TOPSIS and Choquet integral hybrid technique for solving MAGDM problems with interval type-2 fuzzy numbers

There are two very usful methods for solving MAGDM problems, called TOPSIS method and Choquet integral method. Because of the ability of Choquet integral method in managing of interaction criteria, we combined it with TOPSIS method to use from their benefits. First, we will introduce a new method for computing the distance between IT2FNs. Then, we proposed a hybrid method based on TOPSIS and Choquet integral in fuzzy type-2 environment. Numerical examples are considered to illustrate the proposed methods.

[1]  Ming Wang,et al.  Uncertainty degree and modeling of interval type-2 fuzzy sets: Definition, method and application , 2013, Comput. Math. Appl..

[2]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[3]  Lucien Duckstein,et al.  Comparison of fuzzy numbers using a fuzzy distance measure , 2002, Fuzzy Sets Syst..

[4]  Jerry M. Mendel,et al.  Interval Type-2 Fuzzy Logic Systems Made Simple , 2006, IEEE Transactions on Fuzzy Systems.

[5]  Robert Ivor John,et al.  A novel alpha-cut representation for type-2 fuzzy sets , 2010, International Conference on Fuzzy Systems.

[6]  Chen-Tung Chen,et al.  Extensions of the TOPSIS for group decision-making under fuzzy environment , 2000, Fuzzy Sets Syst..

[7]  Jerry M. Mendel,et al.  Type-2 fuzzy sets made simple , 2002, IEEE Trans. Fuzzy Syst..

[8]  Debjani Chakraborty,et al.  A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers , 2010, Int. J. Math. Math. Sci..

[9]  Debjani Chakraborty,et al.  A new approach to fuzzy distance measure and similarity measure between two generalized fuzzy numbers , 2010, Appl. Soft Comput..

[10]  Diyar Akay,et al.  A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method , 2009, Expert Syst. Appl..

[11]  Shyi-Ming Chen,et al.  Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method , 2010, Expert Syst. Appl..

[12]  Shyi-Ming Chen,et al.  Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets , 2012, Expert Syst. Appl..

[13]  Jerry M. Mendel,et al.  Centroid of a type-2 fuzzy set , 2001, Inf. Sci..

[14]  Janusz Kacprzyk,et al.  Distances between intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[15]  Ching-Lai Hwang,et al.  Multiple Attribute Decision Making: Methods and Applications - A State-of-the-Art Survey , 1981, Lecture Notes in Economics and Mathematical Systems.

[16]  William Voxman,et al.  Some remarks on distances between fuzzy numbers , 1998, Fuzzy Sets Syst..

[17]  Shie-Jue Lee,et al.  A Fast Method for Computing the Centroid of a Type-2 Fuzzy Set , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  Humberto Bustince,et al.  DISCRETE INTERVAL-VALUED CHOQUET INTEGRALS , 2011 .

[19]  Zdenko Takác.  On Some Properties of alpha-planes of Type-2 Fuzzy Sets , 2013, Kybernetika.

[20]  Jerry M. Mendel,et al.  $\alpha$-Plane Representation for Type-2 Fuzzy Sets: Theory and Applications , 2009, IEEE Transactions on Fuzzy Systems.

[21]  Jerry M. Mendel,et al.  Advances in Type-2 Fuzzy Sets and Systems - Theory and Applications , 2013, Studies in Fuzziness and Soft Computing.

[22]  Masatoshi Sakawa,et al.  Fuzzy Sets and Interactive Multiobjective Optimization , 1993 .

[23]  Xinwang Liu,et al.  A distance based ranking methods for type-1 fuzzy numbers and interval type-2 fuzzy numbers , 2014, 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[24]  Zdenko Takác,et al.  Intersection and union of type-2 fuzzy sets and connection to (1, 2)-double cuts , 2011, EUSFLAT Conf..

[25]  Guo-Shun Huang,et al.  Some new distances between intuitionistic fuzzy sets , 2005, 2005 International Conference on Machine Learning and Cybernetics.

[26]  Shyi-Ming Chen,et al.  Fuzzy Multiple Attributes Group Decision-Making Based on Ranking Interval Type-2 Fuzzy Sets and the TOPSIS Method , 2014, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[27]  Jerry M. Mendel,et al.  Uncertainty measures for interval type-2 fuzzy sets , 2007, Inf. Sci..

[28]  Przemyslaw Grzegorzewski,et al.  Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric , 2004, Fuzzy Sets Syst..

[29]  Weiqiong Wang,et al.  Distance measure between intuitionistic fuzzy sets , 2005, Pattern Recognit. Lett..

[30]  Jerry M. Mendel,et al.  A Vector Similarity Measure for Interval Type-2 Fuzzy Sets , 2007, 2007 IEEE International Fuzzy Systems Conference.

[31]  H. M. Nehi,et al.  A complex method based on TOPSIS and Choquet integral to solve multi attribute group decision making problems with interval type-2 fuzzy numbers , 2015, 2015 4th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS).

[32]  Jerry M. Mendel,et al.  Uncertainty measures for general type-2 fuzzy sets , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[33]  Miin-Shen Yang,et al.  Similarity measures of intuitionistic fuzzy sets based on Lp metric , 2007, Int. J. Approx. Reason..

[34]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[35]  Ching-Hsue Cheng,et al.  A new approach for ranking fuzzy numbers by distance method , 1998, Fuzzy Sets Syst..

[36]  Ahmad Makui,et al.  Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets , 2009, Appl. Soft Comput..

[37]  Jerry M. Mendel,et al.  Cardinality, Fuzziness, Variance and Skewness of Interval Type-2 Fuzzy Sets , 2007, 2007 IEEE Symposium on Foundations of Computational Intelligence.

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

[39]  Debjani Chakraborty,et al.  A theoretical development on a fuzzy distance measure for fuzzy numbers , 2006, Math. Comput. Model..

[40]  Jerry M. Mendel,et al.  New results about the centroid of an interval type-2 fuzzy set, including the centroid of a fuzzy granule , 2007, Inf. Sci..

[41]  Michel Grabisch,et al.  A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid , 2010, Ann. Oper. Res..

[42]  Kwong-Sak Leung,et al.  Nonlinear nonnegative multiregressions based on Choquet integrals , 2000, Int. J. Approx. Reason..

[43]  Masaharu Mizumoto,et al.  Some Properties of Fuzzy Sets of Type 2 , 1976, Inf. Control..

[44]  Jerry M. Mendel,et al.  A vector similarity measure for linguistic approximation: Interval type-2 and type-1 fuzzy sets , 2008, Inf. Sci..

[45]  M. Rostamy-Malkhalifeh,et al.  EXTENSION OF TOPSIS FOR GROUP DECISION-MAKING BASED ON THE TYPE-2 FUZZY POSITIVE AND NEGATIVE IDEAL SOLUTIONS , 2010 .

[46]  Abazar Keikha,et al.  Fuzzified Choquet Integral and its Applications in MADM: A Review and A New Method , 2015, Int. J. Fuzzy Syst..