Neutrosophic Soft Multi-Attribute Group Decision Making Based On Grey Relational Analysis Method

The objective of the paper is to present neutrosophic soft multi attribute group decision making based on grey relational analysis involving multiple decision makers. The concept of neutrosophic soft sets is derived from the hybridization of the concepts of neutrosophic set and soft set. In the decision making  process,  the decision makers offer the rating of alternatives with respect to the parameters in terms of single valued neutrosophic set. We utilize AND operator of neutrosophic soft sets in order to aggregate the individual decision maker’s opinion into a common opinion based on choice parameters of the evaluator. Then, information entropy method is employed in order to attain the weights of the choice parameters. We determine the order of the alternatives and identify the most suitable alternative based on grey relational analysis. Finally, in order to show the effectiveness of the proposed approach, a numerical example is solved

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

[2]  Iuliana Carmen Barbacioru.  GREY RELATIONAL ANALYSIS METHOD FOR INTUITIONISTIC FUZZY MULTIPLE ATTRIBUTE DECISION MAKING , 2014 .

[3]  Florentin Smarandache,et al.  Linguistic Paradoxes and Tautologies , 2000, math/0010120.

[4]  Khaleed Alhazaymeh,et al.  POSSIBILITY VAGUE SOFT SET AND ITS APPLICATION IN DECISION MAKING , 2012 .

[5]  Gui-Wu Wei,et al.  Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making , 2011, Expert Syst. Appl..

[6]  Nasruddin Hassan,et al.  Possibility Fuzzy Soft Set , 2011, Adv. Decis. Sci..

[7]  A. R. Roy,et al.  An application of soft sets in a decision making problem , 2002 .

[8]  Yao Cenglin.  Application of Gray Relational Analysis Method in Comprehensive Evaluation on the Customer Satisfaction of Automobile 4S Enterprises , 2012 .

[9]  F. Smarandache.  A Unifying Field in Logics: Neutrosophic Logic. , 1999 .

[10]  Filiz Çitak,et al.  Fuzzy parameterized fuzzy soft set theory and its applications , 2010 .

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

[12]  Rajshekhar Sunderraman,et al.  Single Valued Neutrosophic Sets , 2010 .

[13]  Gin-Shuh Liang,et al.  Combining VIKOR with GRA techniques to evaluate service quality of airports under fuzzy environment , 2011, Expert Syst. Appl..

[14]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[15]  Gui-Wu Wei,et al.  GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting , 2010, Knowl. Based Syst..

[16]  Pabitra Kumar Maji,et al.  FUZZY SOFT SETS , 2001 .

[17]  Pabitra Kumar Maji,et al.  Neutrosophic Soft Set , 2013 .

[18]  J. Deng,et al.  Introduction to Grey system theory , 1989 .

[19]  Irfan Deli,et al.  Intuitionistic fuzzy parameterized soft set theory and its decision making , 2013, Appl. Soft Comput..

[20]  Shawkat Alkhazaleh,et al.  Possibility Intuitionistic Fuzzy Soft Set , 2012, Adv. Decis. Sci..

[21]  Naim Çagman,et al.  Intuitionistic fuzzy soft set theory and its decision making , 2013, J. Intell. Fuzzy Syst..

[22]  Pinaki Majumdar,et al.  On similarity and entropy of neutrosophic sets , 2013, J. Intell. Fuzzy Syst..

[23]  Surapati Pramanik,et al.  Interval Neutrosophic Multi-Attribute Decision-Making Based on Grey Relational Analysis , 2015 .

[24]  Surapati Pramanik,et al.  Neutrosophic Decision Making Model of School Choice , 2015 .

[25]  A. R. Roy,et al.  Soft set theory , 2003 .

[26]  D. Molodtsov.  Soft set theory—First results , 1999 .

[27]  N. Çagman,et al.  FUZZY SOFT SET THEORY AND ITS APPLICATIONS , 2011 .

[28]  Jian Ma,et al.  Vague soft sets and their properties , 2010, Comput. Math. Appl..

[29]  Hai-Long Yang,et al.  Notes on "Generalised Fuzzy Soft Sets" , 2011 .

[30]  Pingzhi Fan,et al.  APPLICATION OF GREY-RELATIONAL ANALYSIS TO FIND THE MOST SUITABLE WATERMARKING SCHEME , 2011 .

[31]  B. Giri,et al.  A New Methodology for Neutrosophic Multi-attribute Decision-making with Unknown Weight Information , 2014 .

[32]  Sunil Jacob John.  Generalized Intuitionistic Fuzzy Soft Sets and Its Applications , 2011 .

[33]  Florentin Smarandache,et al.  A unifying field in logics : neutrosophic logic : neutrosophy, neutrosophic set, neutrosophic probability , 2020 .

[34]  Pabitra Kumar Maji,et al.  An Application of Weighted Neutrosophic Soft Sets in a Decision-Making Problem , 2015 .

[35]  Srinivasa Rao Chalamalasetti,et al.  Application of grey relational analysis for optimizing weld bead geometry parameters of pulsed current micro plasma arc welded inconel 625 sheets , 2015 .

[36]  B. Giri,et al.  Entropy Based Grey Relational Analysis Method for Multi- Attribute Decision Making under Single Valued Neutrosophic Assessments , 2014 .

[37]  C. Fu,et al.  Application of grey relational analysis for corrosion failure of oil tubes , 2001 .

[38]  C. Hwang.  Multiple Objective Decision Making - Methods and Applications: A State-of-the-Art Survey , 1979 .

[39]  Pinaki Majumdar,et al.  Generalised fuzzy soft sets , 2010, Comput. Math. Appl..

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

[41]  Pabitra Kumar Maji,et al.  Weighted Neutrosophic Soft Sets , 2015 .

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

[43]  Florentin Smarandache,et al.  Neutrosophic set - a generalization of the intuitionistic fuzzy set , 2004, 2006 IEEE International Conference on Granular Computing.

[44]  Chih-Hung Tsai,et al.  Applying Grey Relational Analysis to the Vendor Evaluation Model Applying Grey Relational Analysis to the Vendor Evaluation Model , .

[45]  Pramanik Surapati,et al.  Grey Relational Analysis based Intuitionistic Fuzzy Multi-Criteria Group Decision-Making Approach for Teacher Selection in Higher Education , 2011 .

[46]  Sanjeev Goyal,et al.  Applying Fuzzy Grey Relational Analysis for Ranking the Advanced Manufacturing Systems , 2012, Grey Syst. Theory Appl..