An extension of the ELECTRE approach with multi-valued neutrosophic information

In this paper, an extension Elimination and Choice Translating Reality (ELECTRE) method is introduced to handle multi-valued neutrosophic multi-criteria decision-making (MCDM) problems. First of all, some outranking relations for multi-valued neutrosophic numbers (MVNNs), which are based on traditional ELECTRE methods, are defined, and several properties are analyzed. In the next place, an outranking method to deal with MCDM problems similar to ELECTRE III, where weights and data are in the form of MVNNs, is developed. At last, an example is provided to demonstrate the proposed approach and testify its validity and feasibility. This study is supported by the comparison analysis with other existing methods.

[1]  Hong-yu Zhang,et al.  Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems , 2016, Int. J. Syst. Sci..

[2]  Jun Ye,et al.  Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment , 2013, Int. J. Gen. Syst..

[3]  Florentin Smarandache,et al.  Interval-Valued Neutrosophic Soft Rough Sets , 2015 .

[4]  B. Roy.  The outranking approach and the foundations of electre methods , 1991 .

[5]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[6]  uan-juan Penga,et al.  An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets , 2014 .

[7]  Florentin Smarandache,et al.  ON NEUTROSOPHIC REFINED SETS AND THEIR APPLICATIONS IN MEDICAL DIAGNOSIS , 2015 .

[8]  Guiwu Wei,et al.  Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making , 2013, Knowl. Based Syst..

[9]  Ting-Yu Chen,et al.  An ELECTRE-based outranking method for multiple criteria group decision making using interval type-2 fuzzy sets , 2014, Inf. Sci..

[10]  Behnam Vahdani,et al.  Extension of the ELECTRE method based on interval-valued fuzzy sets , 2011, Soft Comput..

[11]  E. Triantaphyllou,et al.  Ranking irregularities when evaluating alternatives by using some ELECTRE methods , 2008 .

[12]  V. Torra,et al.  A framework for linguistic logic programming , 2010 .

[13]  Peide Liu,et al.  Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean , 2014, Neural Computing and Applications.

[14]  Hong-yu Zhang,et al.  A Neutrosophic Normal Cloud and Its Application in Decision-Making , 2016, Cognitive Computation.

[15]  Jonathan Lawry,et al.  IEEE International Conference on Fuzzy Systems , 2017 .

[16]  Yusuf Subas,et al.  A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems , 2016, International Journal of Machine Learning and Cybernetics.

[17]  Hong-yu Zhang,et al.  An Improved Weighted Correlation Coefficient Based on Integrated Weight for Interval Neutrosophic Sets and its Application in Multi-criteria Decision-making Problems , 2015, Int. J. Comput. Intell. Syst..

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

[19]  Peide Liu,et al.  Some Generalized Neutrosophic Number Hamacher Aggregation Operators and Their Application to Group Decision Making , 2014 .

[20]  Florentin Smarandache,et al.  N-Valued Interval Neutrosophic Sets and Their Application in Medical Diagnosis , 2015 .

[21]  Pekka Salminen,et al.  ELECTRE III and IV Decision Aids in an Environmental Problem , 1997 .

[22]  Ting-Yu Chen,et al.  Multiple criteria decision analysis using a likelihood-based outranking method based on interval-valued intuitionistic fuzzy sets , 2014, Inf. Sci..

[23]  Vicenç Torra,et al.  On hesitant fuzzy sets and decision , 2009, 2009 IEEE International Conference on Fuzzy Systems.

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

[25]  Jun Ye,et al.  A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets , 2014, J. Intell. Fuzzy Syst..

[26]  Peide Liu,et al.  The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making , 2015, Neural Computing and Applications.

[27]  Cengiz Kahraman,et al.  An integrated fuzzy AHP-ELECTRE methodology for environmental impact assessment , 2011, Expert Syst. Appl..

[28]  Yanqing Zhang,et al.  Interval Neutrosophic Logics: Theory and Applications , 2004, ArXiv.

[29]  Irfan Deli,et al.  Correlation Measure for Neutrosophic Refined Sets and its application in Medical Diagnosis , 2013 .

[30]  Zhang-peng Tian,et al.  Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets , 2015, Int. J. Syst. Sci..

[31]  Jun Ye,et al.  Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses , 2015, Artif. Intell. Medicine.

[32]  Xi Liu,et al.  The neutrosophic number generalized weighted power averaging operator and its application in multiple attribute group decision making , 2015, Int. J. Mach. Learn. Cybern..

[33]  Jun Ye,et al.  Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment , 2014, J. Intell. Syst..

[34]  Agus Harjoko,et al.  ELECTRE Methods in Solving Group Decision Supports System Bioinformatics on Gene Mutation Detection simulation , 2011 .

[35]  Jian-qiang Wang,et al.  Cross-Entropy and Prioritized Aggregation Operator with Simplified Neutrosophic Sets and Their Application in Multi-Criteria Decision-Making Problems , 2016, Int. J. Fuzzy Syst..

[36]  Hong-yu Zhang,et al.  An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets , 2015, Neural Computing and Applications.

[37]  K. Devi,et al.  A multicriteria intuitionistic fuzzy group decision making for plant location selection with ELECTRE method , 2012, The International Journal of Advanced Manufacturing Technology.

[38]  Zeshui Xu,et al.  Projection Models for Intuitionistic Fuzzy Multiple Attribute Decision Making , 2010, Int. J. Inf. Technol. Decis. Mak..

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

[40]  Irfan Deli,et al.  Interval-valued neutrosophic soft sets and its decision making , 2014, Int. J. Mach. Learn. Cybern..

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

[42]  Jun Ye,et al.  Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making , 2014, J. Intell. Fuzzy Syst..

[43]  Jing Wang,et al.  Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems , 2015, Int. J. Comput. Intell. Syst..

[44]  Said Broumi,et al.  Neutrosophic Soft Multi-Set Theory and Its Decision Making , 2014 .

[45]  Mostafa Zandieh,et al.  Extension of the ELECTRE method for decision-making problems with interval weights and data , 2010 .

[46]  Jun Ye.  Single valued neutrosophic cross-entropy for multicriteria decision making problems , 2014 .

[47]  Yanqing Zhang,et al.  Interval Neutrosophic Sets and Logic: Theory and Applications in Computing , 2005, ArXiv.