A Robust Single-Valued Neutrosophic Soft Aggregation Operators in Multi-Criteria Decision Making

Molodtsov originated soft set theory that was provided a general mathematical framework for handling with uncertainties in which we meet the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as neutrosophic set theory. The main object of this paper is to lay a foundation for providing a new approach of single-valued neutrosophic soft tool which is considering many problems that contain uncertainties. In present study, a new aggregation operators of single-valued neutrosophic soft numbers have so far not yet been applied for ranking of the alternatives in decision-making problems. To this propose work, single-valued neutrosophic soft weighted arithmetic averaging (SVNSWA) operator, single-valued neutrosophic soft weighted geometric averaging (SVNSWGA) operator have been used to compare two single-valued neutrosophic soft numbers (SVNSNs) for aggregating different single-valued neutrosophic soft input arguments in neutrosophic soft environment. Then, its related properties have been investigated. Finally, a practical example for Medical diagnosis problems provided to test the feasibility and applicability of the proposed work.

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

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

[3]  Mujahid Abbas,et al.  Distance Measures and Operations in Intuitionistic and Interval-Valued Intuitionistic Fuzzy Soft Set Theory , 2015, Int. J. Fuzzy Syst..

[4]  Madhumangal Pal,et al.  Trapezoidal neutrosophic aggregation operators and its application in multiple attribute decision making process , 2018, Scientia Iranica.

[5]  Madhumangal Pal,et al.  Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decision-making process , 2018, J. Ambient Intell. Humaniz. Comput..

[6]  Madhumangal Pal,et al.  Application of (α, β)-soft intersectional sets on BCK/BCI-algebras , 2017, Int. J. Intell. Syst. Technol. Appl..

[7]  Ridvan cSahin,et al.  Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic environment , 2014, 1412.5202.

[8]  Dragan Pamučar,et al.  A Sensitivity analysis in MCDM problems: A statistical approach , 2018, Decision Making: Applications in Management and Engineering.

[9]  Feng Liu,et al.  A multicriteria model for the selection of the transport service provider: A single valued neutrosophic DEMATEL multicriteria model , 2018, Decision Making: Applications in Management and Engineering.

[10]  Mariano Eriz.  Aggregation Functions: A Guide for Practitioners , 2010 .

[11]  Harish Garg,et al.  Linguistic single-valued neutrosophic prioritized aggregation operators and their applications to multiple-attribute group decision-making , 2018, Journal of Ambient Intelligence and Humanized Computing.

[12]  Florentin Smarandache,et al.  An Extension of Neutrosophic AHP-SWOT Analysis for Strategic Planning and Decision-Making , 2018, Symmetry.

[13]  K. V. Babitha,et al.  Hesitant fuzzy soft sets , 2013 .

[14]  Yongquan Zhou,et al.  Multi-criteria group decision making based on neutrosophic analytic hierarchy process , 2017, J. Intell. Fuzzy Syst..

[15]  Hong-yu Zhang,et al.  The fuzzy cross-entropy for intuitionistic hesitant fuzzy sets and their application in multi-criteria decision-making , 2015, Int. J. Syst. Sci..

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

[17]  Hong-yu Zhang,et al.  Frank Choquet Bonferroni Mean Operators of Bipolar Neutrosophic Sets and Their Application to Multi-criteria Decision-Making Problems , 2018, Int. J. Fuzzy Syst..

[18]  Madhumangal Pal,et al.  Application of Bipolar Intuitionistic Fuzzy Soft Sets in Decision Making Problem , 2018, Int. J. Fuzzy Syst. Appl..

[19]  Tapan Kumar Roy,et al.  IN-cross Entropy Based MAGDM Strategy under Interval Neutrosophic Set Environment , 2018 .

[20]  Jun Ye,et al.  Some Single-Valued Neutrosophic Dombi Weighted Aggregation Operators for Multiple Attribute Decision-Making , 2017, Symmetry.

[21]  P. Năstase,et al.  The concept of a data bank for economic scientific research in education , 1986 .

[22]  Shyi-Ming Chen,et al.  Multiattribute Decision Making Based on Interval-Valued Intuitionistic Fuzzy Sets, PSO Techniques, and Evidential Reasoning Methodology , 2015, IEEE Transactions on Fuzzy Systems.

[23]  Harish Garg,et al.  Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making , 2017, Applied Intelligence.

[24]  Irfan Deli,et al.  ivnpiv-Neutrosophic soft sets and their decision making based on similarity measure , 2016, Neural Computing and Applications.

