Interval Certitude Rule Base Inference Method using the Evidential Reasoning

Authors

  • Liuqian Jin Chongqing University of Posts and Telecommunications
  • Xin Fang Chongqing Technology and Business University

Keywords:

interval certitude rule, knowledge representation, uncertainty inference, evidential reasoning.

Abstract

Development of rule-based systems is an important research area for artificial intelligence and decision making, as rule base is one of the most general purpose forms for expressing human knowledge. In this paper, a new rule-based representation and its inference method based on evidential reasoning are presented based on operational research and fuzzy set theory. In this rule base, the uncertainties of human knowledge and human judgment are designed with interval certitude degrees which are embedded in the antecedent terms and consequent terms. The knowledge representation and inference framework offer an improvement of the recently developed rule base inference method, and the evidential reasoning approach is still applied to the rule fusion. It is noteworthy that the uncertainties will be defined and modeled using interval certitude degrees. In the end, an illustrative example is provided to illustrate the proposed knowledge representation and inference method as well as demonstrate its effectiveness by comparing with some existing approaches.

References

Aczel J., Saaty T.L. (1983); Procedures for synthesizing ratio judgments, Journal of Math- ematical Psychology, 27(2), 93-102, 1983.

Barrenechea E., Fernandez J., Pagola M. et al (2014); Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Application to decision making, Knowledge-Based Systems, 58, 33-44, 2014. https://doi.org/10.1016/j.knosys.2013.10.002

Bielza C., Robles V., Larranaga P. (2011); Regularized logistic regression without a penalty term: an application to cancer classification with microarray data, Expert Systems with Applications, 38(5), 5110-5118, 2011. https://doi.org/10.1016/j.eswa.2010.09.140

Cataron A., Andonie R., Chueh Y. (2013); Asymptotically unbiased estimator of the informational energy with kNN, International Journal of Computers Communications & Control, 8(5), 689-698, 2013. https://doi.org/10.15837/ijccc.2013.5.643

Calzada A., Liu J., Wang H.,Kashyap A. (2013); A GIS-based spatial decision support tool based on extended belief rule-based inference methodology, Eureka-2013 Fourth International Workshop Proceedings, 388-395, 2013.

Chao X.R., Peng Y., Kou G. (2017); A similarity measure-based optimization model for group decision making with multiplicative and fuzzy preference relations, International Journal of Computers Communications & Control, 12(1), 26-40, 2017.

Chen J.N., Huang H.K., Tian F.Z. et al. (2008); A selective bayes classifier for classifying incomplete data based on gain ratio, Knowledge-Based Systems, 21(7), 530-534, 2008. https://doi.org/10.1016/j.knosys.2008.03.013

Chin K.S., Yang J.B., Guo M. et al. (2009); An evidential-reasoning-interval-based method for new product design assessment, IEEE Transactions on Engineering Management, 56(1), 142-156, 2009. https://doi.org/10.1109/TEM.2008.2009792

Conde E., de la Paz Rivera Perez M. (2010); A linear optimization problem to derive relative weights using an interval judgement matrix, European Journal of Operational Research, 201(2), 537-544, 2010. https://doi.org/10.1016/j.ejor.2009.03.029

Couso I., Garrido L., Sanchez L. (2013); Similarity and dissimilarity measures between fuzzy sets: A formal relational study, Information Sciences, 229, 122-141, 2013. https://doi.org/10.1016/j.ins.2012.11.012

Dayanik A. (2010); Feature interval learning algorithms for classification, Knowledge-Based Systems, 23(5), 402-417, 2010. https://doi.org/10.1016/j.knosys.2010.02.002

Dempster A.P. (1967); Upper and lower probabilities induced by a multivalued mapping, Annals of Mathematical Statistics, 38(2), 325-339, 1967. https://doi.org/10.1214/aoms/1177698950

Esposito F., Malerba D., Semeraro G. (1997); A comparative analysis of methods for pruning decision trees, IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(5), 476- 491, 1997. https://doi.org/10.1109/34.589207

Hu B.Q. (2010); Fuzzy theory, Wuhan University Press, 2010.

Jin L.Q., Xu Y. (2014); A rule-based inference method using Dempster-Shafer theory, Knowledge Engineering and Management Proceedings of the Eighth International Conference on Intelligent Systems and Knowledge Engineering (ISKE 2013), 61-72, 2014.

Jin L. Q., Xu Y., Fang X. (2016); A novel interval certitude rule base inference method with evidential reasoning, Proceedings of the 12th International FLINS Conference (FLINS 2016), 50-55, 2016.

