A Method under Uncertain Information for the Selection of Students in Interdisciplinary Studies
We present a method for the selection of students
in interdisciplinary studies based on the hybrid averaging
operator. We assume that the available information given in
the problem is uncertain so it is necessary to use interval
numbers. Therefore, we suggest a new type of hybrid
aggregation called uncertain induced generalized hybrid
averaging (UIGHA) operator. It is an aggregation operator
that considers the weighted average (WA) and the ordered
weighted averaging (OWA) operator in the same formulation.
Therefore, we are able to consider the degree of optimism of
the decision maker and grades of importance in the same
approach. By using interval numbers, we are able to represent
the information considering the best and worst possible results
so the decision maker gets a more complete view of the
decision problem. We develop an illustrative example of the
proposed scheme in the selection of students in
interdisciplinary studies. We see that with the use of the
UIGHA operator we get a more complete representation of the
selection problem. Then, the decision maker is able to
consider a wide range of alternatives depending on his
interests. We also show other potential applications that could
be used by using the UIGHA operator in educational problems
about selection of different types of resources such as
students, professors, etc.
[1] G. Beliakov, A. Pradera, and T. Calvo, Aggregation Functions: A guide
for practitioners, Springer-Verlag, Berlin, 2007.
[2] J.M. Merig├│, New Extensions to the OWA Operators and its application
in decision making, PhD Thesis (in Spanish), Dept. Business
Administration, Univ. Barcelona, Barcelona, Spain, 2008.
[3] J.M. Merig├│, and M. Casanovas, "Induced aggregation operators in
decision making with Dempster-Shafer belief structure", Int. J.
Intelligent Systems (to be published).
[4] J.M. Merig├│, M. Casanovas, "The induced generalized hybrid averaging
operator and its application in financial decision making", International Journal of Business, Economics, Finance and Management Sciences
(submitted for publication).
[5] J.M. Merig├│, M. Casanovas, "Uncertain decision making with
Dempster-Shafer theory", In Proceedings of the IPMU International
Conference, Torremolinos - Málaga, Spain, 2008, pp. 425-432.
[6] J.M. Merig├│, and A.M. Gil-Lafuente, "The induced generalized OWA
operator", Information Sciences, vol. 179, pp. 729-741, 2009.
[7] Z.S. Xu, "A Note on Linguistic Hybrid Arithmetic Averaging Operator
in Multiple Attribute Group Decision Making with Linguistic
Information", Group Decision and Negotiation, vol. 15, pp. 593-604,
2006.
[8] Z.S. Xu, "An approach based on the uncertain LOWG and induced
uncertain LOWG operators to group decision making with uncertain
multiplicative linguistic preference relations", Decision Support Systems,
vol. 41, pp. 488-499, 2006.
[9] R.R. Yager, and J. Kacprzyck, The Ordered Weighted Averaging
Operators: Theory and Applications, Kluwer Academic Publishers,
Norwell, MA, 1997.
[10] R.R. Yager, "On Ordered Weighted Averaging Aggregation Operators
in Multi-Criteria Decision Making", IEEE Trans. Systems, Man and
Cybernetics, vol. 18, pp. 183-190, 1988.
[11] Z.S. Xu, and Q.L. Da, "An Overview of Operators for Aggregating
Information", Int. J. Intelligent Systems, vol. 18, pp. 953-969, 2003.
[12] R.R. Yager, and D.P. Filev, "Induced ordered weighted averaging
operators", IEEE Trans. Syst. Man Cybern., vol. 29, pp. 141-150, 1999.
[13] Z.S. Xu, and Q.L. Da, "The Uncertain OWA Operator", Int. J. Intelligent
Systems, vol. 17, pp. 569-575, 2002.
[14] N. Karayiannis, "Soft Learning Vector Quantization and Clustering
Algorithms Based on Ordered Weighted Aggregation Operators", IEEE
Trans. Neural Networks, vol. 11, 1093-1105, 2000.
[15] R.R. Yager, "Generalized OWA Aggregation Operators", Fuzzy Opt.
Decision Making, vol. 3, pp.93-107, 2004.
[16] G. Beliakov, "Learning Weights in the Generalized OWA Operators",
Fuzzy Opt. Decision Making, vol. 4, pp. 119-130, 2005.
[17] T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New Trends
and applications, Physica-Verlag, New York, 2002.
[18] J. Fodor, J.L. Marichal, and M. Roubens, "Characterization of the
ordered weighted averaging operators", IEEE Trans. Fuzzy Systems, vol.
3, pp. 236-240, 1995.
