Novel classes of fuzzy soft $$\beta $$β-coverings-based fuzzy rough sets with applications to multi-criteria fuzzy group decision making

In this article, we put forward the concepts of fuzzy soft $$\beta $$β-minimal descriptions and fuzzy soft $$\beta $$β-maximal descriptions and construct four types of fuzzy soft $$\beta $$β-neighborhoods. Secondly, we define five kinds of fuzzy soft $$\beta $$β-coverings-based fuzzy rough sets and investigate the relationships among them. Furthermore, we investigate under what conditions two different fuzzy soft $$\beta $$β-coverings induce the same lower (upper) approximation operators. Then, we introduce the concepts of intersection and union reducible elements. Finally, we put forward the algorithms with respect to the first and the fifth types of fuzzy soft $$\beta $$β-coverings-based fuzzy rough sets, respectively. Through comparison, we find that although these two models are different, the obtained results are the same and the complexity of the algorithm based on the fifth type model is easier than the one based on the first model.

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

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

[3]  Bao Qing Hu,et al.  Topological and lattice structures of L-fuzzy rough sets determined by lower and upper sets , 2013, Inf. Sci..

[4]  Fei-Yue Wang,et al.  Reduction and axiomization of covering generalized rough sets , 2003, Inf. Sci..

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

[6]  Xiaonan Li,et al.  Linguistic value soft set-based approach to multiple criteria group decision-making , 2017, Appl. Soft Comput..

[7]  William Zhu,et al.  Generalized rough sets based on relations , 2007, Inf. Sci..

[8]  Naime Tozlu,et al.  A Topological Approach to Soft Covering Approximation Space , 2015, 1503.07896.

[9]  Jianming Zhan,et al.  Reviews on decision making methods based on (fuzzy) soft sets and rough soft sets , 2015, J. Intell. Fuzzy Syst..

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

[11]  Muhammad Irfan Ali,et al.  Another approach to soft rough sets , 2013, Knowl. Based Syst..

[12]  Muhammad Irfan Ali,et al.  Representation of graphs based on neighborhoods and soft sets , 2016, International Journal of Machine Learning and Cybernetics.

[13]  Yiyu Yao,et al.  Relational Interpretations of Neigborhood Operators and Rough Set Approximation Operators , 1998, Inf. Sci..

[14]  Wen-Xiu Zhang,et al.  Measuring roughness of generalized rough sets induced by a covering , 2007, Fuzzy Sets Syst..

[15]  Tao Feng,et al.  The reduction and fusion of fuzzy covering systems based on the evidence theory , 2012, Int. J. Approx. Reason..

[16]  Chris Cornelis,et al.  Neighborhood operators for covering-based rough sets , 2016, Inf. Sci..

[17]  Qingguo Li,et al.  The relationship between L-fuzzy rough set and L-topology , 2011, Fuzzy Sets Syst..

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

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

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

[21]  Naime Tozlu,et al.  An application of multicriteria group decision making by soft covering based rough sets , 2015 .

[22]  Bao Qing Hu,et al.  Generalized interval-valued fuzzy variable precision rough sets determined by fuzzy logical operators , 2014, Int. J. Gen. Syst..

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

[24]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[25]  Naime Tozlu,et al.  Soft Covering Based Rough Sets and Their Application , 2014, TheScientificWorldJournal.

[26]  Bin Yang,et al.  A fuzzy covering-based rough set model and its generalization over fuzzy lattice , 2016, Inf. Sci..

[27]  Jianming Zhan,et al.  Certain types of soft coverings based rough sets with applications , 2019, Int. J. Mach. Learn. Cybern..

[28]  Jianhua Dai,et al.  Uncertainty measurement for incomplete interval-valued information systems based on α-weak similarity , 2017, Knowl. Based Syst..

[29]  Yong Yang,et al.  Erratum to "A note on soft sets, rough soft sets and fuzzy soft sets" [Appl. Soft Comput. 11 (2011) 3329-3332 , 2011, Appl. Soft Comput..

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

[31]  Wen-Xiu Zhang,et al.  An axiomatic characterization of a fuzzy generalization of rough sets , 2004, Inf. Sci..

[32]  Yiyu Yao,et al.  Covering based rough set approximations , 2012, Inf. Sci..

[33]  Jianming Zhan,et al.  Fuzzy soft $$\beta$$β-covering based fuzzy rough sets and corresponding decision-making applications , 2019, Int. J. Mach. Learn. Cybern..

[34]  Jianming Zhan,et al.  A STUDY ON Z-SOFT ROUGH FUZZY SEMIGROUPS AND ITS DECISION-MAKING , 2017 .

[35]  Qinghua Hu,et al.  Communication between information systems with covering based rough sets , 2012, Inf. Sci..

[36]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[37]  José Carlos Rodriguez Alcantud,et al.  Some formal relationships among soft sets, fuzzy sets, and their extensions , 2016, Int. J. Approx. Reason..

[38]  Guoqiu Wen,et al.  Soft coverings and their parameter reductions , 2015, Appl. Soft Comput..

[39]  José Carlos Rodriguez Alcantud,et al.  A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set , 2016, Inf. Fusion.

[40]  Daniel S. Yeung,et al.  Approximations and reducts with covering generalized rough sets , 2008, Comput. Math. Appl..

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

[42]  Yee Leung,et al.  Generalized fuzzy rough approximation operators based on fuzzy coverings , 2008, Int. J. Approx. Reason..

[43]  Yiyu Yao,et al.  A semantically sound approach to Pawlak rough sets and covering-based rough sets , 2016, Int. J. Approx. Reason..

[44]  Liwen Ma,et al.  On some types of neighborhood-related covering rough sets , 2012, Int. J. Approx. Reason..

[45]  Wei-Zhi Wu,et al.  Maximal-Discernibility-Pair-Based Approach to Attribute Reduction in Fuzzy Rough Sets , 2018, IEEE Transactions on Fuzzy Systems.

[46]  William Zhu,et al.  Topological approaches to covering rough sets , 2007, Inf. Sci..

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

[48]  Jianming Zhan,et al.  A survey of parameter reduction of soft sets and corresponding algorithms , 2019, Artificial Intelligence Review.

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

[50]  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..

[51]  Bijan Davvaz,et al.  Soft sets combined with fuzzy sets and rough sets: a tentative approach , 2010, Soft Comput..

[52]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[53]  Chris Cornelis,et al.  A comprehensive study of fuzzy covering-based rough set models: Definitions, properties and interrelationships , 2017, Fuzzy Sets Syst..

[54]  Muhammad Irfan Ali,et al.  A note on soft sets, rough soft sets and fuzzy soft sets , 2011, Appl. Soft Comput..

[55]  Young Bae Jun,et al.  Soft sets and soft rough sets , 2011, Inf. Sci..

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

[57]  J. Alcantud.  Revealed indifference and models of choice behavior , 2002 .