Multi-Attribute Group Decision-Making Methods Based on Pythagorean Fuzzy N-Soft Sets

In this paper, by integrating Pythagorean fuzzy set with <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>-soft set, we propose a generalization of <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>-soft set called the theory of Pythagorean fuzzy <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>-soft set and explore some of related operations concerning this theory including the weak complement, extended union and intersection, restricted union and intersection. Then two algorithms are introduced to Pythagorean fuzzy <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>-soft sets for dealing with multi-attribute group decision-making problems. Finally, a practical example is provided to illustrate the validity and practicality of Pythagorean fuzzy <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>-soft sets in multi-attribute group decision-making problems. Compared with the existing models, we also elaborate the advantages of this model.

[1]  T. V. Ramakrishnan,et al.  Multi-fuzzy sets: An extension of fuzzy sets , 2011 .

[2]  Ronald R. Yager,et al.  Pythagorean Membership Grades in Multicriteria Decision Making , 2014, IEEE Transactions on Fuzzy Systems.

[3]  Lianglin Xiong,et al.  On Interval-Valued Hesitant Fuzzy Soft Sets , 2015 .

[4]  Deng-feng Li,et al.  Intuitionistic Fuzzy Soft Set , 2010, 2010 2nd International Workshop on Intelligent Systems and Applications.

[5]  Shu-Ping Wan,et al.  Pythagorean fuzzy mathematical programming method for multi-attribute group decision making with Pythagorean fuzzy truth degrees , 2017, Knowledge and Information Systems.

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

[7]  Ahmed Mostafa Khalil,et al.  Commentary on "Generalized intuitionistic fuzzy soft sets with applications in decision-making" , 2015, Appl. Soft Comput..

[8]  Annick Laruelle,et al.  Dis&approval voting: a characterization , 2014, Social Choice and Welfare.

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

[10]  Zeshui Xu,et al.  Pythagorean fuzzy TODIM approach to multi-criteria decision making , 2016, Appl. Soft Comput..

[11]  Yong Yang,et al.  Pythagorean Fuzzy Information Measures and Their Applications , 2017, Int. J. Intell. Syst..

[12]  Congcong Meng,et al.  The multi-fuzzy soft set and its application in decision making , 2013 .

[13]  Jianming Zhan,et al.  A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making , 2016, Soft Computing.

[14]  Jianming Zhan,et al.  On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods , 2017, Appl. Soft Comput..

[15]  Zeshui Xu,et al.  Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information , 2018, Inf. Sci..

[16]  Muhammad Akram,et al.  New decision-making hybrid model: intuitionistic fuzzy N-soft rough sets , 2019, Soft Computing.

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

[18]  Muhammad Akram,et al.  Group decision-making methods based on hesitant N-soft sets , 2019, Expert Syst. Appl..

[19]  Xiaohong Chen,et al.  Hesitant Fuzzy Soft Set and Its Applications in Multicriteria Decision Making , 2014, J. Appl. Math..

[20]  Jianming Zhan,et al.  A survey of decision making methods based on certain hybrid soft set models , 2016, Artificial Intelligence Review.

[21]  Melih Yucesan,et al.  Risk evaluation and prevention in hydropower plant operations: A model based on Pythagorean fuzzy AHP , 2019, Energy Policy.

[22]  Yong Yang,et al.  Interval-valued Hesitant Fuzzy Soft Sets and their Application in Decision Making , 2015, Fundam. Informaticae.

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

[24]  Guiwu Wei,et al.  Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications , 2018, Int. J. Intell. Syst..

[25]  Michele Fedrizzi,et al.  Fuzzy m-ary adjacency relations in social network analysis: Optimization and consensus evaluation , 2014, Inf. Fusion.

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

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

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

[29]  Ronald R. Yager,et al.  Pythagorean fuzzy subsets , 2013, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS).

[30]  Aslam Muhammad,et al.  On lattice ordered soft sets , 2015, Appl. Soft Comput..

[31]  Keyun Qin,et al.  Fuzzy Soft Sets and Fuzzy Soft Lattices , 2012, Int. J. Comput. Intell. Syst..

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

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

[34]  Haidong Zhang,et al.  Possibility Pythagorean fuzzy soft set and its application , 2019, J. Intell. Fuzzy Syst..

[35]  Yong Yang,et al.  Some Results for Pythagorean Fuzzy Sets , 2015, Int. J. Intell. Syst..

[36]  Hua Zhao,et al.  Lattice Structures of Fuzzy Soft Sets , 2010, ICIC.

[37]  Harish Garg,et al.  A NEW IMPROVED SCORE FUNCTION OF AN INTERVAL-VALUED PYTHAGOREAN FUZZY SET BASED TOPSIS METHOD , 2017 .

[38]  Zeshui Xu,et al.  Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets , 2014, Int. J. Intell. Syst..

[39]  Selcuk Cebi,et al.  A novel approach to risk assessment for occupational health and safety using Pythagorean fuzzy AHP & fuzzy inference system , 2018 .

[40]  Juan Carlos Augusto,et al.  Ordering based decision making - A survey , 2013, Inf. Fusion.

[41]  José Carlos Rodriguez Alcantud,et al.  N-soft sets and their decision making algorithms , 2017, Soft Computing.

[42]  Jianming Zhan,et al.  A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making , 2017, Appl. Soft Comput..

[43]  Harish Garg,et al.  A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making , 2016, Int. J. Intell. Syst..

[44]  Xiaolu Zhang,et al.  Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methods , 2016, Inf. Sci..

[45]  Muhammad Akram,et al.  Fuzzy N-soft sets: A novel model with applications , 2018, J. Intell. Fuzzy Syst..

[46]  S. Meysam Mousavi,et al.  Enhancing decision-making flexibility by introducing a new last aggregation evaluating approach based on multi-criteria group decision making and Pythagorean fuzzy sets , 2017, Appl. Soft Comput..

[47]  Mustafa Mat Deris,et al.  On Multi-soft Sets Construction in Information Systems , 2009, ICIC.

[48]  Lan Shu,et al.  Dual Hesitant Fuzzy Soft Set and Its Properties , 2016 .