Measures of uncertainty based on Gaussian kernel for a fully fuzzy information system

Abstract The uncertainty of information plays an important role in practical applications, so how to capture the uncertainty of information systems becomes more and more popular. Uncertainty measures can supply new viewpoints for processing information systems, and they can help us in disclosing the substantive characteristics of information. Fuzzy information systems are important research objects in artificial intelligence. As a special kind of fuzzy information system, fully fuzzy information system (FFIS) is worth studying. This article is devoted to search indicators for measuring uncertainty in a FFIS according to fuzzy information structures in view of Gaussian kernel, and the fuzzy information structures can be viewed as granular structures under granular computing. Firstly, by employing Gaussian kernel for calculating similarities among objects in a FFIS, the fuzzy T c o s -similarity relation is obtained. Then, based on this relation, fuzzy information structures in a FFIS are introduced. Next, according to the information structures, granulation measure of a given FFIS is advanced. Moreover, entropy measure is also considered for a given FFIS. Finally, two numerical experiments are conducted to interpret the realistic significance and potential applications for measuring uncertainty in a FFIS. Theoretical research, numerical experiments and validity analysis make clear that the proposed measures are efficacious and applicable for a FFIS.

[1]  Ling Shao,et al.  A rapid learning algorithm for vehicle classification , 2015, Inf. Sci..

[2]  Jiye Liang,et al.  Fuzzy Granular Structure Distance , 2015, IEEE Transactions on Fuzzy Systems.

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

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

[5]  Bernhard Moser,et al.  On Representing and Generating Kernels by Fuzzy Equivalence Relations , 2006, J. Mach. Learn. Res..

[6]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[7]  Matthew X. Yao,et al.  Granularity measures and complexity measures of partition-based granular structures , 2019, Knowl. Based Syst..

[8]  Yiyu Yao,et al.  A measurement theory view on the granularity of partitions , 2012, Inf. Sci..

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

[10]  Guoyin Wang,et al.  The uncertainty of probabilistic rough sets in multi-granulation spaces , 2016, Int. J. Approx. Reason..

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

[12]  Witold Pedrycz,et al.  Gaussian kernel based fuzzy rough sets: Model, uncertainty measures and applications , 2010, Int. J. Approx. Reason..

[13]  Hong Wang,et al.  Entropy measures and granularity measures for interval and set-valued information systems , 2016, Soft Comput..

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

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

[16]  Zeshui Xu,et al.  Entropy Measures for Probabilistic Hesitant Fuzzy Information , 2019, IEEE Access.

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

[18]  Duoqian Miao,et al.  Three-layer granular structures and three-way informational measures of a decision table , 2017, Inf. Sci..

[19]  Ying Han,et al.  Bipolar-Valued Rough Fuzzy Set and Its Applications to the Decision Information System , 2015, IEEE Transactions on Fuzzy Systems.

[20]  Jiye Liang,et al.  Information Granularity in Fuzzy Binary GrC Model , 2011, IEEE Transactions on Fuzzy Systems.

[21]  Yuhui Zheng,et al.  Image segmentation by generalized hierarchical fuzzy C-means algorithm , 2015, J. Intell. Fuzzy Syst..

[22]  Qinghua Hu,et al.  Fuzzy Probabilistic Approximation Spaces and Their Information Measures , 2006, IEEE Trans. Fuzzy Syst..

[23]  Gangqiang Zhang,et al.  A multi-granulation decision-theoretic rough set method for distributed fc-decision information systems: An application in medical diagnosis , 2017, Appl. Soft Comput..

[24]  Witold Pedrycz,et al.  Granular representation and granular computing with fuzzy sets , 2012, Fuzzy Sets Syst..

[25]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[26]  Xu Weihua,et al.  Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems , 2009 .

[27]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[28]  Qinghua Hu,et al.  Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation , 2007, Pattern Recognit..

[29]  Jianhua Dai,et al.  Attribute selection based on information gain ratio in fuzzy rough set theory with application to tumor classification , 2013, Appl. Soft Comput..

[30]  Jianhua Dai,et al.  Uncertainty measurement for interval-valued information systems , 2013, Inf. Sci..

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

[32]  Jianhua Dai,et al.  Approximations and uncertainty measures in incomplete information systems , 2012, Inf. Sci..

[33]  Guoyin Wang,et al.  A Novel Three-way decision model with decision-theoretic rough sets using utility theory , 2018, Knowl. Based Syst..

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

[35]  Shi-Jinn Horng,et al.  Dynamic variable precision rough set approach for probabilistic set-valued information systems , 2017, Knowl. Based Syst..

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

[37]  Mingjie Cai,et al.  Incremental approaches to updating reducts under dynamic covering granularity , 2019, Knowl. Based Syst..

[38]  Shu Yang,et al.  Bilinear Analysis for Kernel Selection and Nonlinear Feature Extraction , 2007, IEEE Transactions on Neural Networks.

[39]  Guoyin Wang,et al.  Fuzzy equivalence relation and its multigranulation spaces , 2016, Inf. Sci..

[40]  Jiye Liang,et al.  A fuzzy multigranulation decision-theoretic approach to multi-source fuzzy information systems , 2016, Knowl. Based Syst..

[41]  Yanqing Zhang,et al.  Constructive granular systems with universal approximation and fast knowledge discovery , 2005, IEEE Transactions on Fuzzy Systems.

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

[43]  Qingguo Li,et al.  A characterization of novel rough fuzzy sets of information systems and their application in decision making , 2019, Expert Syst. Appl..

[44]  Qinghua Zhang,et al.  Measuring Uncertainty of Probabilistic Rough Set Model From Its Three Regions , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[45]  Bingyang Li,et al.  Feature Selection for Partially Labeled Data Based on Neighborhood Granulation Measures , 2019, IEEE Access.

[46]  Qinghua Hu,et al.  Neighbor Inconsistent Pair Selection for Attribute Reduction by Rough Set Approach , 2018, IEEE Transactions on Fuzzy Systems.

[47]  Didier Dubois,et al.  The role of fuzzy sets in decision sciences: Old techniques and new directions , 2011, Fuzzy Sets Syst..

[48]  Martin Stepnicka,et al.  Implication-based models of monotone fuzzy rule bases , 2013, Fuzzy Sets Syst..

[49]  Bin Yang,et al.  Communication between fuzzy information systems using fuzzy covering-based rough sets , 2018, Int. J. Approx. Reason..

[50]  Wei Li,et al.  Granule structures, distances and measures in neighborhood systems , 2019, Knowl. Based Syst..

[51]  Jianhua Dai,et al.  An Uncertainty Measure for Incomplete Decision Tables and Its Applications , 2013, IEEE Transactions on Cybernetics.

[52]  Bernhard Moser,et al.  On the T , 2006, Fuzzy Sets Syst..

[53]  Bin Gu,et al.  Incremental Support Vector Learning for Ordinal Regression , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[54]  Lotfi A. Zadeh,et al.  Fuzzy sets and information granularity , 1996 .

[55]  Xiaofeng Liu,et al.  Measures of uncertainty for a distributed fully fuzzy information system , 2019, Int. J. Gen. Syst..

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

[57]  Lin Sun,et al.  Feature selection using neighborhood entropy-based uncertainty measures for gene expression data classification , 2019, Inf. Sci..

[58]  C. A. Murthy,et al.  Roughness and granularity measures using Hausdorff metric: a new approach , 2016, Int. J. Gen. Syst..