An Integrated TOPSIS Approach to MADM with Interval-Valued Intuitionistic Fuzzy Settings

In this paper, the three-parameter characterization of intuitionistic fuzzy sets and normalized hamming distance are employed to develop mathematical programming-based TOPSIS techniques in interval-valued intuitionistic fuzzy settings. A pair of linear fractional programming models are generated which are simplified for producing intervals to measure relative closeness coefficients of alternatives. Possibility degree matrix is obtained by pairwise comparisons of closeness coefficients and optimal degrees are estimated for final ranking of alternatives. The proposed approach is illustrated through a numerical example.

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

[2]  Ting-Yu Chen,et al.  The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making , 2015, Appl. Soft Comput..

[3]  Z. Xu,et al.  Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making , 2007 .

[4]  K. Atanassov,et al.  Interval-Valued Intuitionistic Fuzzy Sets , 2019, Studies in Fuzziness and Soft Computing.

[5]  Zeshui Xu,et al.  Corrigendum to "Dynamic intuitionistic fuzzy multi-attribute decision making" [Int. J. Approx. Reasoning 48 (2008) 246-262] , 2009, Int. J. Approx. Reason..

[6]  Shouzhen Zeng,et al.  TOPSIS method for intuitionistic fuzzy multiple-criteria decision making and its application to investment selection , 2016, Kybernetes.

[7]  G. Facchinetti,et al.  Note on ranking fuzzy triangular numbers , 1998 .

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

[9]  A. Biswas,et al.  Use of Possibility Measures for Ranking of Interval Valued Intuitionistic Fuzzy Numbers in Solving Multicriteria Decision Making Problems , 2017, CICBA.

[10]  Deng-Feng Li,et al.  Linear programming method for MADM with interval-valued intuitionistic fuzzy sets , 2010, Expert Syst. Appl..

[11]  Animesh Biswas,et al.  A fuzzy goal programming technique for multi-objective chance constrained programming with normally distributed fuzzy random variables and fuzzy numbers , 2013, Int. J. Math. Oper. Res..

[12]  A. Biswas,et al.  Priority based fuzzy goal programming technique to fractional fuzzy goals using dynamic programming , 2012 .

[13]  Xiaofei Zhao,et al.  TOPSIS method for interval-valued intuitionistic fuzzy multiple attribute decision making and its application to teaching quality evaluation , 2014, J. Intell. Fuzzy Syst..

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

[15]  Ching-Lai Hwang,et al.  Methods for Multiple Attribute Decision Making , 1981 .

[16]  Jun Ye,et al.  Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment , 2009, Expert Syst. Appl..

[17]  Animesh Biswas,et al.  Using Fuzzy Goal Programming Technique to Solve Multiobjective Chance Constrained Programming Problems in a Fuzzy Environment , 2012, Int. J. Fuzzy Syst. Appl..

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

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

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

[21]  Animesh Biswas,et al.  A Fuzzy Programming Method for Solving Multiobjective Chance Constrained Programming Problems Involving Log-Normally Distributed Fuzzy Random Variables , 2012, SEMCCO.