[19] J.M. Merig├│, and M. Casanovas, "The fuzzy generalized OWA
operator", In Proceedings of the Conference SIGEF 2007, pp. 504-517,
Poiana-Brasov, Romania, 2007.
[20] J.M. Merig├│, M. Casanovas, "The uncertain generalized OWA operator
and its application in the selection of financial strategies", In
Proceedings of the International Conference AEDEM 2007, pp. 547-
556, Krakow, Poland, 2007.
[21] J.H. Wang, and J. Hao, "A new version of 2-tuple fuzzy linguistic
representation model for computing with words", IEEE Trans. Fuzzy
Systems, vol. 14, pp. 435-445, 2006.
[22] P.A. Schaefer, and H.B. Mitchell, "A generalized OWA operator", Int. J.
Intelligent Systems, vol. 14, pp. 123-143, 1999.
[23] Z.S. Xu, "A method based on linguistic aggregation operators for group
decision making with linguistic preference relations", Information
Sciences, vol. 166, pp. 19-30, 2004.
[24] R.R. Yager, "On generalized measures of realization in uncertain
environments", Theory and Decision, vol. 33, pp. 41-69, 1992.
[25] R.R. Yager, "Families of OWA operators", Fuzzy Sets and Systems, vol.
59, pp. 125-148, 1993.
[26] R.R. Yager, "Quantifier Guided Aggregation Using OWA operators",
Int. J. Intelligent Systems, vol. 11, pp. 49-73, 1996.
[27] R.R. Yager, E-Z OWA weights, In Proceedings of the 10th International
Fuzzy Systems Association (IFSA) World Congress, Istanbul, Turkey, pp.
39-42, 2003.
[28] R.R. Yager, "Induced aggregation operators", Fuzzy Sets and Systems,
vol. 137, pp. 59-69, 2003.
[29] R.R. Yager, "Centered OWA operators", Soft Computing, vol. 11, pp.
631-639, 2007.
[30] R.R. Yager, and D.P. Filev, "Parameterized "andlike" and "orlike"
OWA operators", Int. J. General Systems, vol. 22, pp. 297-316, 1994.
[31] R. Moore, Interval analysis, Prentice-Hall, Englewood Cliffs, NJ, 1966.
[1] G. Beliakov, A. Pradera, and T. Calvo, Aggregation Functions: A guide
for practitioners, Springer-Verlag, Berlin, 2007.
[2] J.M. Merig├│, New Extensions to the OWA Operators and its application
in decision making, PhD Thesis (in Spanish), Dept. Business
Administration, Univ. Barcelona, Barcelona, Spain, 2008.
[3] J.M. Merig├│, and M. Casanovas, "Induced aggregation operators in
decision making with Dempster-Shafer belief structure", Int. J.
Intelligent Systems (to be published).
[4] J.M. Merig├│, M. Casanovas, "The induced generalized hybrid averaging
operator and its application in financial decision making", International Journal of Business, Economics, Finance and Management Sciences
(submitted for publication).
[5] J.M. Merig├│, M. Casanovas, "Uncertain decision making with
Dempster-Shafer theory", In Proceedings of the IPMU International
Conference, Torremolinos - Málaga, Spain, 2008, pp. 425-432.
[6] J.M. Merig├│, and A.M. Gil-Lafuente, "The induced generalized OWA
operator", Information Sciences, vol. 179, pp. 729-741, 2009.
[7] Z.S. Xu, "A Note on Linguistic Hybrid Arithmetic Averaging Operator
in Multiple Attribute Group Decision Making with Linguistic
Information", Group Decision and Negotiation, vol. 15, pp. 593-604,
2006.
[8] Z.S. Xu, "An approach based on the uncertain LOWG and induced
uncertain LOWG operators to group decision making with uncertain
multiplicative linguistic preference relations", Decision Support Systems,
vol. 41, pp. 488-499, 2006.
[9] R.R. Yager, and J. Kacprzyck, The Ordered Weighted Averaging
Operators: Theory and Applications, Kluwer Academic Publishers,
Norwell, MA, 1997.
[10] R.R. Yager, "On Ordered Weighted Averaging Aggregation Operators
in Multi-Criteria Decision Making", IEEE Trans. Systems, Man and
Cybernetics, vol. 18, pp. 183-190, 1988.
[11] Z.S. Xu, and Q.L. Da, "An Overview of Operators for Aggregating
Information", Int. J. Intelligent Systems, vol. 18, pp. 953-969, 2003.
[12] R.R. Yager, and D.P. Filev, "Induced ordered weighted averaging
operators", IEEE Trans. Syst. Man Cybern., vol. 29, pp. 141-150, 1999.
