An improved method to construct basic probability assignment based on the confusion matrix for classification problem

The determination of basic probability assignment (BPA) is a crucial issue in the application of Dempster-Shafer evidence theory. Classification is a process of determining the class label that a sample belongs to. In classification problem, the construction of BPA based on the confusion matrix has been studied. However, the existing methods do not make full use of the available information provided by the confusion matrix. In this paper, an improved method to construct the BPA is proposed based on the confusion matrix. The proposed method takes into account both the precision rate and the recall rate of each class. An illustrative case regarding the prediction of transmembrane protein topology is given to demonstrate the effectiveness of the proposed method.

[1]  Yong Deng,et al.  Generalized evidence theory , 2014, Applied Intelligence.

[2]  Hong-yu Zhang,et al.  Intuitionistic fuzzy multi-criteria decision-making method based on evidential reasoning , 2013, Appl. Soft Comput..

[3]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[4]  Cengiz Kahraman,et al.  Fuzzy Multicriteria Decision-Making: A Literature Review , 2015, Int. J. Comput. Intell. Syst..

[5]  Qi Liu,et al.  A HMM-based method to predict the transmembrane regions of \beta-barrel membrane proteins , 2003, Comput. Biol. Chem..

[6]  Yong Deng,et al.  Scoring hidden Markov models to discriminate -barrel membrane proteins , 2004, Comput. Biol. Chem..

[7]  Lin Wang,et al.  Evolutionary games on multilayer networks: a colloquium , 2015, The European Physical Journal B.

[8]  Sankaran Mahadevan,et al.  Evidential cognitive maps , 2012, Knowl. Based Syst..

[9]  Malcolm J. Beynon,et al.  Evidence-based modelling of strategic fit: An introduction to RCaRBS , 2010, Eur. J. Oper. Res..

[10]  Yin Zhong,et al.  Extended s-wave pairing symmetry on the triangular lattice heavy fermion system , 2015 .

[11]  A. Elofsson,et al.  Best α‐helical transmembrane protein topology predictions are achieved using hidden Markov models and evolutionary information , 2004 .

[12]  S. Kokubo,et al.  Insight into the so-called spatial reciprocity. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Hakan Altinçay,et al.  On the independence requirement in Dempster-Shafer theory for combining classifiers providing statistical evidence , 2006, Applied Intelligence.

[14]  S. Kokubo,et al.  Universal scaling for the dilemma strength in evolutionary games. , 2015, Physics of life reviews.

[15]  Philippe Smets,et al.  The Transferable Belief Model , 1994, Artif. Intell..

[16]  Ronald R. Yager Combining various types of belief structures , 2015, Inf. Sci..

[17]  Sankaran Mahadevan,et al.  Environmental impact assessment based on D numbers , 2014, Expert Syst. Appl..

[18]  Qiang Miao,et al.  Improved information fusion approach based on D-S evidence theory , 2008 .

[19]  G. von Heijne,et al.  Prediction of membrane-protein topology from first principles , 2008, Proceedings of the National Academy of Sciences.

[20]  Yong Deng,et al.  D-CFPR: D numbers extended consistent fuzzy preference relations , 2014, Knowl. Based Syst..

[21]  R. Yager On the dempster-shafer framework and new combination rules , 1987, Inf. Sci..

[22]  Arne Elofsson,et al.  OCTOPUS: improving topology prediction by two-track ANN-based preference scores and an extended topological grammar , 2008, Bioinform..

[23]  Francisco José Madrid-Cuevas,et al.  Shape from silhouette using Dempster-Shafer theory , 2010, Pattern Recognit..

[24]  Jeng-Ming Yih,et al.  An evaluation of airline service quality using the fuzzy weighted SERVQUAL method , 2011, Appl. Soft Comput..

[25]  S H White,et al.  MPtopo: A database of membrane protein topology , 2001, Protein science : a publication of the Protein Society.

[26]  Yaxin Bi,et al.  The combination of multiple classifiers using an evidential reasoning approach , 2008, Artif. Intell..

[27]  Brahim Chaib-draa,et al.  Computing equilibria in discounted dynamic games , 2015, Appl. Math. Comput..

[28]  Quan Pan,et al.  A new belief-based K-nearest neighbor classification method , 2013, Pattern Recognit..

[29]  Geoffrey I. Webb,et al.  Encyclopedia of Machine Learning , 2011, Encyclopedia of Machine Learning.

[30]  Quan Pan,et al.  A belief classification rule for imprecise data , 2013, Applied Intelligence.

[31]  Florentin Smarandache,et al.  Advances and Applications of DSmT for Information Fusion , 2004 .

[32]  Xi Liu,et al.  Group decision making with fuzzy linguistic preference relations via cooperative games method , 2015, Comput. Ind. Eng..

[33]  Attila Szolnoki,et al.  Evolution of public cooperation on interdependent networks: The impact of biased utility functions , 2012, ArXiv.

[34]  Jian-Bo Yang,et al.  Belief rule-based methodology for mapping consumer preferences and setting product targets , 2012, Expert Syst. Appl..

