Analyzing the monotonicity of belief interval based uncertainty measures in belief function theory

Measuring the uncertainty of pieces of evidence is an open issue in belief function theory. A rational uncertainty measure for belief functions should meet some desirable properties, where monotonicity is a very important property. Recently, measuring the total uncertainty of a belief function based on its associated belief intervals becomes a new research idea and has attracted increasing interest. Several belief interval based uncertainty measures have been proposed for belief functions. In this paper, we summarize the properties of these uncertainty measures and especially investigate whether the monotonicity is satisfied by the measures. This study provide a comprehensive comparison to these belief interval based uncertainty measures and is very useful for choosing the appropriate uncertainty measure in the practical applications.

[1]  Wen Jiang,et al.  An evidential dynamical model to predict the interference effect of categorization on decision making results , 2018, Knowl. Based Syst..

[2]  Yafei Song,et al.  Uncertainty measure in evidence theory with its applications , 2017, Applied Intelligence.

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

[4]  Yong Deng,et al.  Dependent Evidence Combination Based on Shearman Coefficient and Pearson Coefficient , 2018, IEEE Access.

[5]  Xinyang Deng,et al.  An Evidential Axiomatic Design Approach for Decision Making Using the Evaluation of Belief Structure Satisfaction to Uncertain Target Values , 2018, Int. J. Intell. Syst..

[6]  Yi Yang,et al.  A new distance-based total uncertainty measure in the theory of belief functions , 2016, Knowl. Based Syst..

[7]  Prakash P. Shenoy,et al.  Entropy of Belief Functions in the Dempster-Shafer Theory: A New Perspective , 2016, BELIEF.

[8]  Ronald R. Yager,et al.  Soft likelihood functions in combining evidence , 2017, Inf. Fusion.

[9]  Joaquín Abellán.  Combining nonspecificity measures in Dempster–Shafer theory of evidence , 2011, Int. J. Gen. Syst..

[10]  George J. Klir,et al.  Uncertainty-Based Information , 1999 .

[11]  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.

[12]  Zhansheng Duan,et al.  Evaluation of Probability Transformations of Belief Functions for Decision Making , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[13]  Naif Alajlan,et al.  Evaluating Belief Structure Satisfaction to Uncertain Target Values , 2016, IEEE Transactions on Cybernetics.

[14]  Wen Jiang,et al.  An improved soft likelihood function for Dempster–Shafer belief structures , 2018, Int. J. Intell. Syst..

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

[16]  Xinyang Deng,et al.  Evidence Combination From an Evolutionary Game Theory Perspective , 2015, IEEE Transactions on Cybernetics.

[17]  Wen Jiang,et al.  A Method to Identify the Incomplete Framework of Discernment in Evidence Theory , 2017 .

[18]  Ronald R. Yager,et al.  The entailment principle for dempster—shafer granules , 1986, Int. J. Intell. Syst..

[19]  H. Farmer.  A new perspective. , 1988, The Journal of the Florida Medical Association.

[20]  Fuyuan Xiao,et al.  An improved distance-based total uncertainty measure in belief function theory , 2017, Applied Intelligence.

[21]  Wen Jiang,et al.  Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making , 2018, Int. J. Syst. Sci..

[22]  Wen Jiang,et al.  An Uncertainty Measure for Interval-valued Evidences , 2017, Int. J. Comput. Commun. Control.

[23]  Chunhe Xie,et al.  Failure mode and effects analysis based on a novel fuzzy evidential method , 2017, Appl. Soft Comput..

[24]  Andrés R. Masegosa,et al.  Requirements for total uncertainty measures in Dempster–Shafer theory of evidence , 2008, Int. J. Gen. Syst..

[25]  Fuyuan Xiao,et al.  An Improved Method for Combining Conflicting Evidences Based on the Similarity Measure and Belief Function Entropy , 2018, Int. J. Fuzzy Syst..

[26]  G. Klir,et al.  MEASURING TOTAL UNCERTAINTY IN DEMPSTER-SHAFER THEORY: A NOVEL APPROACH , 1994 .

[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]  Ronald R. Yager,et al.  On the fusion of non-independent belief structures , 2009, Int. J. Gen. Syst..

[29]  T. Denœux.  Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence , 2008 .

[30]  G. Klir,et al.  Uncertainty-based information: Elements of generalized information theory (studies in fuzziness and soft computing). , 1998 .

[31]  Ronald R. Yager,et al.  Entropy and Specificity in a Mathematical Theory of Evidence , 2008, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[32]  D. Dubois,et al.  A NOTE ON MEASURES OF SPECIFICITY FOR FUZZY SETS , 1985 .

[33]  Thierry Denoeux,et al.  Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence , 2008, Artif. Intell..

[34]  Éloi Bossé,et al.  Measuring ambiguity in the evidence theory , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[35]  Naif Alajlan,et al.  Maxitive Belief Structures and Imprecise Possibility Distributions , 2017, IEEE Transactions on Fuzzy Systems.

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