A λ-rough set model and its applications with TOPSIS method to decision making

Abstract As an extension of classical rough sets, the concept of λ -rough sets is introduced in information systems. We put forward the notions of λ -indiscernibility relation and λ -approximation space in information systems. The properties of roughness for λ -approximation space are explored. To illustrate the usefulness of λ -approximation spaces, we provide two approaches to deal with a special type of multiattribute decision-making problems. By comparative analysis, the ranking results based on two different approaches have a high consensus. Although there are some different ranking results of these two methods, the optimal selected alternative is the same.

[1]  Z. Pawlak,et al.  Decision analysis using rough sets , 1994 .

[2]  L. Zadeh,et al.  Data mining, rough sets and granular computing , 2002 .

[3]  Taho Yang,et al.  Solving a multiresponse simulation-optimization problem with discrete variables using a multiple-attribute decision-making method , 2005, Math. Comput. Simul..

[4]  Guoyin Wang,et al.  Extension of rough set under incomplete information systems , 2002, 2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291).

[5]  Qingguo Li,et al.  Characteristic matrixes-based knowledge reduction in dynamic covering decision information systems , 2015, Knowl. Based Syst..

[6]  Dug Hun Hong,et al.  Multicriteria fuzzy decision-making problems based on vague set theory , 2000, Fuzzy Sets Syst..

[7]  Qingguo Li,et al.  Reduction about approximation spaces of covering generalized rough sets , 2010, Int. J. Approx. Reason..

[8]  Zhoujun Li,et al.  A novel variable precision (θ, σ)-fuzzy rough set model based on fuzzy granules , 2014, Fuzzy Sets Syst..

[9]  Z. Pawlak.  Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[10]  Daisuke Yamaguchi,et al.  Attribute dependency functions considering data efficiency , 2009, Int. J. Approx. Reason..

[11]  Saint John Walker.  Big Data: A Revolution That Will Transform How We Live, Work, and Think , 2014 .

[12]  Li Jinlong,et al.  The group decision-making rules based on rough sets on large scale engineering emergency☆ , 2012 .

[13]  Tzung-Pei Hong,et al.  Learning cross-level certain and possible rules by rough sets , 2008, Expert Syst. Appl..

[14]  William Zhu,et al.  Rough matroids based on relations , 2013, Inf. Sci..

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

[16]  Z. Pawlak,et al.  Rough set approach to multi-attribute decision analysis , 1994 .

[17]  Alan Pearman,et al.  Models and Methods in Multiple Criteria Decision Making , 1991 .

[18]  Yin-Feng Xu,et al.  Multiple attribute consensus rules with minimum adjustments to support consensus reaching , 2014, Knowl. Based Syst..

[19]  Marzena Kryszkiewicz,et al.  Rough Set Approach to Incomplete Information Systems , 1998, Inf. Sci..

[20]  Salvatore Greco,et al.  Rough sets theory for multicriteria decision analysis , 2001, Eur. J. Oper. Res..

[21]  Keith W. Hipel,et al.  A Decision Rule Aggregation Approach to Multiple Criteria-Multiple Participant Sorting , 2012 .

[22]  E. Stanley Lee,et al.  An extension of TOPSIS for group decision making , 2007, Math. Comput. Model..

[23]  Andrzej Skowron,et al.  Attributes and rough properties in information systems , 1988, Int. J. Approx. Reason..

[24]  Jeremy Ginsberg,et al.  Detecting influenza epidemics using search engine query data , 2009, Nature.

[25]  Tzung-Pei Hong,et al.  Learning rules from incomplete training examples by rough sets , 2002, Expert Syst. Appl..

[26]  Jiye Liang,et al.  International Journal of Approximate Reasoning Multigranulation Decision-theoretic Rough Sets , 2022 .

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

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

[29]  Andrzej Skowron,et al.  Rough set methods in feature selection and recognition , 2003, Pattern Recognit. Lett..

[30]  Hsu-Shih Shih,et al.  A hybrid MCDM model for strategic vendor selection , 2006, Math. Comput. Model..

[31]  Xiao-Jun Zeng,et al.  Core-generating approximate minimum entropy discretization for rough set feature selection in pattern classification , 2011, Int. J. Approx. Reason..

[32]  Yuhua Qian,et al.  Multigranulation fuzzy rough set over two universes and its application to decision making , 2017, Knowl. Based Syst..

[33]  Cengiz Kahraman,et al.  Information systems outsourcing decisions using a group decision-making approach , 2009, Eng. Appl. Artif. Intell..

[34]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[35]  Nick Cercone,et al.  Integrating rough set theory and medical applications , 2008, Appl. Math. Lett..

[36]  Mingjie Cai,et al.  Related families-based attribute reduction of dynamic covering decision information systems , 2018, Knowl. Based Syst..

[37]  Yiyu Yao,et al.  Quantitative rough sets based on subsethood measures , 2014, Inf. Sci..

[38]  Ching-Lai Hwang,et al.  Multiple Attribute Decision Making: Methods and Applications - A State-of-the-Art Survey , 1981, Lecture Notes in Economics and Mathematical Systems.

[39]  Maite López-Sánchez,et al.  Rough set based approaches to feature selection for Case-Based Reasoning classifiers , 2011, Pattern Recognit. Lett..

[40]  Min-Soo Kim,et al.  Decision-making model for early diagnosis of congestive heart failure using rough set and decision tree approaches , 2012, J. Biomed. Informatics.

[41]  Salvatore Greco,et al.  Rough Set Based Decision Support , 2005 .

[42]  Yiyu Yao,et al.  Data mining using extensions of the rough set model , 1998, KDD 1998.

[43]  Witold Pedrycz,et al.  Rough sets in distributed decision information systems , 2016, Knowl. Based Syst..

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

[45]  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..

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

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

[48]  Roman Slowinski,et al.  Rough Set Learning of Preferential Attitude in Multi-Criteria Decision Making , 1993, ISMIS.

[49]  Shouhong Wang,et al.  Discovering patterns of missing data in survey databases: An application of rough sets , 2009, Expert Syst. Appl..

[50]  Witold Pedrycz,et al.  Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making , 2015, Appl. Soft Comput..

[51]  Chun-Che Huang,et al.  Rough set approach to case-based reasoning application , 2004, Expert Syst. Appl..

[52]  Gwo-Hshiung Tzeng,et al.  Combining grey relation and TOPSIS concepts for selecting an expatriate host country , 2004, Math. Comput. Model..

[53]  Morteza Yazdani,et al.  A state-of the-art survey of TOPSIS applications , 2012, Expert Syst. Appl..

[54]  Ralph Schroeder,et al.  Causation, Correlation, and Big Data in Social Science Research , 2015 .

[55]  Qinghua Hu,et al.  Communication Between Information Systems Using Fuzzy Rough Sets , 2013, IEEE Transactions on Fuzzy Systems.