Requirements for total uncertainty measures in Dempster–Shafer theory of evidence

Abellán, Joaquín; Masegosa, Andrés R.

doi:10.1080/03081070802082486

Cited by 77 publications

(55 citation statements)

References 25 publications

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“…H * is a total uncertainty measure which is well known for this type of set ( Abellán & Masegosa, 2008 ). H * separates the different types of uncertainty found on these general sets: conflict and non-specificity ( Abellán, Klir, & Moral, 2006 ).…”

Section: Credal Decision Treesmentioning

confidence: 99%

Analysis of Credal-C4.5 for classification in noisy domains

Mantas

Abellán

Castellano

2016

Expert Systems with Applications

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Section: Credal Decision Treesmentioning

confidence: 99%

Analysis of Credal-C4.5 for classification in noisy domains

Mantas

Abellán

Castellano

2016

Expert Systems with Applications

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“…(21) and (22) are denoted by "Tr AM min". The approaches of "Tr AM max" and "Tr AM min" can be generally denoted by "Tr AM opt".…”

Section: Novel Approaches For the Transformation Of Fmf Into Bpa 299mentioning

confidence: 99%

Novel Approaches for the Transformation of Fuzzy Membership Function Into Basic Probability Assignment Based on Uncertainty Optimization

Han

Deng

2013

Int. J. Unc. Fuzz. Knowl. Based Syst.

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With the development of uncertainty reasoning and information fusion, there have emerged several theories including fuzzy set theory, Dempster-Shafer evidence theory, probability theory and rough set theory, etc., for representing and dealing with the uncertain information. When the fusion of the uncertain information originated from different sources is needed, how to construct a general framework for different theories of uncertainty or how to establish the connection between different theoretical frameworks has become a crucial problem. Particularly, to combine two kinds of information represented respectively by the BPA and the FMF, this paper proposes two transformations of an FMF into a BPA by solving a constrained maximization or minimization optimization problem. The objective function is the uncertainty degree of the body of evidence (BOE) and the corresponding constraints are established based on the given FMF. In fact the transformation of an FMF into a BPA is the transformation of fuzzy sets into random sets, which is currently accepted as a unified framework for several theories of uncertainty. Our proposed approaches have no predefinition of focal elements and they can be used as the general transformations of fuzzy sets into random sets. Some examples and analyses are provided to illustrate and justify the rationality and effectiveness of the proposed approaches.

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“…In Section 4, we propose six properties that an entropy function for BPA should satisfy. We compare our properties with those proposed by Klir and Wierman [26], and also with a set monotonicity property proposed by Abellán and Masegosa [3]. In Section 5, we discuss the various definitions that have been proposed in the literature, and how they compare vis-a-vis our list of six properties.…”

Section: Introductionmentioning

confidence: 99%

A new definition of entropy of belief functions in the Dempster–Shafer theory

Jiroušek

Shenoy

2018

International Journal of Approximate Reasoning

132

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We propose a new definition of entropy of basic probability assignments (BPAs) in the Dempster-Shafer (DS) theory of belief functions, which is interpreted as a measure of total uncertainty in the BPA. Our definition is different from those proposed by Höhle, Smets, Yager, Nguyen, Dubois-Prade, Lamata-Moral, Klir-Ramer, Klir-Parviz, Pal et al., Maeda-Ichihashi, Harmanec-Klir, Abellán-Moral, Jousselme et al., Pouly et al., and Deng. We state a list of six desired properties of entropy for DS belief functions theory, four of which are motivated by Shannon's definition of entropy of probability functions, and the remaining two are requirements that adapt this measure to the philosophy of the DS theory. Three of our six desired properties are different from the five properties proposed by Klir and Wierman. We demonstrate that our definition satisfies all six properties in our list, whereas none of the existing definitions do. Our new definition has two components. The first component is Shannon's entropy of an equivalent probability mass function obtained using the plausibility transform, which constitutes the conflict measure of entropy. The second component is Dubois-Prade's definition of entropy of basic probability assignments in the DS theory, which constitutes the non-specificity measure of entropy. Our new definition is the sum of these two components. Our definition does not satisfy the subadditivity property. Whether there exists a definition that satisfies our six properties plus subadditivity remains an open question. 1

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Requirements for total uncertainty measures in Dempster–Shafer theory of evidence

Cited by 77 publications

References 25 publications

Analysis of Credal-C4.5 for classification in noisy domains

Analysis of Credal-C4.5 for classification in noisy domains

Novel Approaches for the Transformation of Fuzzy Membership Function Into Basic Probability Assignment Based on Uncertainty Optimization

A new definition of entropy of belief functions in the Dempster–Shafer theory

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