[13] Z.S. Xu, and Q.L. Da, "The Uncertain OWA Operator", Int. J. Intelligent
Systems, vol. 17, pp. 569-575, 2002.
[14] N. Karayiannis, "Soft Learning Vector Quantization and Clustering
Algorithms Based on Ordered Weighted Aggregation Operators", IEEE
Trans. Neural Networks, vol. 11, 1093-1105, 2000.
[15] R.R. Yager, "Generalized OWA Aggregation Operators", Fuzzy Opt.
Decision Making, vol. 3, pp.93-107, 2004.
[16] G. Beliakov, "Learning Weights in the Generalized OWA Operators",
Fuzzy Opt. Decision Making, vol. 4, pp. 119-130, 2005.
[17] T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New Trends
and applications, Physica-Verlag, New York, 2002.
[18] J. Fodor, J.L. Marichal, and M. Roubens, "Characterization of the
ordered weighted averaging operators", IEEE Trans. Fuzzy Systems, vol.
3, pp. 236-240, 1995.
[19] J.M. Merig├│, and M. Casanovas, "The fuzzy generalized OWA
operator", In Proceedings of the Conference SIGEF 2007, pp. 504-517,
Poiana-Brasov, Romania, 2007.
[20] J.M. Merig├│, M. Casanovas, "The uncertain generalized OWA operator
and its application in the selection of financial strategies", In
Proceedings of the International Conference AEDEM 2007, pp. 547-
556, Krakow, Poland, 2007.
[21] J.H. Wang, and J. Hao, "A new version of 2-tuple fuzzy linguistic
representation model for computing with words", IEEE Trans. Fuzzy
Systems, vol. 14, pp. 435-445, 2006.
[22] P.A. Schaefer, and H.B. Mitchell, "A generalized OWA operator", Int. J.
Intelligent Systems, vol. 14, pp. 123-143, 1999.
[23] Z.S. Xu, "A method based on linguistic aggregation operators for group
decision making with linguistic preference relations", Information
Sciences, vol. 166, pp. 19-30, 2004.
[24] R.R. Yager, "On generalized measures of realization in uncertain
environments", Theory and Decision, vol. 33, pp. 41-69, 1992.
[25] R.R. Yager, "Families of OWA operators", Fuzzy Sets and Systems, vol.
59, pp. 125-148, 1993.
[26] R.R. Yager, "Quantifier Guided Aggregation Using OWA operators",
Int. J. Intelligent Systems, vol. 11, pp. 49-73, 1996.
[27] R.R. Yager, E-Z OWA weights, In Proceedings of the 10th International
Fuzzy Systems Association (IFSA) World Congress, Istanbul, Turkey, pp.
39-42, 2003.
[28] R.R. Yager, "Induced aggregation operators", Fuzzy Sets and Systems,
vol. 137, pp. 59-69, 2003.
[29] R.R. Yager, "Centered OWA operators", Soft Computing, vol. 11, pp.
631-639, 2007.
[30] R.R. Yager, and D.P. Filev, "Parameterized "andlike" and "orlike"
OWA operators", Int. J. General Systems, vol. 22, pp. 297-316, 1994.
[31] R. Moore, Interval analysis, Prentice-Hall, Englewood Cliffs, NJ, 1966.
@article{"International Journal of Business, Human and Social Sciences:64143", author = "José M. Merigó and Pilar López-Jurado and M.Carmen Gracia and Montserrat Casanovas", title = "A Method under Uncertain Information for the Selection of Students in Interdisciplinary Studies", abstract = "We present a method for the selection of students
in interdisciplinary studies based on the hybrid averaging
operator. We assume that the available information given in
the problem is uncertain so it is necessary to use interval
numbers. Therefore, we suggest a new type of hybrid
aggregation called uncertain induced generalized hybrid
averaging (UIGHA) operator. It is an aggregation operator
that considers the weighted average (WA) and the ordered
weighted averaging (OWA) operator in the same formulation.
Therefore, we are able to consider the degree of optimism of
the decision maker and grades of importance in the same
approach. By using interval numbers, we are able to represent
the information considering the best and worst possible results
so the decision maker gets a more complete view of the
decision problem. We develop an illustrative example of the
proposed scheme in the selection of students in
interdisciplinary studies. We see that with the use of the
UIGHA operator we get a more complete representation of the
selection problem. Then, the decision maker is able to
consider a wide range of alternatives depending on his
interests. We also show other potential applications that could
be used by using the UIGHA operator in educational problems
about selection of different types of resources such as
students, professors, etc.", keywords = "Decision making, Selection of students,
Uncertainty, Aggregation operators.", volume = "3", number = "7", pages = "1660-8", }
