A Parametric Method for Ranking Intuitionistic Fuzzy Numbers and Its Application to Solve Intuitionistic Fuzzy Network Data Envelopment Analysis Models

In this study, a new parametric method is proposed to rank intuitionistic fuzzy numbers in a general form. One of the advantages of the proposed method is that the decision maker’s idea is taken into account by selecting appropriate amounts of decision level and hesitation degree parameters. In some illustrative examples, the superiority of the proposed method over some other approaches is demonstrated. Furthermore, to show the ability of the method to solve intuitionistic fuzzy optimization problems, the proposed method is applied to solve intuitionistic fuzzy network data envelopment analysis (IFNDEA) problems. Also, in three appropriate examples, the validity of the suggested method and its capacity to solve real-world problems are illustrated.

[1]  Jiang-Xia Nan,et al.  A Ranking Method of Triangular Intuitionistic Fuzzy Numbers and Application to Decision Making , 2010, Int. J. Comput. Intell. Syst..

[2]  Dong Zhang,et al.  (1802-4282) THE 2-ADDITIVE FUZZY CHOQUET INTEGRAL BASED-TODIM METHOD WITH IMPROVED SCORE FUNCTION UNDER HESITANT FUZZY ENVIRONMENT , 2019 .

[3]  Ali Asghar Foroughi,et al.  Solving generalized fuzzy data envelopment analysis model: a parametric approach , 2016, Central European Journal of Operations Research.

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

[5]  C. Kao,et al.  Efficiency decomposition for parallel production systems , 2012, J. Oper. Res. Soc..

[6]  Przemyslaw Grzegorzewski,et al.  Distances and orderings in a family of intuitionistic fuzzy numbers , 2003, EUSFLAT Conf..

[7]  Jun Ye,et al.  Expected value method for intuitionistic trapezoidal fuzzy multicriteria decision-making problems , 2011, Expert Syst. Appl..

[8]  Shiv Prasad Yadav,et al.  Intuitionistic fuzzy data envelopment analysis: An application to the banking sector in India , 2015, Expert Syst. Appl..

[9]  Etienne E. Kerre,et al.  Reasonable properties for the ordering of fuzzy quantities (II) , 2001, Fuzzy Sets Syst..

[10]  Shyi-Ming Chen,et al.  Multiattribute group decision making based on intuitionistic fuzzy partitioned Maclaurin symmetric mean operators , 2020, Inf. Sci..

[11]  Rituparna Chutia,et al.  Ranking intuitionistic fuzzy numbers at levels of decision-making and its application , 2018, Expert Syst. J. Knowl. Eng..

[12]  Shib Sankar Sana,et al.  Self-assessment of parallel network systems with intuitionistic fuzzy data: a case study , 2019, Soft Comput..

[13]  Zeshui Xu,et al.  DEA Evaluation Method Based on Interval Intuitionistic Bayesian Network and Its Application in Enterprise Logistics , 2019, IEEE Access.

[14]  Eulalia Szmidt,et al.  Distances and Similarities in Intuitionistic Fuzzy Sets , 2013, Studies in Fuzziness and Soft Computing.

[15]  Xiaohong Chen,et al.  Multi-criteria group decision making based on trapezoidal intuitionistic fuzzy information , 2015, Appl. Soft Comput..

[16]  E. Zavadskas,et al.  AN INTUITIONISTIC FUZZY DATA ENVELOPMENT ANALYSIS FOR EFFICIENCY EVALUATION UNDER UNCERTAINTY: CASE OF A FINANCE AND CREDIT INSTITUTION , 2013 .

[17]  Shashi Aggarwal,et al.  Solving Intuitionistic Fuzzy Solid Transportation Problem Via New Ranking Method Based on Signed Distance , 2016, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[18]  Debashree Guha,et al.  Ranking of Intuitionistic Fuzzy Number by Centroid Point , 2013 .

[19]  Roohollah Abbasi Shureshjani,et al.  A new parametric method for ranking fuzzy numbers , 2013 .

[20]  Shiv Prasad Yadav,et al.  Development and optimization of unrestricted LR-type intuitionistic fuzzy mathematical programming problems , 2017, Expert Syst. Appl..

[21]  Sanjeet Singh,et al.  Intuitionistic fuzzy DEA/AR and its application to flexible manufacturing systems , 2018, RAIRO Oper. Res..

[22]  Joe Zhu,et al.  Data envelopment analysis : a handbook on the modeling of internal structures and networks , 2014 .

