PF-TOPSIS method based on CPFRS models: An application to unconventional emergency events

Abstract To improve the utilization of rough sets, some novel uncertain models via rough sets have been appeared. Although many rough set models can only handle some intuitionistic fuzzy data, they can’t handle the data in the Pythagorean environment. For effectively solving the complicated problems in the Pythagorean environment, by applying the notion of Pythagorean fuzzy set (PFS) theory which is a natural generalization of intuitionistic fuzzy set (IFS) theory together with combining the covering-based rough set models and fuzzy rough set models, we introduce the concept of covering-based Pythagorean fuzzy rough set (CPFRS) models via Pythagorean fuzzy β -neighborhoods. Particularly, two kinds of uncertain degrees of our extended models are investigated. We find that our proposed models can effectively handle the complex data in the Pythagoras environment for the theoretical analysis with CPFRS models. We set forth two different Pythagorean fuzzy TOPSIS methodologies to deal with the multi-attribute decision-making (MADM) problem by taking the advantage of the CPFRS models. Finally, we compare and analyze the results of the two methods with two existing through a practical example.

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

[2]  Liwen Ma.  Some twin approximation operators on covering approximation spaces , 2015, Int. J. Approx. Reason..

[3]  Guijun Wang,et al.  TOPSIS approach for multi-attribute decision making problems based on n-intuitionistic polygonal fuzzy sets description , 2018, Comput. Ind. Eng..

[4]  Luis Martínez-López,et al.  Hesitant linguistic expression soft sets: Application to group decision making , 2019, Comput. Ind. Eng..

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

[6]  Ying Sai,et al.  A comparison of two types of rough sets induced by coverings , 2009, Int. J. Approx. Reason..

[7]  Xindong Peng,et al.  Approaches to Pythagorean Fuzzy Stochastic Multi‐criteria Decision Making Based on Prospect Theory and Regret Theory with New Distance Measure and Score Function , 2017, Int. J. Intell. Syst..

[8]  Yiyu Yao,et al.  Three-way decisions with probabilistic rough sets , 2010, Inf. Sci..

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

[10]  Ronald R. Yager,et al.  Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making , 2005, Int. J. Syst. Sci..

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

[12]  Vicenç Torra,et al.  Decomposition theorems and extension principles for hesitant fuzzy sets , 2018, Inf. Fusion.

[13]  Wei-Zhi Wu,et al.  Constructive and axiomatic approaches of fuzzy approximation operators , 2004, Inf. Sci..

[14]  Wanlu Li,et al.  On measurements of covering rough sets based on granules and evidence theory , 2015, Inf. Sci..

[15]  Chen-Tung Chen,et al.  Extensions of the TOPSIS for group decision-making under fuzzy environment , 2000, Fuzzy Sets Syst..

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

[17]  Xia Xiao,et al.  Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes , 2017, Int. J. Approx. Reason..

[18]  Omolbanin Yazdanbakhsh,et al.  On Pythagorean and Complex Fuzzy Set Operations , 2016, IEEE Transactions on Fuzzy Systems.

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

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

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

[22]  Xiaonan Li,et al.  Heterogeneous multigranulation fuzzy rough set-based multiple attribute group decision making with heterogeneous preference information , 2018, Comput. Ind. Eng..

[23]  Bing Huang,et al.  An intuitionistic fuzzy graded covering rough set , 2016, Knowl. Based Syst..

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

[25]  Ma Weimin,et al.  An approach to evaluation of emergency plans for unconventional emergency events based on soft fuzzy rough set , 2016 .

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

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

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

[29]  Kai Zhang,et al.  Fuzzy β-covering based (I, T)-fuzzy rough set models and applications to multi-attribute decision-making , 2019, Comput. Ind. Eng..

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

[31]  Xiaolu Zhang,et al.  A Novel Approach Based on Similarity Measure for Pythagorean Fuzzy Multiple Criteria Group Decision Making , 2016, Int. J. Intell. Syst..

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

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

[34]  Qionghai Dai,et al.  A novel approach to fuzzy rough sets based on a fuzzy covering , 2007, Inf. Sci..

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

[36]  Zeshui Xu,et al.  The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets , 2017, Appl. Soft Comput..

[37]  Xiao Zhang,et al.  Evidence-theory-based numerical algorithms of attribute reduction with neighborhood-covering rough sets , 2014, Int. J. Approx. Reason..

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

[39]  William Zhu,et al.  Relationship between generalized rough sets based on binary relation and covering , 2009, Inf. Sci..

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

[41]  F. Chiclana,et al.  Strategic weight manipulation in multiple attribute decision making , 2018 .

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

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

[44]  Luis Martínez-López,et al.  Improving decision making approaches based on fuzzy soft sets and rough soft sets , 2018, Appl. Soft Comput..

[45]  Duoqian Miao,et al.  Three-way attribute reducts , 2017, Int. J. Approx. Reason..

[46]  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..

[47]  Rashed Khanjani Shiraz,et al.  Selecting a model for generating OWA operator weights in MAGDM problems by maximum entropy membership function , 2018, Comput. Ind. Eng..

[48]  Anna Maria Radzikowska,et al.  A comparative study of fuzzy rough sets , 2002, Fuzzy Sets Syst..

[49]  Edmundas Kazimieras Zavadskas,et al.  Fuzzy multiple criteria decision-making techniques and applications - Two decades review from 1994 to 2014 , 2015, Expert Syst. Appl..

[50]  Ping Zhu,et al.  Covering rough sets based on neighborhoods: An approach without using neighborhoods , 2009, Int. J. Approx. Reason..

[51]  Yejun Xu,et al.  A two-stage consensus method for large-scale multi-attribute group decision making with an application to earthquake shelter selection , 2018, Comput. Ind. Eng..

[52]  Yiyu Yao,et al.  Three-Way Decisions and Cognitive Computing , 2016, Cognitive Computation.

[53]  Bing Huang,et al.  Intuitionistic fuzzy multigranulation rough sets , 2014, Inf. Sci..

[54]  W. Zakowski.  APPROXIMATIONS IN THE SPACE (U,π) , 1983 .

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

[56]  Xindong Peng,et al.  Pythagorean fuzzy set: state of the art and future directions , 2017, Artificial Intelligence Review.

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

[58]  Harish Garg,et al.  Generalized Pythagorean Fuzzy Geometric Aggregation Operators Using Einstein t‐Norm and t‐Conorm for Multicriteria Decision‐Making Process , 2017, Int. J. Intell. Syst..

[59]  Zeshui Xu,et al.  Dynamic intuitionistic fuzzy multi-attribute decision making , 2008, Int. J. Approx. Reason..

[60]  Ronald R. Yager,et al.  Properties and Applications of Pythagorean Fuzzy Sets , 2016, Imprecision and Uncertainty in Information Representation and Processing.

[61]  Jianming Zhan,et al.  Covering-based intuitionistic fuzzy rough sets and applications in multi-attribute decision-making , 2018, Artificial Intelligence Review.