Fuzzy Multi-Person Decision Making with Fuzzy Probabilistic Aggregation Operators

We present a fuzzy multi-person decision making model with fuzzy probabilistic information. For doing so, we present the fuzzy probabilistic ordered weighted averaging (FPOWA) operator. It is an aggregation operator that unifies the fuzzy probabilistic aggregation and the fuzzy OWA (FOWA) operator in the same formulation considering the degree of importance that each concept has in the analysis. We study its applicability and we see that it is very broad because all the previous studies that use the probability or the OWA operator can be revised and extended with this new approach. We focus on a multi-person decision making problem that unifies risk and uncertain environments in the same formulation. We implement this approach in a political management problem regarding the selection of fiscal policies.

[1]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[2]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[3]  Lotfi A. Zadeh,et al.  On Fuzzy Mapping and Control , 1996, IEEE Trans. Syst. Man Cybern..

[4]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[5]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

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

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

[8]  Dimitar Filev,et al.  On the concept of immediate probabilities , 1995, Int. J. Intell. Syst..

[9]  Ronald R. Yager,et al.  Constrained OWA aggregation , 1996, Fuzzy Sets Syst..

[10]  R. Yager,et al.  MODELLING DECISION MAKING USING IMMEDIATE PROBABILITIES , 1996 .

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

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

[13]  Ronald R. Yager,et al.  Including decision attitude in probabilistic decision making , 1999, Int. J. Approx. Reason..

[14]  Ronald R. Yager,et al.  Heavy OWA Operators , 2002, Fuzzy Optim. Decis. Mak..

[15]  Shyi-Ming Chen,et al.  A NEW METHOD FOR HANDLING MULTICRITERIA FUZZY DECISION-MAKING PROBLEMS USING FN-IOWA OPERATORS , 2003, Cybern. Syst..

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

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

[18]  Radko Mesiar,et al.  Weighted means and weighting functions , 2006, Kybernetika.

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

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

[21]  Ronald R. Yager,et al.  Weighted Maximum Entropy OWA Aggregation With Applications to Decision Making Under Risk , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[22]  Yin-Feng Xu,et al.  Linguistic multiperson decision making based on the use of multiple preference relations , 2009, Fuzzy Sets Syst..

[23]  Zeshui Xu Fuzzy harmonic mean operators , 2009 .

[24]  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..

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

[26]  Yin-Feng Xu,et al.  The OWA-based consensus operator under linguistic representation models using position indexes , 2010, Eur. J. Oper. Res..

[27]  Peide Liu,et al.  Method for Multiple Attribute Decision-making under Risk with Interval Numbers , 2010 .

[28]  Huayou Chen,et al.  A novel approach for question answering and automatic diagnosis based on pervasive agent ontology in medicine , 2010 .

[29]  José M. Merigó,et al.  Linguistic Aggregation Operators for Linguistic Decision Making Based on the Dempster-Shafer Theory of Evidence , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[31]  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..

[32]  Marek Reformat,et al.  Rule- and OWA-based Semantic Similarity for User Profiling , 2010 .

[33]  Guiwu Wei,et al.  Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making , 2010, Appl. Soft Comput..

[34]  Q. Da,et al.  Linear goal programming approach to obtaining the weights of intuitionistic fuzzy ordered weighted averaging operator , 2010 .

[35]  J. Merigó,et al.  Fuzzy Generalized Hybrid Aggregation Operators and its Application in Fuzzy Decision Making , 2010 .

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

[37]  Peide Liu,et al.  Method for aggregating triangular fuzzy intuitionistic fuzzy information and its application to decision making , 2010 .

[38]  J. Merigó,et al.  Induced and heavy aggregation operators with distance measures , 2010 .

[39]  Vicenç Torra,et al.  Some relationships between Losonczi’s based OWA generalizations and the Choquet–Stieltjes integral , 2010, Soft Comput..

[40]  José M. Merigó,et al.  THE FUZZY GENERALIZED OWA OPERATOR AND ITS APPLICATION IN STRATEGIC DECISION MAKING , 2010, Cybern. Syst..

[41]  Zeshui Xu A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making , 2010 .

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

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

[44]  J. Merigó The uncertain probabilistic weighted average and its application in the theory of expertons , 2011 .

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

[46]  Peide Liu,et al.  A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers , 2011, Expert Syst. Appl..

[47]  José M. Merigó,et al.  Induced and uncertain heavy OWA operators , 2011, Comput. Ind. Eng..

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

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

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

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