[35]  Thierry Denoeux,et al.  A k-nearest neighbor classification rule based on Dempster-Shafer theory , 1995, IEEE Trans. Syst. Man Cybern..

[36]  Yang Liu,et al.  An Improved Genetic Algorithm with Initial Population Strategy for Symmetric TSP , 2015 .

[37]  Jean Dezert,et al.  On the consistency of PCR6 with the averaging rule and its application to probability estimation , 2013, Proceedings of the 16th International Conference on Information Fusion.

[38]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[39]  Zied Elouedi,et al.  How to preserve the conflict as an alarm in the combination of belief functions? , 2013, Decis. Support Syst..

[40]  Xinyang Deng,et al.  Comprehensive consideration of strategy updating promotes cooperation in the prisoner’s dilemma game , 2014 .

[41]  F. Chan,et al.  IFSJSP: A novel methodology for the Job-Shop Scheduling Problem based on intuitionistic fuzzy sets , 2013 .

[42]  S. Mahadevan,et al.  Dependence Assessment in Human Reliability Analysis Using Evidence Theory and AHP , 2015, Risk analysis : an official publication of the Society for Risk Analysis.

[43]  Michael J. Pont,et al.  Application of Dempster-Shafer theory in condition monitoring applications: a case study , 2001, Pattern Recognit. Lett..

[44]  Xianfeng Fan,et al.  Fault diagnosis of machines based on D-S evidence theory. Part 2: Application of the improved D-S evidence theory in gearbox fault diagnosis , 2006, Pattern Recognit. Lett..

[45]  Attila Szolnoki,et al.  Rewarding evolutionary fitness with links between populations promotes cooperation , 2014, Journal of theoretical biology.

[46]  Otman A. Basir,et al.  Concept-based evidential reasoning for multimodal fusion in human-computer interaction , 2010, Appl. Soft Comput..

[47]  Yong Hu,et al.  An evidential game theory framework in multi-criteria decision making process , 2014, Appl. Math. Comput..

[48]  Shi Wen-kang,et al.  Combining belief functions based on distance of evidence , 2004 .

[49]  Zhen Wang,et al.  A belief-based evolutionarily stable strategy , 2014, Journal of theoretical biology.

[50]  Galina L. Rogova,et al.  Combining the results of several neural network classifiers , 1994, Neural Networks.

[51]  Adam Godzik,et al.  Cd-hit: a fast program for clustering and comparing large sets of protein or nucleotide sequences , 2006, Bioinform..

[52]  Xinyang Deng,et al.  Impact of Roles Assignation on Heterogeneous Populations in Evolutionary Dictator Game , 2014, Scientific Reports.

[53]  Günther Palm,et al.  Using Dempster-Shafer Theory in MCF Systems to Reject Samples , 2005, Multiple Classifier Systems.

[54]  Erik Blasch,et al.  Information fusion with belief functions: A comparison of proportional conflict redistribution PCR5 and PCR6 rules for networked sensors , 2015, 2015 18th International Conference on Information Fusion (Fusion).

[55]  Adam Krzyżak,et al.  Methods of combining multiple classifiers and their applications to handwriting recognition , 1992, IEEE Trans. Syst. Man Cybern..

[56]  Xinyang Deng,et al.  Supplier selection using AHP methodology extended by D numbers , 2014, Expert Syst. Appl..

[57]  Michael J. Pont,et al.  Improving the performance of CMFD applications using multiple classifiers and a fusion framework , 2003 .

[58]  D. Dubois,et al.  A set-theoretic view of belief functions: Logical operations and approximations by fuzzy sets , 1986 .

[59]  Reza Ebrahimpour,et al.  Combining complementary information sources in the Dempster-Shafer framework for solving classification problems with imperfect labels , 2012, Knowl. Based Syst..

[60]  Reza Ebrahimpour,et al.  Knitted fabric defect classification for uncertain labels based on Dempster-Shafer theory of evidence , 2011, Expert Syst. Appl..

[61]  Yong Deng A Threat Assessment Model under Uncertain Environment , 2015 .

[62]  Xinyang Deng,et al.  An improved operator of combination with adapted conflict , 2014, Ann. Oper. Res..

[63]  Éloi Bossé,et al.  Robust combination rules for evidence theory , 2009, Inf. Fusion.

[64]  Sankaran Mahadevan,et al.  Parameter estimation based on interval-valued belief structures , 2014, Eur. J. Oper. Res..

[65]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[66]  Zhen Wang,et al.  Impact of Social Punishment on Cooperative Behavior in Complex Networks , 2013, Scientific Reports.

[67]  Attila Szolnoki,et al.  Interdependent network reciprocity in evolutionary games , 2013, Scientific Reports.

[68]  Catherine K. Murphy Combining belief functions when evidence conflicts , 2000, Decis. Support Syst..

[69]  Yong Hu,et al.  TOPPER: Topology Prediction of Transmembrane Protein Based on Evidential Reasoning , 2013, TheScientificWorldJournal.

[70]  Mohamed A. Deriche,et al.  A New Technique for Combining Multiple Classifiers using The Dempster-Shafer Theory of Evidence , 2002, J. Artif. Intell. Res..