Transformation of basic probability assignments to probabilities based on a new entropy measure

Dempster-Shafer evidence theory is an efficient mathematical tool to deal with uncertain information. In that theory, basic probability assignment (BPA) is the basic element for the expression and inference of uncertainty. Decision-making based on BPA is still an open issue in Dempster-Shafer evidence theory. In this paper, a novel approach of transforming basic probability assignments to probabilities is proposed based on Deng entropy which is a new measure for the uncertainty of BPA. The principle of the proposed method is to minimize the difference of uncertainties involving in the given BPA and obtained probability distribution. Numerical examples are given to show the proposed approach.

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

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

[3]  Thierry Denoeux,et al.  A neural network classifier based on Dempster-Shafer theory , 2000, IEEE Trans. Syst. Man Cybern. Part A.

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

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

[6]  Shuang Yao,et al.  Induced Ordered Weighted Evidential Reasoning Approach for Multiple Attribute Decision Analysis with Uncertainty , 2014, Int. J. Intell. Syst..

[7]  Fabio Cuzzolin,et al.  On the relative belief transform , 2012, Int. J. Approx. Reason..

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

[9]  Yong Deng,et al.  Deng entropy: a generalized Shannon entropy to measure uncertainty , 2015 .

[10]  Quan Pan,et al.  Evidential classifier for imprecise data based on belief functions , 2013, Knowl. Based Syst..

[11]  Koichi Yamada,et al.  A Descriptive Decision-Making Model under Uncertainty: Combination of Dempster-Shafer Theory and Prospect Theory , 2013, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[12]  Sankaran Mahadevan,et al.  A new method to determine basic probability assignment from training data , 2013, Knowledge-Based Systems.

[13]  Johan Schubert,et al.  Conflict management in Dempster-Shafer theory using the degree of falsity , 2011, Int. J. Approx. Reason..

[14]  Naif Alajlan,et al.  Probabilistically Weighted OWA Aggregation , 2014, IEEE Transactions on Fuzzy Systems.

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

[16]  Thierry Denoeux,et al.  ECM: An evidential version of the fuzzy c , 2008, Pattern Recognit..

[17]  Sankaran Mahadevan,et al.  A non-parametric method to determine basic probability assignment for classification problems , 2014, Applied Intelligence.

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

[19]  Rehan Sadiq,et al.  Quantifying influence of weather indices on PM$$_{2.5}$$2.5 based on relation map , 2014 .

[20]  Xue Han,et al.  A response surface approach for structural reliability analysis using evidence theory , 2014, Adv. Eng. Softw..

[21]  Philippe Smets,et al.  The Transferable Belief Model , 1991, Artif. Intell..

[22]  José M. Merigó,et al.  Decision Making with Dempster-Shafer Theory Using Fuzzy Induced Aggregation Operators , 2011, Recent Developments in the Ordered Weighted Averaging Operators.

[23]  Yong Hu,et al.  A new method to determine basic probability assignment using core samples , 2014, Knowl. Based Syst..

[24]  Thierry Denoeux,et al.  Maximum Likelihood Estimation from Uncertain Data in the Belief Function Framework , 2013, IEEE Transactions on Knowledge and Data Engineering.

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

[26]  Antonella Certa,et al.  A Multistep Methodology for the Evaluation of Human Resources Using the Evidence Theory , 2013, Int. J. Intell. Syst..

[27]  Prakash P. Shenoy,et al.  On the plausibility transformation method for translating belief function models to probability models , 2006, Int. J. Approx. Reason..

[28]  Fabio Cuzzolin,et al.  A Geometric Approach to the Theory of Evidence , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[29]  Philippe Smets,et al.  Decision making in the TBM: the necessity of the pignistic transformation , 2005, Int. J. Approx. Reason..

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

[31]  Milan Daniel.  On transformations of belief functions to probabilities , 2006, Int. J. Intell. Syst..

[32]  Sankaran Mahadevan,et al.  A new decision-making method by incomplete preferences based on evidence distance , 2014, Knowl. Based Syst..

[33]  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.

[34]  Fatih Karahan,et al.  On the Persistence of Income Shocks Over the Life Cycle: Evidence and Implications , 2009 .

[35]  Ronald R. Yager,et al.  The use of ordered weighted averaging method for decision making under uncertainty , 2014, Int. Trans. Oper. Res..

[36]  Chongzhao Han,et al.  A novel approximation of basic probability assignment based on rank-level fusion , 2013 .

[37]  Yong Deng,et al.  FUZZY SENSOR FUSION BASED ON EVIDENCE THEORY AND ITS APPLICATION , 2013, Appl. Artif. Intell..

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

[39]  Naif Alajlan,et al.  On characterizing features of OWA aggregation operators , 2014, Fuzzy Optim. Decis. Mak..

[40]  Weiru Liu,et al.  Analyzing the degree of conflict among belief functions , 2006, Artif. Intell..