Study on Interval Intuitionistic Fuzzy Multi-Attribute Group Decision Making Method based on Choquet Integral

In this paper, a method based on Choquet integral is proposed to solve the interval intuitionistic fuzzy multiple attribute group decision making problems. Firstly, some concepts about interval intuitionistic fuzzy measure are defined, through the strict mathematical reasoning to prove the measure we proposed satisfying the axiomatic system of fuzzy measure. Then, on the basis of fuzzy measure and game theory, we propose two models to determine fuzzy measure based on interval intuitionistic fuzzy entropy and weight information matrix. By calculating the Shapely value to determine expert weights, we establish a linear programming model based on relative entropy to determine the fuzzy measure of attribute weights to reflect the interactive characteristics among the criteria, using the Choquet integral to aggregate the decision-making information. Finally, we give the process of decision making in details.

[1]  Francisco Herrera,et al.  A Consensus Model for Group Decision Making With Incomplete Fuzzy Preference Relations , 2007, IEEE Transactions on Fuzzy Systems.

[2]  Christer Carlsson,et al.  Decision making with a fuzzy ontology , 2012, Soft Comput..

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

[4]  Umberto Straccia.  Multi Criteria Decision Making in Fuzzy Description Logics: A First Step , 2009, KES.

[5]  Jean-Luc Marichal,et al.  An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria , 2000, IEEE Trans. Fuzzy Syst..

[6]  Kwong-Sak Leung,et al.  Classification of Heterogeneous Fuzzy Data by Choquet Integral With Fuzzy-Valued Integrand , 2007, IEEE Transactions on Fuzzy Systems.

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

[9]  Francisco Herrera,et al.  Linguistic decision analysis: steps for solving decision problems under linguistic information , 2000, Fuzzy Sets Syst..

[10]  Gang Li,et al.  A fuzzy decision support method for customer preferences analysis based on Choquet Integral , 2012, 2012 IEEE International Conference on Fuzzy Systems.

[11]  Michel Grabisch,et al.  An Empirical Study of Statistical Properties of the Choquet and Sugeno Integrals , 2008, IEEE Transactions on Fuzzy Systems.

[12]  Francisco Chiclana,et al.  Intuitionistic fuzzy sets: Spherical representation and distances , 2009 .

[13]  Ronald R. Yager,et al.  A Linguistic Approach to Influencing Decision Behavior , 2012, IEEE Transactions on Fuzzy Systems.

[14]  Zeshui Xu,et al.  Choquet integrals of weighted intuitionistic fuzzy information , 2010, Inf. Sci..

[15]  Fernando Ortega.  Managing vagueness in ontologies , 2011 .

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

[17]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[18]  K. Atanassov.  More on intuitionistic fuzzy sets , 1989 .

[19]  Christer Carlsson,et al.  Consensus in distributed soft environments , 1992 .

[20]  Francisco Herrera,et al.  A Sequential Selection Process in Group Decision Making with a Linguistic Assessment Approach , 1995, Inf. Sci..

[21]  E. Herrera-Viedma,et al.  A new consensus model for group decision making using fuzzy ontology , 2013, Soft Comput..

[22]  Jalal Ashayeri,et al.  Supply chain partners and configuration selection: An intuitionistic fuzzy Choquet integral operator based approach , 2012, Expert Syst. Appl..

[23]  L. A. ZADEH,et al.  The concept of a linguistic variable and its application to approximate reasoning - I , 1975, Inf. Sci..

[24]  Francisco Chiclana,et al.  Consistency of 2D and 3D distances of intuitionistic fuzzy sets , 2012, Expert Syst. Appl..

[25]  Enrique Herrera-Viedma,et al.  Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks , 2010, Soft Comput..

[26]  Chunqiao Tan,et al.  A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS , 2011, Expert Syst. Appl..

[27]  M. Sugeno,et al.  An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy , 1989 .

[28]  Serena Doria,et al.  Characterization of a coherent upper conditional prevision as the Choquet integral with respect to its associated Hausdorff outer measure , 2012, Ann. Oper. Res..

[29]  Deng-Feng Li,et al.  Intuitionistic Fuzzy Aggregation Operators and Multiattribute Decision-Making Methods with Intuitionistic Fuzzy Sets , 2014 .

[30]  Salvatore Greco,et al.  The Choquet integral with respect to a level dependent capacity , 2011, Fuzzy Sets Syst..

[31]  Francisco Herrera,et al.  Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations , 1998, Fuzzy Sets Syst..

[32]  J. Kacprzyk,et al.  Multiperson decision making models using fuzzy sets and possibility theory , 1990 .

[33]  Francisco Herrera,et al.  A model of consensus in group decision making under linguistic assessments , 1996, Fuzzy Sets Syst..

[34]  P. Wakker,et al.  Nonmonotonic Choquet Integrals , 2001 .

[35]  M. Sugeno,et al.  A theory of fuzzy measures: Representations, the Choquet integral, and null sets , 1991 .

[36]  Enrique Herrera-Viedma,et al.  Consensual Processes , 2011, Studies in Fuzziness and Soft Computing.

[37]  Francisco Chiclana,et al.  Non-dominance and attitudinal prioritisation methods for intuitionistic and interval-valued intuitionistic fuzzy preference relations , 2012, Expert Syst. Appl..

[38]  G. Klir,et al.  Fuzzy Measure Theory , 1993 .

[39]  M. Sugeno,et al.  Some quantities represented by the Choquet integral , 1993 .

[40]  Cengiz Kahraman,et al.  Multi-criteria warehouse location selection using Choquet integral , 2010, Expert Syst. Appl..

[41]  Francisco Herrera,et al.  Direct approach processes in group decision making using linguistic OWA operators , 1996, Fuzzy Sets Syst..

[42]  Enrique Herrera-Viedma,et al.  A Mobile Decision Support System for Dynamic Group Decision-Making Problems , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[43]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[44]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[45]  Michele Fedrizzi,et al.  Modelling group processes and effort estimation in project management using the Choquet integral: An MCDM approach , 2012, Expert Syst. Appl..