[23]  Boris Pérez-Cañedo,et al.  On LR-type fully intuitionistic fuzzy linear programming with inequality constraints: Solutions with unique optimal values , 2019, Expert Syst. Appl..

[24]  Peide Liu,et al.  Multiple Attribute Group Decision Making Method Based on Intuitionistic Fuzzy Einstein Interactive Operations , 2020, Int. J. Fuzzy Syst..

[25]  V. Lakshmana Gomathi Nayagam,et al.  Total ordering for intuitionistic fuzzy numbers , 2016, Complex..

[26]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[27]  Muhammad Akram,et al.  An algorithm for computing certain metrics in intuitionistic fuzzy graphs , 2016, J. Intell. Fuzzy Syst..

[28]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[29]  V. Lakshmana Gomathi Nayagam,et al.  A linear ordering on the class of Trapezoidal intuitionistic fuzzy numbers , 2016, Expert Syst. Appl..

[30]  Rituparna Chutia,et al.  A new method of ranking parametric form of fuzzy numbers using value and ambiguity , 2017, Appl. Soft Comput..

[31]  A. U.S.,et al.  Measuring the efficiency of decision making units , 2003 .

[32]  Adel Hatami-Marbini,et al.  The State of the Art in Fuzzy Data Envelopment Analysis , 2014 .

[33]  Chiang Kao,et al.  Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan , 2008, Eur. J. Oper. Res..

[34]  Deng-Feng Li,et al.  Decision and Game Theory in Management With Intuitionistic Fuzzy Sets , 2013, Studies in Fuzziness and Soft Computing.

[35]  Peide Liu,et al.  Some Maclaurin symmetric mean aggregation operators based on Schweizer-Sklar operations for intuitionistic fuzzy numbers and their application to decision making , 2019, J. Intell. Fuzzy Syst..

[36]  Deng-Feng Li,et al.  A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems , 2010, Comput. Math. Appl..

[37]  S. P. Yadav,et al.  A new approach to rank the decision making units in presence of infeasibility in intuitionistic fuzzy environment , 2020 .

[38]  Muhammad Akram,et al.  A novel decision-making approach based on hypergraphs in intuitionistic fuzzy environment , 2018, J. Intell. Fuzzy Syst..

[39]  Przemyslaw Grzegorzewski,et al.  Metrics and orders in space of fuzzy numbers , 1998, Fuzzy Sets Syst..

[40]  Cerry M. Klein,et al.  A simple approach to ranking a group of aggregated fuzzy utilities , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[41]  Shiv Prasad Yadav,et al.  Development of intuitionistic fuzzy super-efficiency slack based measure with an application to health sector , 2018, Comput. Ind. Eng..

[42]  Jian-qiang Wang,et al.  Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems , 2009 .

[43]  V. Lakshmana Gomathi Nayagam,et al.  An improved ranking method for comparing trapezoidal intuitionistic fuzzy numbers and its applications to multicriteria decision making , 2016, Neural Computing and Applications.

[44]  S. Vengataasalam,et al.  A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept , 2016, Mathematical Sciences.

[45]  Etienne E. Kerre,et al.  Reasonable properties for the ordering of fuzzy quantities (II) , 2001, Fuzzy Sets Syst..

[46]  Amit Kumar,et al.  A Note on "A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers" , 2015, Int. J. Comput. Intell. Syst..

[47]  V. Lakshmana Gomathi Nayagam,et al.  Ranking of intuitionistic fuzzy numbers , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[48]  Shiv Prasad Yadav,et al.  Development of intuitionistic fuzzy data envelopment analysis models and intuitionistic fuzzy input–output targets , 2019, Soft Comput..

[49]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[50]  M. Amparo Vila,et al.  On a canonical representation of fuzzy numbers , 1998, Fuzzy Sets Syst..

[51]  H. M. Nehi.  A New Ranking Method for Intuitionistic Fuzzy Numbers , 2010 .

[52]  Renato De Leone,et al.  Data Envelopment Analysis , 2009, Encyclopedia of Optimization.

[53]  Abraham Kandel,et al.  A new fuzzy arithmetic , 1999, Fuzzy Sets Syst..

[54]  Shu-Ping Wan,et al.  Multi-Attribute Decision Making Method Based on Possibility variance coefficient of triangular Intuitionistic Fuzzy numbers , 2013, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[55]  Jiang-Xia Nan,et al.  A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers , 2010, Int. J. Comput. Intell. Syst..

[56]  Z. Zhong,et al.  Multi-criteria decision-making method with incomplete certain information based on intuitionistic fuzzy number , 2009 .