A Method for Decision Making Based on Generalized Aggregation Operators

A new method for decision making based on generalized aggregation operators is presented. We use a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index uses distance measures and other techniques that are very useful for decision making. In this paper, it is suggested a generalization by using generalized and quasi‐arithmetic means. As a result, it is obtained the generalized and quasi‐arithmetic weighted IMAM (GWIMAM and quasi‐WIMAM) and the generalized ordered weighted averaging IMAM (GOWAIMAM) and the quasi‐OWAIMAM operator. The main advantage is that it provides a parameterized family of aggregation operators that includes a wide range of special cases such as the generalized IMAM and the OWAIMAM. Thus, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. We also develop an application of the new approach in a decision‐making problem regarding product selection.

[1]  Ronald R. Yager,et al.  On the dispersion measure of OWA operators , 2009, Inf. Sci..

[2]  Chunqiao Tan,et al.  Induced choquet ordered averaging operator and its application to group decision making , 2010 .

[3]  J. Merigó,et al.  Induced aggregation operators in decision making with the Dempster-Shafer belief structure , 2009 .

[4]  Mitio Nagumo.  Über eine Klasse der Mittelwerte , 1930 .

[5]  Francisco Herrera,et al.  Group decision making with incomplete fuzzy linguistic preference relations , 2009, Int. J. Intell. Syst..

[6]  Jaime Gil-Aluja,et al.  The Interactive Management of Human Resources in Uncertainty , 1997 .

[7]  A. M. G. Lafuente,et al.  Decision making techniques in business and economics based on the OWA operator , 2012 .

[8]  Zeshui Xu,et al.  Ordered weighted distance measure , 2008 .

[9]  Xiaohong Chen,et al.  Induced choquet ordered averaging operator and its application to group decision making , 2010, Int. J. Intell. Syst..

[10]  José M. Merigó,et al.  Decision-making with distance measures and induced aggregation operators , 2011, Comput. Ind. Eng..

[11]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[12]  Zeshui Xu,et al.  Fuzzy harmonic mean operators , 2009, Int. J. Intell. Syst..

[13]  Vicente Liern,et al.  Soft computing-based aggregation methods for human resource management , 2008, Eur. J. Oper. Res..

[14]  Ronald R. Yager,et al.  Prioritized OWA aggregation , 2009, Fuzzy Optim. Decis. Mak..

[15]  A. Bonaert.  Introduction to the theory of Fuzzy subsets , 1977, Proceedings of the IEEE.

[16]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[17]  Gui-Wu Wei,et al.  Uncertain Linguistic Hybrid Geometric Mean Operator and its Application to Group Decision Making under Uncertain Linguistic Environment , 2009, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[18]  Ping-Tao Yi,et al.  Cluster‐reliability‐induced OWA operators , 2012, Int. J. Intell. Syst..

[19]  J. Kacprzyk,et al.  Towards a general and unified characterization of individual and collective choice functions under fuzzy and nonfuzzy preferences and majority via the ordered weighted average operators , 2009 .

[20]  José M. Merigó,et al.  Fuzzy induced generalized aggregation operators and its application in multi-person decision making , 2011, Expert Syst. Appl..

[21]  Ronald R. Yager,et al.  Centered OWA Operators , 2007, Soft Comput..

[22]  José M. Merigó,et al.  A New Minkowski Distance Based on Induced Aggregation Operators , 2011, Int. J. Comput. Intell. Syst..

[23]  J. Merigó,et al.  The Induced Generalized OWA Operator , 2009, EUSFLAT Conf..

[24]  A. M. Gil-Lafuente.  Fuzzy Logic in Financial Analysis , 2005 .

[25]  J. Gil-Aluja.  Elements for a Theory of Decision in Uncertainty , 2010 .

[26]  János C. Fodor,et al.  Characterization of the ordered weighted averaging operators , 1995, IEEE Trans. Fuzzy Syst..

[27]  Jaime Gil-Aluja.  Handbook of Management under Uncertainty , 2011 .

[28]  José M. Merigó,et al.  Induced aggregation operators in the Euclidean distance and its application in financial decision making , 2011, Expert Syst. Appl..

[29]  Gleb Beliakov,et al.  Aggregation Functions: A Guide for Practitioners , 2007, Studies in Fuzziness and Soft Computing.

[30]  R. Yager.  Families of OWA operators , 1993 .

[31]  Ronald R. Yager,et al.  Generalized OWA Aggregation Operators , 2004, Fuzzy Optim. Decis. Mak..

[32]  Janusz Kacprzyk,et al.  Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice , 2011, Studies in Fuzziness and Soft Computing.

[33]  Zeshui Xu,et al.  Generalized aggregation operators for intuitionistic fuzzy sets , 2010 .

[34]  Zeshui Xu,et al.  Dynamic intuitionistic fuzzy multi-attribute decision making , 2008, Int. J. Approx. Reason..

[35]  Slawomir Zadrozny,et al.  Towards a general and unified characterization of individual and collective choice functions under fuzzy and nonfuzzy preferences and majority via the ordered weighted average operators , 2009, Int. J. Intell. Syst..

[36]  Hui Li,et al.  The induced continuous ordered weighted geometric operators and their application in group decision making , 2009, Comput. Ind. Eng..

[37]  Byeong Seok Ahn.  Some remarks on the LSOWA approach for obtaining OWA operator weights , 2009, Int. J. Intell. Syst..

[38]  J. Merigó,et al.  The generalized adequacy coefficient and its application in strategic decision making , 2008 .

[39]  José M. Merigó,et al.  New decision-making techniques and their application in the selection of financial products , 2010, Inf. Sci..

[40]  José M. Merigó,et al.  Induced aggregation operators in decision making with the Dempster‐Shafer belief structure , 2009, Int. J. Intell. Syst..

[41]  A. M. G. Lafuente,et al.  Unification Point In Methods For The Selection Of Financial Products , 2007 .

[42]  Nicolaos B. Karayiannis,et al.  Soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators , 2000, IEEE Trans. Neural Networks Learn. Syst..

[43]  Ching-Hsue Cheng,et al.  OWA-weighted based clustering method for classification problem , 2009, Expert Syst. Appl..

[44]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decision-making , 1988 .