World Academy of Science, Engineering and Technology
Published June 24, 2008 | Version 11348
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Decision Making using Maximization of Negret

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We analyze the problem of decision making under ignorance with regrets. Recently, Yager has developed a new method for decision making where instead of using regrets he uses another type of transformation called negrets. Basically, the negret is considered as the dual of the regret. We study this problem in detail and we suggest the use of geometric aggregation operators in this method. For doing this, we develop a different method for constructing the negret matrix where all the values are positive. The main result obtained is that now the model is able to deal with negative numbers because of the transformation done in the negret matrix. We further extent these results to another model developed also by Yager about mixing valuations and negrets. Unfortunately, in this case we are not able to deal with negative numbers because the valuations can be either positive or negative.

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References

  • 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.
  • 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.
  • T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New Trends and applications, Physica-Verlag, New York, 2002.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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. [10] J.M. Merig├│, and M. Casanovas, "Geometric Operators in Decision Making with Minimization of Regret", Int. J. Computer Systems Science and Engineering, submitted for publication. [11] Z.S. Xu, "An Overview of Methods for Determining OWA Weights", Int. J. Intelligent Systems, vol. 20, pp. 843-865, 2005. [12] 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. [13] Z.S. Xu, and Q.L. Da, "The Ordered Weighted Geometric Averaging Operators", Int. J. Intelligent Systems, vol. 17, pp. 709-716, 2002. [14] R.R. Yager, "On generalized measures of realization in uncertain environments", Theory and Decision, vol. 33, pp. 41-69, 1992. [15] R.R. Yager, Families of OWA operators, Fuzzy Sets and Systems, vol. 59, pp. 125-148, 1993. [16] R.R. Yager, "On weighted median aggregation", Int. J. Uncertainty Fuzziness Knowledge-Based Systems, vol. 2, pp. 101-113, 1994. [17] R.R. Yager, and D.P. Filev, "Parameterized "andlike" and "orlike" OWA operators", Int. J. General Systems, vol. 22, pp. 297-316, 1994. [18] R.R. Yager, "Quantifier Guided Aggregation Using OWA operators", Int. J. Intelligent Systems, vol. 11, pp. 49-73, 1996. [19] R.R. Yager, "E-Z OWA weights", in: Proc. 10th IFSA World Congress, Istanbul, Turkey, 2003, pp. 39-42. [20] R.R. Yager, "Decision making using minimization of regret", Int. J. Approximate Reasoning, vol. 36, pp. 109-128, 2004. [21] R.R. Yager, "Centered OWA operators", Soft Computing, vol. 11, pp. 631-639, 2007. [22] R.R. Yager, and J. Kacprzyck, The Ordered Weighted Averaging Operators: Theory and Applications, Kluwer Academic Publishers, Norwell, MA, 1997. [23] 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. [24] 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. [25] L.J. Savage, "The theory of statistical decision", J. American Statistical Association, vol. 46, pp. 55-67, 1951. [26] L.J. Savage, The foundations of statistics, John Wiley & Sons, New York, 1954. [27] T.L. Saaty, The Analytic Hierarchy Process, McGraw-Hill, New York, 1980. [28] J. Azcel, and T.L. Saaty, "Procedures for synthesizing ratio judgements", J. Mathematical Psychology, vol. 27, pp. 93-102, 1983. [29] J. Azcel, and C. Alsina, "Synthesizing judgements: A functional equations approach", Mathematical Modelling, vol. 9, pp. 311-320, 1987.