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Decision Making Using Maximization Of Negret

Authors: José M. Merigó; Montserrat Casanovas;

Decision Making Using Maximization Of Negret

Abstract

{"references": ["R.R. Yager, \"On Ordered Weighted Averaging Aggregation Operators\nin Multi-Criteria Decision Making\", IEEE Trans. Systems, Man and\nCybernetics, vol. 18, pp. 183-190, 1988.", "F. Chiclana, F. Herrera, and E. Herrera-Viedma, \"The ordered weighted\ngeometric operator: Properties and application\", in Proc. 8th Conf.\nInform. Processing and Management of Uncertainty in Knowledgebased\nSystems (IPMU), Madrid, Spain, 2000, pp. 985-991.", "T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New\nTrends and applications, Physica-Verlag, New York, 2002.", "C.H. Cheng, and J.R. Chang, \"MCDM aggregation model using\nsituational ME-OWA and ME-OWGA operators\", Int. J. Uncertainty,\nFuzziness and Knowledge-Based Systems, vol. 14, pp. 421-443, 2006.", "F. Chiclana, F. Herrera, E. Herrera-Viedma, \"Integrating multiplicative\npreference relations in a multipurpose decision-making model based on\nfuzzy preference relations\", Fuzzy Sets and Systems, vol. 122, pp. 277-\n291, 2001.", "F. Chiclana, F. Herrera, E. Herrera-Viedma, \"Multiperson Decision\nMaking Based on Multiplicative Preference Relations\", European J.\nOperational Research, vol. 129, pp. 372-385, 2001.", "F. Chiclana, F. Herrera, E. Herrera-Viedma, and S. Alonso, \"Induced\nordered weighted geometric operators and their use in the aggregation of\nmultiplicative preference relations\", Int. J. Intelligent Systems, vol. 19,\npp. 233-255, 2004.", "F. Herrera, E. Herrera-Viedma, and F. Chiclana, \"A study of the origin\nand uses of the ordered weighted geometric operator in multicriteria\ndecision making\", Int. J. Intelligent Systems, vol. 18, pp. 689-707,\n2003.", "J.M. Merig\u251c\u2502, New Extensions to the OWA Operators and its application\nin business decision making, Thesis (in Spanish), Dept. Business\nAdministration, Univ. Barcelona, Barcelona, Spain, 2007.\n[10] J.M. Merig\u251c\u2502, and M. Casanovas, \"Geometric Operators in Decision\nMaking with Minimization of Regret\", Int. J. Computer Systems\nScience and Engineering, submitted for publication.\n[11] Z.S. Xu, \"An Overview of Methods for Determining OWA Weights\",\nInt. J. Intelligent Systems, vol. 20, pp. 843-865, 2005.\n[12] Z.S. Xu, \"An approach based on the uncertain LOWG and induced\nuncertain LOWG operators to group decision making with uncertain\nmultiplicative linguistic preference relations\", Decision Support\nSystems, vol. 41, pp. 488-499, 2006.\n[13] Z.S. Xu, and Q.L. Da, \"The Ordered Weighted Geometric Averaging\nOperators\", Int. J. Intelligent Systems, vol. 17, pp. 709-716, 2002.\n[14] R.R. Yager, \"On generalized measures of realization in uncertain\nenvironments\", Theory and Decision, vol. 33, pp. 41-69, 1992.\n[15] R.R. Yager, Families of OWA operators, Fuzzy Sets and Systems, vol.\n59, pp. 125-148, 1993.\n[16] R.R. Yager, \"On weighted median aggregation\", Int. J. Uncertainty\nFuzziness Knowledge-Based Systems, vol. 2, pp. 101-113, 1994.\n[17] R.R. Yager, and D.P. Filev, \"Parameterized \"andlike\" and \"orlike\"\nOWA operators\", Int. J. General Systems, vol. 22, pp. 297-316, 1994.\n[18] R.R. Yager, \"Quantifier Guided Aggregation Using OWA operators\",\nInt. J. Intelligent Systems, vol. 11, pp. 49-73, 1996.\n[19] R.R. Yager, \"E-Z OWA weights\", in: Proc. 10th IFSA World Congress,\nIstanbul, Turkey, 2003, pp. 39-42.\n[20] R.R. Yager, \"Decision making using minimization of regret\", Int. J.\nApproximate Reasoning, vol. 36, pp. 109-128, 2004.\n[21] R.R. Yager, \"Centered OWA operators\", Soft Computing, vol. 11, pp.\n631-639, 2007.\n[22] R.R. Yager, and J. Kacprzyck, The Ordered Weighted Averaging\nOperators: Theory and Applications, Kluwer Academic Publishers,\nNorwell, MA, 1997.\n[23] R.R. Yager, and Z.S. Xu, \"The continuous ordered weighted geometric\noperator and its application to decision making\", Fuzzy Sets and\nSystems, vol. 157, pp. 1393-1402, 2006.\n[24] Z.S. Xu, and R.R. Yager, \"Some geometric aggregation operators based\non intuitionistic fuzzy sets\", Int. J. General Systems, vol. 35, pp. 417-\n433, 2006.\n[25] L.J. Savage, \"The theory of statistical decision\", J. American Statistical\nAssociation, vol. 46, pp. 55-67, 1951.\n[26] L.J. Savage, The foundations of statistics, John Wiley & Sons, New\nYork, 1954.\n[27] T.L. Saaty, The Analytic Hierarchy Process, McGraw-Hill, New York,\n1980.\n[28] J. Azcel, and T.L. Saaty, \"Procedures for synthesizing ratio\njudgements\", J. Mathematical Psychology, vol. 27, pp. 93-102, 1983.\n[29] J. Azcel, and C. Alsina, \"Synthesizing judgements: A functional\nequations approach\", Mathematical Modelling, vol. 9, pp. 311-320,\n1987."]}

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.

Keywords

OWG operator., Decision Making, Negret, Aggregation operators, OWA operator

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