 1997.
[24] K.T. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, vol.
20, pp. 87-96, 1986.
[25] G.W. Wei, "Maximizing deviation method for multiple attribute decision
making in intuitionistic fuzzy setting", Knowledge-Based Systems,
vol.21, pp. 833-836, 2008.
[26] G.W. Wei, "Some induced geometric aggregation operators with
intuitionistic fuzzy information and their application to group decision
making", Applied Soft Computing, vol. 10, pp. 423-431, 2010.
[27] Z.S. Xu, "Intuitionistic fuzzy aggregation operators", IEEE Transactions
on Fuzzy Systems, vol. 15, pp. 1179-1187, 2007.
[28] J. Ye, "Fuzzy decision-making method based on the weighted correlation
coefficient under intuitionistic fuzzy environment", European Journal of
Operational Research, vol. 205, pp. 202-204, 2010.
[29] Z.S. Xu, and R.R. Yager, "Some geometric aggregation operators based
on intuitionistic fuzzy sets", International Journal of General Systems,
vol. 35,pp. 417-433, 2006.
[30] Y.J. Xu, and H.M. Wang, "The induced generalized aggregation
operators for intuitionistic fuzzy sets and their application in group
decision making", Applied Soft Computing, vol. 2012, pp. 1168-1179,
2012.
[31] S.Z. Zeng, and W.H. Su, "Intuitionistic fuzzy ordered weighted distance
operator" , Knowledge-Based Systems, vol. 24, pp. 1224-1232, 2011.
[32] S.Z. Zeng, "Some intuitionistic fuzzy weighted distance measures and
their application to group decision making", Group Decision and
Negotiation, in press. DOI:10.1007/s10726-011-9262-6.
@article{"International Journal of Business, Human and Social Sciences:49642", author = "Shouzhen Zeng", title = "The Intuitionistic Fuzzy Ordered Weighted Averaging-Weighted Average Operator and its Application in Financial Decision Making", abstract = "We present a new intuitionistic fuzzy aggregation
operator called the intuitionistic fuzzy ordered weighted
averaging-weighted average (IFOWAWA) operator. The main
advantage of the IFOWAWA operator is that it unifies the OWA
operator with the WA in the same formulation considering the degree
of importance that each concept has in the aggregation. Moreover, it is
able to deal with an uncertain environment that can be assessed with
intuitionistic fuzzy numbers. We study some of its main properties and
we see that it has a lot of particular cases such as the intuitionistic
fuzzy weighted average (IFWA) and the intuitionistic fuzzy OWA
(IFOWA) operator. Finally, we study the applicability of the new
approach on a financial decision making problem concerning the
selection of financial strategies.", keywords = "Intuitionistic fuzzy numbers, Weighted average,
OWA operator, Financial decision making", volume = "6", number = "8", pages = "1958-7", }