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

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

[27]  Le Hoang Son,et al.  Bipolar neutrosophic soft sets and applications in decision making , 2017, J. Intell. Fuzzy Syst..

[28]  Mehmet Sahin,et al.  Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making , 2018, Neural Computing and Applications.

[29]  Xindong Peng,et al.  A modified TOPSIS method based on vague parameterized vague soft sets and its application to supplier selection problems , 2019, Neural Computing and Applications.

[30]  Luige Vladareanu,et al.  Applications of Neutrosophic Logic to Robotics , 2015 .

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

[32]  Surapati Pramanik,et al.  TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment , 2014, Neural Computing and Applications.

[33]  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..

[34]  Afshin Salajegheh,et al.  Improving early OSV design robustness by applying ‘Multivariate Big Data Analytics’ on a ship's life cycle , 2018, Journal of Industrial Information Integration.

[35]  Peide Liu,et al.  Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making , 2017, Neural Computing and Applications.

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

[37]  Shawkat Alkhazaleh,et al.  Fuzzy Soft Expert Set and Its Application , 2014 .

[38]  Harish Garg,et al.  Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment , 2017 .

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

[40]  Gavin Brown,et al.  Individual Confidence-Weighting and Group Decision-Making. , 2017, Trends in ecology & evolution.

[41]  Guiwu Wei,et al.  Some single-valued neutrosophic Bonferroni power aggregation operators in multiple attribute decision making , 2019, J. Ambient Intell. Humaniz. Comput..

[42]  Humberto Bustince,et al.  On averaging operators for Atanassov's intuitionistic fuzzy sets , 2011, Inf. Sci..

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

[44]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[45]  F. Smarandache,et al.  Shortest Path Problem Under Interval Valued Neutrosophic Setting , 2018 .

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

[47]  Jens Krause,et al.  Detection Accuracy of Collective Intelligence Assessments for Skin Cancer Diagnosis. , 2015, JAMA dermatology.

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

[49]  Dragan Pamučar,et al.  A Novel Approach for the Selection of Power-Generation Technology Using a Linguistic Neutrosophic CODAS Method: A Case Study in Libya , 2018, Energies.

[50]  Athar Kharal,et al.  On Fuzzy Soft Sets , 2009, Adv. Fuzzy Syst..

[51]  Faruk Karaaslan,et al.  Possibility neutrosophic soft sets and PNS-decision making method , 2014, Appl. Soft Comput..

[52]  Madhumangal Pal,et al.  Picture fuzzy Dombi aggregation operators: Application to MADM process , 2019, Appl. Soft Comput..

[53]  Tsau Young Lin,et al.  Combination of interval-valued fuzzy set and soft set , 2009, Comput. Math. Appl..

[54]  Jun Ye,et al.  Dombi Aggregation Operators of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making , 2018, Algorithms.

[55]  Gordon D. A. Brown,et al.  Multi-attribute decision by sampling : an account of the attraction, compromise and similarity effects , 2017 .

[56]  Florentin Smarandache,et al.  SINGLE VALUED NEUTROSOPHIC SOFT EXPERT SETS AND THEIR APPLICATION IN DECISION MAKING , 2016 .

[57]  J. Shamma,et al.  Belief consensus and distributed hypothesis testing in sensor networks , 2006 .

[58]  Romualdas Bausys,et al.  Multicriteria Decision Making Approach by Vikor Under Interval Neutrosophic Set Environment , 2017 .

[59]  Ralf H. J. M. Kurvers,et al.  Collective Intelligence Meets Medical Decision-Making: The Collective Outperforms the Best Radiologist , 2015, PloS one.

[60]  Isabel da Silva Lopes,et al.  Classification methodology for spare parts management combining maintenance and logistics perspectives , 2018 .

[61]  Zeshui Xu,et al.  Intuitionistic Fuzzy Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.

[62]  Dragan Pamučar,et al.  NORMALIZED WEIGHTED GEOMETRIC BONFERRONI MEAN OPERATOR OF INTERVAL ROUGH NUMBERS – APPLICATION IN INTERVAL ROUGH DEMATEL-COPRAS , 2018, Facta Universitatis, Series: Mechanical Engineering.

[63]  Jian-qiang Wang,et al.  Some new operation rules and a new ranking method for interval-valued intuitionistic linguistic numbers , 2017, J. Intell. Fuzzy Syst..

[64]  Hai Liu,et al.  Interval-valued intuitionistic fuzzy soft sets and their properties , 2010, Comput. Math. Appl..

[65]  Enrique Herrera-Viedma,et al.  A framework for context-aware heterogeneous group decision making in business processes , 2016, Knowl. Based Syst..