**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31100

##### Geometric Operators in Decision Making with Minimization of Regret

**Authors:**
José M. Merigó,
Montserrat Casanovas

**Abstract:**

**Keywords:**
Decision Making,
OWA operator,
regret,
Aggregation operators,
OWG operator

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1077985

**References:**

[1] F. Chiclana, F. Herrera, and E. Herrera-Viedma, "The ordered weighted geometric operator: Properties and application", in Proc. 8th Conf. Inform. Processing and Management of Uncertainty in Knowledgebased Systems (IPMU), Madrid, Spain, 2000, pp. 985-991.

[2] 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.

[3] T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New Trends and applications, Physica-Verlag, New York, 2002.

[4] J.M. Merig├│, New Extensions to the OWA Operators and its application in business decision making, Thesis (in Spanish), Dept. Business Administration, Univ. Barcelona, Barcelona, Spain, 2007.

[5] V. Torra, Information Fusion in Data Mining, Springer, New York, 2002.

[6] Z.S. Xu, "An Overview of Methods for Determining OWA Weights", Int. J. Intelligent Systems, vol. 20, pp. 843-865, 2005.

[7] Z.S. Xu, and Q.L. Da, "An Overview of Operators for Aggregating Information", Int. J. Intelligent Systems, vol. 18, pp. 953-969, 2003.

[8] R.R. Yager, "On generalized measures of realization in uncertain environments", Theory and Decision, vol. 33, pp. 41-69, 1992.

[9] R.R. Yager, Families of OWA operators, Fuzzy Sets and Systems, vol. 59, pp. 125-148, 1993.

[10] R.R. Yager, "On weighted median aggregation", Int. J. Uncertainty Fuzziness Knowledge-Based Systems, vol. 2, pp. 101-113, 1994.

[11] R.R. Yager, and D.P. Filev, "Parameterized "andlike" and "orlike" OWA operators", Int. J. General Systems, vol. 22, pp. 297-316, 1994.

[12] R.R. Yager, "Constrained OWA Aggregation", Fuzzy Sets and Systems, vol. 81, pp. 89-101, 1996.

[13] R.R. Yager, "Quantifier Guided Aggregation Using OWA operators", Int. J. Intelligent Systems, vol. 11, pp. 49-73, 1996.

[14] R.R. Yager, "E-Z OWA weights", in: Proc. 10th IFSA World Congress, Istanbul, Turkey, 2003, pp. 39-42.

[15] R.R. Yager, "Decision making using minimization of regret", Int. J. Approximate Reasoning, vol. 36, pp. 109-128, 2004.

[16] R.R. Yager, "Generalized OWA Aggregation Operators", Fuzzy Opt. Decision Making, vol. 3, pp.93-107, 2004.

[17] R.R. Yager, "Centered OWA operators", Soft Computing, vol. 11, pp. 631-639, 2007.

[18] R.R. Yager, and J. Kacprzyck, The Ordered Weighted Averaging Operators: Theory and Applications, Kluwer Academic Publishers, Norwell, MA, 1997.

[19] C.H. Cheng, and J.R. Chang, "MCDM aggregation model using situational ME-OWA and ME-OWGA operators", Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 14, pp. 421-443, 2006.

[20] F. Chiclana, F. Herrera, E. Herrera-Viedma, "Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations", Fuzzy Sets and Systems, vol. 122, pp. 277- 291, 2001.

[21] F. Chiclana, F. Herrera, E. Herrera-Viedma, "Multiperson Decision Making Based on Multiplicative Preference Relations", European J. Operational Research, vol. 129, pp. 372-385, 2001.

[22] F. Chiclana, F. Herrera, E. Herrera-Viedma, and S. Alonso, "Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations", Int. J. Intelligent Systems, vol. 19, pp. 233-255, 2004.

[23] F. Herrera, E. Herrera-Viedma, and F. Chiclana, "A study of the origin and uses of the ordered weighted geometric operator in multicriteria decision making", Int. J. Intelligent Systems, vol. 18, pp. 689-707, 2003.

[24] J.I. Pel├íez, J.M. Do├▒a and A. Mesas, "Majority Multiplicative Ordered Weighted Geometric Operators and Their Use in the Aggregation of Multiplicative Preference Relations", Mathware & Soft Computing, vol. 12, pp. 107-120, 2005.

[25] Z.S. Xu, "EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations", Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 12, pp. 791-810, 2004.

[26] 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.

[27] Z.S. Xu, and Q.L. Da, "The Ordered Weighted Geometric Averaging Operators", Int. J. Intelligent Systems, vol. 17, pp. 709-716, 2002.

[28] Z.S. Xu, and R.R. Yager, "Some geometric aggregation operators based on intuitionistic fuzzy sets", Int. J. General Systems, vol. 35, pp. 417- 433, 2006.

[29] R.R. Yager, and Z.S. Xu, "The continuous ordered weighted geometric operator and its application to decision making", Fuzzy Sets and Systems, vol. 157, pp. 1393-1402, 2006.

[30] L.J. Savage, "The theory of statistical decision", J. American Statistical Association, vol. 46, pp. 55-67, 1951.

[31] L.J. Savage, The foundations of statistics, John Wiley & Sons, New York, 1954.

[32] J. Azcel, and T.L. Saaty, "Procedures for synthesizing ratio judgements", J. Mathematical Psychology, vol. 27, pp. 93-102, 1983.

[33] J. Azcel, and C. Alsina, "Synthesizing judgements: A functional equations approach", Mathematical Modelling, vol. 9, pp. 311-320, 1987.