Jin L.Q., Liu J., Xu Y., Fang X. (2015); A novel rule base representation and its inference method using the evidential reasoning approach, Knowledge-Based Systems, 87, 80-91, 2015. https://doi.org/10.1016/j.knosys.2015.06.018

Kononenko I. (1994); Estimating attributes: analysis and extension of relief, Proceedings of the Seventh European Conference in Machine Learning, Springer-Verlag, 171-182, 1994. https://doi.org/10.1007/3-540-57868-4_57

Li D.F. (2011); Linear programming approach to solve interval-valued matrix games, Omega, 39, 655-666, 2011. https://doi.org/10.1016/j.omega.2011.01.007

Li M., Wu C., Zhang L. et al. (2015); An intuitionistic Fuzzy-TODIM method to solve distributor evaluation and selection problem, International Journal of Simulation Modelling, 14(3), 511-524, 2015. https://doi.org/10.2507/IJSIMM14(3)CO12

Liu J., Martinez L., Calzada A. et al (2013); A novel belief rule base representation, generation and its inference methodology, Knowledge-Based Systems, 53, 129-141, 2013. https://doi.org/10.1016/j.knosys.2013.08.019

Nadaban S., Dzitac S., Dzitac I. (2016); Fuzzy TOPSIS: A General View, Procedia Computer Science, 91, 823-831, 2016. https://doi.org/10.1016/j.procs.2016.07.088

Park J.H., Park I.Y, Kwun Y.C. et al (2011); Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment, Applied Mathemat- ical Modelling, 35, 2544-2556, 2011. https://doi.org/10.1016/j.apm.2010.11.025

Saez J.A., Derrac J., Luengo J. et al (2014); Statistical computation of feature weighting schemes through data estimation for nearest neighbor classifiers, Pattern Recognition, 47(12), 3941-3948, 2014. https://doi.org/10.1016/j.patcog.2014.06.012

Saaty T.L. (1980); The Analytic Hierarchy Process, McGraw-Hill Press, 1980.

Soman K.P., Diwakar S., Ajay V. (2011); Insight into data mining theory and practice, China Machine Press, 2011.

Sun R. (1995); Robust reasoning: integrating rule based and similarity based reasoning, Artificial Intelligence, 75(2), 241-295, 1995. https://doi.org/10.1016/0004-3702(94)00028-Y

Wang Y.M. (2009); Reply to the note on article "The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees", European Journal of Operational Research, 197, 813-817, 2009. https://doi.org/10.1016/j.ejor.2008.06.035

Wang Z.D., Wang H.Q., Lv H.W. et al (2014); Spectrum migration approach based on Predecision Aid and interval mamdani fuzzy inference in cognitive radio networks, International Journal of Computers Communications & Control, 9(1), 85-92, 2014. https://doi.org/10.15837/ijccc.2014.1.869

Wang J.Q., Wu J.T., Wang J. et al. (2014); Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems, Information Sciences, 288, 55-72, 2014. https://doi.org/10.1016/j.ins.2014.07.034

Wang Y.M., Yang J.B., Xu D.L. et al (2006); The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees, European Journal of Operational Research, 175, 35-66, 2006. https://doi.org/10.1016/j.ejor.2005.03.034

Wang Y.M., Yang J.B., Xu D.L. et al. (2006); The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees, European Journal of Operational Research, 175, 35-66, 2006. https://doi.org/10.1016/j.ejor.2005.03.034

Wang Y.M., Yang J.B., Xu D.L. et al. (2007); On the combination and normalization of interval-valued belief structures, Information Sciences, 177, 1230-1247, 2007. https://doi.org/10.1016/j.ins.2006.07.025

Wang T., Zhang G.X., Perez-Jimenez, M.J. (2015); Fuzzy membrane computing: Theory and applications, International Journal of Computers Communications & Control, 10(6), 144-175, 2015. https://doi.org/10.15837/ijccc.2015.6.2080

Xu D.L., Yang J.B., Wang Y.M. (2006); The evidential reasoning approach for multiattribute decision analysis under interval uncertainty, European Journal of Operational Research, 174, 1914-1943, 2006. https://doi.org/10.1016/j.ejor.2005.02.064

Xu Y., Qiao Q.X., Chen C.P. et al. (1994); Uncertainty inference, Southwest Jiaotong University Press, 1994.

Xu Z.S. (2013); Group decision making model and approach based on interval preference orderings, Computers & Industrial Engineering, 64, 797-803, 2013. https://doi.org/10.1016/j.cie.2012.12.013

Yang J.B., Liu J., Wang J. (2006); Belief rule-base inference methodology using the evidential reasoning approach—-RIMER, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 36(2), 266-285, 2006. https://doi.org/10.1109/TSMCA.2005.851270

Yang J.B., Singh M.G. (1994); An evidential reasoning approach for multiple-attribute decision making with uncertainty, IEEE Transactions on Systems, Man, and Cybernetics, 24(1), 1-18, 1994. https://doi.org/10.1109/21.259681

Yang J.B., Xu D.L. (2013); Evidential reasoning rule for evidence combination, Artificial Intelligence, 205, 1-29, 2013. https://doi.org/10.1016/j.artint.2013.09.003

Yue Z.L. (2013); Group decision making with multi-attribute interval data, Information Fusion, 14, 551-561, 2013. https://doi.org/10.1016/j.inffus.2013.01.003

Published

2017-12-04

Most read articles by the same author(s)

Obs.: This plugin requires at least one statistics/report plugin to be enabled. If your statistics plugins provide more than one metric then please also select a main metric on the admin's site settings page and/or on the journal manager's settings pages.