Algorithms for a Generalized Multipolar Neutrosophic Soft Set with Information Measures to Solve Medical Diagnoses and Decision-Making Problems

The aim of this paper is to propose the generalized version of the multipolar neutrosophic soft set with operations and basic properties. Here, we define the AND, OR, Truth-Favorite, and False-Favorite operators along with their properties. Also, we define the necessity and possibility of operations for them. Later on, to extend it to solve the decision-making problems, we define some information measures such as distance, similarity, and correlation coefficient for the generalized multipolar neutrosophic soft set. Several desirable properties and their relationship between them are derived. Finally, based on these information measures, a decision-making algorithm is stated under the neutrosophic environment to tackle the uncertain and vague information. The applicability of the proposed algorithm is demonstrated through a case study of the medical-diagnosis and the decision-making problems. A comparative analysis with several existing studies reveals the effectiveness of the approach.

[1]  Harish Garg,et al.  A Novel Correlation Coefficients between Pythagorean Fuzzy Sets and Its Applications to Decision‐Making Processes , 2016, Int. J. Intell. Syst..

[2]  Ding-An Chiang,et al.  Correlation of fuzzy sets , 1999, Fuzzy Sets Syst..

[3]  Huiling Xue,et al.  Research on Novel Correlation Coefficient of Neutrosophic Cubic Sets and Its Applications , 2019, Mathematical Problems in Engineering.

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

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

[6]  I. Turksen.  Interval valued fuzzy sets based on normal forms , 1986 .

[7]  Harish Garg,et al.  An improved cosine similarity measure for intuitionistic fuzzy sets and their applications to decision-making process , 2017 .

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

[9]  Harish Garg,et al.  TOPSIS method based on correlation coefficient for solving decision-making problems with intuitionistic fuzzy soft set information , 2020 .

[10]  Xiaoyan Liu,et al.  On some new operations in soft set theory , 2009, Comput. Math. Appl..

[11]  Tadeusz Gerstaenkorn,et al.  Correlation of intuitionistic fuzzy sets , 1991 .

[12]  Aslihan Sezgin Sezer,et al.  On operations of soft sets , 2011, Comput. Math. Appl..

[13]  Florentin Smarandache,et al.  m-Polar Neutrosophic Topology with Applications to Multi-criteria Decision-Making in Medical Diagnosis and Clustering Analysis , 2019, International Journal of Fuzzy Systems.

[14]  Imran Siddique,et al.  TOPSIS Method Based on Correlation Coefficient under Pythagorean Fuzzy Soft Environment and Its Application towards Green Supply Chain Management , 2021, Sustainability.

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

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

[17]  Harish Garg,et al.  Exponential similarity measures for Pythagorean fuzzy sets and their applications to pattern recognition and decision-making process , 2019, Complex & Intelligent Systems.

[18]  Harish Garg,et al.  An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making , 2018, Soft Computing.

[19]  Said Broumi,et al.  Generalized Neutrosophic Soft Set , 2013, ArXiv.

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

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

[22]  Jong-Wuu Wu,et al.  Correlation of intuitionistic fuzzy sets by centroid method , 2002, Inf. Sci..

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

[24]  Dug Hun Hong,et al.  A note on correlation of interval-valued intuitionistic fuzzy sets , 1998, Fuzzy Sets Syst..

[25]  Na Li,et al.  Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making , 2020, Int. J. Intell. Syst..

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

[27]  Xinyang Deng,et al.  Single-Valued Neutrosophic Set Correlation Coefficient and Its Application in Fault Diagnosis , 2020, Symmetry.

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

[29]  Shenggang Li,et al.  m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets , 2014, TheScientificWorldJournal.

[30]  Simiao Zhao,et al.  Machine Learning Prediction for 50 Anti-Cancer Food Molecules from 968 Anti-Cancer Drugs , 2020, International Journal of Intelligence Science.

[31]  Hong-yu Zhang,et al.  Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems , 2016, Neural Computing and Applications.

[32]  Faruk Karaaslan,et al.  Correlation coefficients of single-valued neutrosophic refined soft sets and their applications in clustering analysis , 2015, Neural Computing and Applications.

[33]  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.

[34]  Harish Garg,et al.  Aggregation operators of Pythagorean fuzzy soft sets with their application for green supplier chain management , 2021, J. Intell. Fuzzy Syst..

[35]  Muhammad Saeed,et al.  Multi-Polar Neutrosophic Soft Sets with Application in Medical Diagnosis and Decision-Making , 2020 .

[36]  Harish Garg,et al.  Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight , 2020, Soft Computing.

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

[38]  Tapan Kumar Roy,et al.  Vikor Based Magdm Strategy Under Bipolar Neutrosophic Set Environment , 2018 .

[39]  P. Dey,et al.  Neutrosophic Soft Multi-Attribute Decision Making Based on Grey Relational Projection Method , 2016 .

[40]  Chunhai Yu.  Correlation of fuzzy numbers , 1993 .

[41]  Zeshui Xu,et al.  Clustering algorithm for intuitionistic fuzzy sets , 2008, Inf. Sci..

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

[43]  H. B. Mitchell.  A correlation coefficient for intuitionistic fuzzy sets , 2004, Int. J. Intell. Syst..

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

[45]  Surapati Pramanik,et al.  TOPSIS for Single Valued Neutrosophic Soft Expert Set Based Multi-Attribute Decision Making Problems , 2015 .

[46]  Surapati Pramanik,et al.  Bipolar Neutrosophic Projection Based Models for Solving Multi-attribute Decision Making Problems , 2017 .

[47]  Faruk Karaaslan,et al.  Correlation Coefficient between Possibility Neutrosophic Soft Sets , 2016 .

[48]  Harish Garg,et al.  Multiparametric similarity measures on Pythagorean fuzzy sets with applications to pattern recognition , 2019, Applied Intelligence.

[49]  Harish Garg,et al.  A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making , 2018, Applied Intelligence.