Two Types of Single Valued Neutrosophic Covering Rough Sets and an Application to Decision Making

In this paper, to combine single valued neutrosophic sets (SVNSs) with covering-based rough sets, we propose two types of single valued neutrosophic (SVN) covering rough set models. Furthermore, a corresponding application to the problem of decision making is presented. Firstly, the notion of SVN β-covering approximation space is proposed, and some concepts and properties in it are investigated. Secondly, based on SVN β-covering approximation spaces, two types of SVN covering rough set models are proposed. Then, some properties and the matrix representations of the newly defined SVN covering approximation operators are investigated. Finally, we propose a novel method to decision making (DM) problems based on one of the SVN covering rough set models. Moreover, the proposed DM method is compared with other methods in an example.

[1]  Xiaohong Zhang,et al.  Four Operators of Rough Sets Generalized to Matroids and a Matroidal Method for Attribute Reduction , 2018, Symmetry.

[2]  Jianhua Dai,et al.  Uncertainty measurement for interval-valued decision systems based on extended conditional entropy , 2012, Knowl. Based Syst..

[3]  Jian Liu,et al.  Decision process in MCDM with large number of criteria and heterogeneous risk preferences , 2018 .

[4]  Peide Liu,et al.  The Aggregation Operators Based on Archimedean t-Conorm and t-Norm for Single-Valued Neutrosophic Numbers and their Application to Decision Making , 2016, International Journal of Fuzzy Systems.

[5]  Theresa Beaubouef,et al.  Rough Sets , 2019, Lecture Notes in Computer Science.

[6]  Huangjian Yi,et al.  Rough sets and matroids from a lattice-theoretic viewpoint , 2016, Inf. Sci..

[7]  Jesús Medina,et al.  Multi-adjoint t-concept lattices , 2010, Inf. Sci..

[8]  Ioan-Daniel Borlea,et al.  Model-Free Sliding Mode and Fuzzy Controllers for Reverse Osmosis Desalination Plants , 2018 .

[9]  Yiyu Yao,et al.  Attribute reduction in decision-theoretic rough set models , 2008, Inf. Sci..

[10]  Liwen Ma,et al.  Two fuzzy covering rough set models and their generalizations over fuzzy lattices , 2016, Fuzzy Sets Syst..

[11]  Qin Liu,et al.  An approach to decision making based on intuitionistic fuzzy rough sets over two universes , 2013, J. Oper. Res. Soc..

[12]  Fei Li,et al.  Approaches to knowledge reduction of covering decision systems based on information theory , 2009, Inf. Sci..

[13]  Zeshui Xu,et al.  The Extended TOPSIS Method for Multi-criteria Decision Making Based on Hesitant Heterogeneous Information , 2014, ICSE 2014.

[14]  Jinkun Chen,et al.  Relations of reduction between covering generalized rough sets and concept lattices , 2015, Inf. Sci..

[15]  Fei-Yue Wang,et al.  Conditions for coverings to induce matroids , 2014, Int. J. Mach. Learn. Cybern..

[16]  Bin Yang,et al.  On some types of fuzzy covering-based rough sets , 2017, Fuzzy Sets Syst..

[17]  Xiaohong Zhang,et al.  Fuzzy anti-grouped filters and fuzzy normal filters in pseudo-BCI algebras , 2017, J. Intell. Fuzzy Syst..

[18]  Yixiong Feng,et al.  Structural Optimization of a High-Speed Press Considering Multi-Source Uncertainties Based on a New Heterogeneous TOPSIS , 2018 .

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

[20]  Wei-Zhi Wu,et al.  Attribute reduction based on evidence theory in incomplete decision systems , 2008, Inf. Sci..

[21]  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..

[22]  Muhammad Akram,et al.  A New Multi-Attribute Decision-Making Method Based on m-Polar Fuzzy Soft Rough Sets , 2017, Symmetry.

[23]  Artur Karczmarczyk,et al.  Generalised framework for multi-criteria method selection , 2018, Omega.

[24]  Jianhua Dai,et al.  On the union and intersection operations of rough sets based on various approximation spaces , 2015, Inf. Sci..

[25]  Gianpiero Cattaneo,et al.  Entropies and Co-Entropies of Coverings with Application to Incomplete Information Systems , 2007, Fundam. Informaticae.

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

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

[28]  Shahzad Faizi,et al.  Group Decision-Making for Hesitant Fuzzy Sets Based on Characteristic Objects Method , 2017, Symmetry.

[29]  William Zhu,et al.  Applications of Matrices to a Matroidal Structure of Rough Sets , 2013, J. Appl. Math..

[30]  John V. Monaco,et al.  Using a predefined passphrase to evaluate a speaker verification system , 2014, Artif. Intell. Res..

[31]  Xiaohong Zhang,et al.  Two Types of Intuitionistic Fuzzy Covering Rough Sets and an Application to Multiple Criteria Group Decision Making , 2018, Symmetry.

[32]  Xiuwu Liao,et al.  A hybrid model of single valued neutrosophic sets and rough sets: single valued neutrosophic rough set model , 2017, Soft Comput..

[33]  Xiaohong Zhang,et al.  Matrix approaches for some issues about minimal and maximal descriptions in covering-based rough sets , 2019, Int. J. Approx. Reason..

[34]  Qinghua Hu,et al.  Data compression with homomorphism in covering information systems , 2011, Int. J. Approx. Reason..

[35]  Xiaohong Zhang,et al.  Soft set theoretical approach to pseudo-BCI algebras , 2018, J. Intell. Fuzzy Syst..

[36]  Przemyslaw Kazienko,et al.  Fuzzy multi-objective modeling of effectiveness and user experience in online advertising , 2016, Expert Syst. Appl..

[37]  Jianming Zhan,et al.  A novel type of soft rough covering and its application to multicriteria group decision making , 2019, Artificial Intelligence Review.

[38]  William Zhu,et al.  Applications of Bipartite Graphs and their Adjacency Matrices to Covering-based Rough Sets , 2017, Fundam. Informaticae.

[39]  Xiaohong Zhang,et al.  Constructive methods of rough approximation operators and multigranulation rough sets , 2016, Knowl. Based Syst..

[40]  Shahzad Faizi,et al.  Decision Making with Uncertainty Using Hesitant Fuzzy Sets , 2017, International Journal of Fuzzy Systems.

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

[42]  Chris Cornelis,et al.  Fuzzy neighborhood operators based on fuzzy coverings , 2017, Fuzzy Sets Syst..

[43]  William Zhu,et al.  Relationship among basic concepts in covering-based rough sets , 2009, Inf. Sci..

[44]  László T. Kóczy,et al.  Signatures: Definitions, operators and applications to fuzzy modelling , 2012, Fuzzy Sets Syst..

[45]  Urszula Wybraniec-Skardowska,et al.  Extensions and Intentions in the Ruogh Set Theory , 1998, Inf. Sci..

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

[47]  Xiaohong Zhang,et al.  New inclusion relation of neutrosophic sets with applications and related lattice structure , 2018, Int. J. Mach. Learn. Cybern..

[48]  Francesc Rosselló,et al.  On the coverings by tolerance classes , 2004, Inf. Sci..