Uncertainty Measurement for Fuzzy Set-Valued Data

Uncertainty measurement (UM) can offer new visual angle for data analysis. A fuzzy set-valued information system (FSVIS) indicates an information system (IS) where its information values are fuzzy sets. This article investigates UM for fuzzy set-valued data based on Chebyshev distance. First, the distance between information values is founded in a given subsystem. After that, the tolerance relation induced by this subsystem is obtained by means of this distance. Moreover, the information structure of this subsystem is proposed. Next, the uncertainty of a FSVIS are measured. Eventually, to show the feasibility of the proposed measures, effectiveness analysis is carried out from a statistical view. The obtained outcomes may be helpful for comprehending the nature of uncertainty in a FSVIS.

[1]  Yiyu Yao,et al.  Probabilistic approaches to rough sets , 2003, Expert Syst. J. Knowl. Eng..

[2]  Jianhua Dai,et al.  Entropy measures and granularity measures for set-valued information systems , 2013, Inf. Sci..

[3]  Theresa Beaubouef,et al.  Information-Theoretic Measures of Uncertainty for Rough Sets and Rough Relational Databases , 1998, Inf. Sci..

[4]  Gangqiang Zhang,et al.  Information Structures and Uncertainty Measures in an Incomplete Probabilistic Set-Valued Information System , 2019, IEEE Access.

[5]  Qinghua Hu,et al.  Fuzzy information systems and their homomorphisms , 2014, Fuzzy Sets Syst..

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

[7]  Chris Cornelis,et al.  Attribute selection with fuzzy decision reducts , 2010, Inf. Sci..

[8]  Witold Pedrycz,et al.  Selecting Discrete and Continuous Features Based on Neighborhood Decision Error Minimization , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[10]  Yu Xue,et al.  Measures of uncertainty for neighborhood rough sets , 2017, Knowl. Based Syst..

[11]  Theresa Beaubouef,et al.  Fuzzy rough set techniques for uncertainty processing in a relational database , 2000, Int. J. Intell. Syst..

[12]  Andrzej Skowron,et al.  Rough sets and Boolean reasoning , 2007, Inf. Sci..

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

[14]  Wen-Xiu Zhang,et al.  Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems , 2009, Appl. Soft Comput..

[15]  Ivo Düntsch,et al.  Uncertainty Measures of Rough Set Prediction , 1998, Artif. Intell..

[16]  Wei-Zhi Wu,et al.  Information structures and uncertainty measures in a fully fuzzy information system , 2018, Int. J. Approx. Reason..

[17]  Jiye Liang,et al.  Information entropy, rough entropy and knowledge granulation in incomplete information systems , 2006, Int. J. Gen. Syst..

[18]  Jiye Liang,et al.  The Information Entropy, Rough Entropy And Knowledge Granulation In Rough Set Theory , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[19]  Todd Schenk.  Uncertain decision-making , 2017 .

[20]  Gangqiang Zhang,et al.  Uncertainty Measurement for a Fuzzy Relation Information System , 2019, IEEE Transactions on Fuzzy Systems.

[21]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[22]  M. J. Wierman,et al.  MEASURING UNCERTAINTY IN ROUGH SET THEORY , 1999 .

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

[24]  L. A. ZADEH,et al.  The concept of a linguistic variable and its application to approximate reasoning - I , 1975, Inf. Sci..

[25]  Yanyong Guan,et al.  Set-valued information systems , 2006, Inf. Sci..

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

[28]  Xiaofeng Liu,et al.  Information structures in a covering information system , 2020, Inf. Sci..

[29]  Roman Słowiński,et al.  Sequential covering rule induction algorithm for variable consistency rough set approaches , 2011, Inf. Sci..

[30]  Gianpiero Cattaneo,et al.  Information Entropy and Granulation Co-Entropy of Partitions and Coverings: A Summary , 2009, Trans. Rough Sets.

[31]  Marzena Kryszkiewicz,et al.  Rules in Incomplete Information Systems , 1999, Inf. Sci..

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

[33]  Pierpaolo D'Urso,et al.  Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review , 2017, Inf. Sci..

[34]  Gangqiang Zhang,et al.  Uncertainty measurement for a covering information system , 2018, Soft Computing.

[35]  Didier Dubois,et al.  Rough Sets, Coverings and Incomplete Information , 2011, Fundam. Informaticae.