Decisión making with induced aggregation operators and the adequacy coefficient

We present a method for decision making by using induced aggregation operators. This method is very useful for business decision making problems such as product management, investment selection and strategic management. We introduce a new aggregation operator that uses the induced ordered weighted averaging (IOWA) operator and the weighted average in the adequacy coefficient. We call it the induced ordered weighted averaging weighted averaging adequacy coefficient (IOWAWAAC) operator. The main advantage is that it is able to deal with complex attitudinal characters in the aggregation process. Thus, we are able to give a better representation of the problem considering the complex environment that affects the decisions. Moreover, it is able to provide a unified framework between the OWA and the weighted average. We generalize it by using generalized aggregation operators, obtaining the induced generalized OWAWAAC (IGOWAWAAC) operator. We study some of the main properties of this approach. We end the paper with a numerical example of the new approach in a group decision making problem in strategic management.

[1]  Huayou Chen,et al.  An approach to group decision making with interval fuzzy preference relations based on induced generalized continuous ordered weighted averaging operator , 2011, Expert Syst. Appl..

[2]  Anna Maria Gil Lafuente,et al.  OWA operators in human resource management , 2011 .

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

[4]  Ronald R. Yager,et al.  Induced aggregation operators , 2003, Fuzzy Sets Syst..

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

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

[7]  Weihua Su,et al.  Intuitionistic fuzzy ordered weighted distance operator , 2011, Knowl. Based Syst..

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

[9]  Huayou Chen,et al.  Generalized ordered weighted logarithm aggregation operators and their applications to group decision making , 2010, Int. J. Intell. Syst..

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

[11]  Mariano Eriz.  Aggregation Functions: A Guide for Practitioners , 2010 .

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

[13]  José M. Merigó,et al.  A unified model between the weighted average and the induced OWA operator , 2011, Expert Syst. Appl..

[14]  Zeshui Xu,et al.  Induced generalized intuitionistic fuzzy operators , 2011, Knowl. Based Syst..

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

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

[17]  J. Merigó,et al.  Induced and Linguistic Generalized Aggregation Operators and Their Application in Linguistic Group Decision Making , 2010, Group Decision and Negotiation.

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

[19]  Vicenç Torra,et al.  Modeling decisions - information fusion and aggregation operators , 2007 .

[20]  José M. Merigó,et al.  DECISION MAKING WITH DISTANCE MEASURES AND INDUCED AGGREGATION OPERATORS , 2008 .

[21]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

[22]  Yejun Xu,et al.  The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making , 2012, Appl. Soft Comput..

[23]  Z. S. Xu,et al.  An overview of operators for aggregating information , 2003, Int. J. Intell. Syst..

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

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

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

[27]  V. Torra.  The weighted OWA operator , 1997, International Journal of Intelligent Systems.

[28]  Ronald R. Yager,et al.  Norms Induced from OWA Operators , 2010, IEEE Transactions on Fuzzy Systems.

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

[30]  Dimitar Filev,et al.  Induced ordered weighted averaging operators , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[31]  Ronald R. Yager.  Choquet Aggregation Using Order Inducing Variables , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[33]  J. Kacprzyk,et al.  The Ordered Weighted Averaging Operators: Theory and Applications , 1997 .

[34]  Yejun Xu,et al.  Power Geometric Operators for Group Decision Making under Multiplicative Linguistic Preference Relations , 2012, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[35]  José M. Merigó,et al.  Computational Intelligence in Business and Economics: Proceedings of the Ms'10 International Conference , 2010 .

[36]  Zeshui Xu,et al.  Uncertain Power Average Operators for Aggregating Interval Fuzzy Preference Relations , 2012 .

[37]  E. Zavadskas,et al.  Multiple criteria decision making (MCDM) methods in economics: an overview , 2011 .

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

[39]  José M. Merigó,et al.  Fuzzy decision making with immediate probabilities , 2010, Comput. Ind. Eng..

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

[41]  José M. Merigó,et al.  The uncertain induced quasi‐arithmetic OWA operator , 2011, Int. J. Intell. Syst..

[42]  J. Merigó,et al.  Probabilistic aggregation operators and their application in uncertain multi-person decision-making , 2011 .

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

[44]  José M. Merigó,et al.  A method for decision making with the OWA operator , 2012, Comput. Sci. Inf. Syst..

[45]  JOSE M. MERIGO,et al.  DECISION MAKING WITH THE INDUCED GENERALIZED ADEQUACY COEFFICIENT , 2011 .

[46]  Guiwu Wei,et al.  Some Induced Aggregating Operators with Fuzzy Number Intuitionistic Fuzzy Information and their Applications to Group Decision Making , 2010, Int. J. Comput. Intell. Syst..

[47]  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..

[48]  Gui-Wu Wei,et al.  FIOWHM operator and its application to multiple attribute group decision making , 2011, Expert Syst. Appl..