# A Simple Proportional Conflict Redistribution Rule

@article{Smarandache2004ASP, title={A Simple Proportional Conflict Redistribution Rule}, author={Florentin Smarandache and Jean Dezert}, journal={International journal of applied mathematics and statistics}, year={2004}, volume={3}, pages={1-36} }

One proposes a first alternative rule of combination to WAO (Weighted Average Operator) proposed recently by Josang, Daniel and Vannoorenberghe, called Proportional Conflict Redistribution rule (denoted PCR1). PCR1 and WAO are particular cases of WO (the Weighted Operator) because the conflicting mass is redistributed with respect to some weighting factors. In this first PCR rule, the proportionalization is done for each non-empty set with respect to the non-zero sum of its corresponding mass…

## Topics from this paper

## 40 Citations

Proportional Conflict Redistribution Rules for Information Fusion

- Computer Science
- 2004

Five versions of a Proportional Conflict Redistribution rule (PCR) for information fusion together with several examples are proposed and improved PCR rules are proposed in this paper.

Information fusion based on new proportional conflict redistribution rules

- Computer Science, Mathematics2005 7th International Conference on Information Fusion
- 2005

This paper proposes anew family of fusion rules for the combination of uncertainty and conflicting information, based on new Proportional Conflict Redistributions (PCR) allowing us to deal with highly conflicting sources for static and dynamic fusion applications.

Advances and Applications of DSmT

- Engineering
- 2004

In this chapter we propose five versions of a Proportional Conflict Redistribution rule (PCR) for information fusion together with several examples. From PCR1 to PCR2, PCR3, PCR4, PCR5 one increases…

Adaptative combination rule and proportional conflict redistribution rule for information fusion

- Mathematics, Computer ScienceArXiv
- 2006

This work presents two new promising combina- tion rules for the fusion of uncertain and potentially highl y conflicting sources of evidences in the theory of belief: the class of Adaptive Combination Rules (ACR) and a new effi- cient Proportional Conflict Redistribution (PCR) rule.

A Modified Approach to Conflict Management From the Perspective of Non-Conflicting Element Set

- Computer ScienceIEEE Access
- 2020

A new conflict handling method based on the concept of non-conflict element set is proposed and the similarity between the evidences is characterized by the correlation coefficient; based on this, a new weighting scheme of evidence is developed.

Analysis and improvement for Proportional Conflict Redistribution rules

- Computer Science2010 International Conference on Computer Application and System Modeling (ICCASM 2010)
- 2010

The six PCR rules (PCR1-PCR6) and improved PCR rule are analyzed and compared through numerical examples, and the results show that the improved rule is effective.

Measuring Conflict Functions in Generalized Power Space

- Mathematics
- 2011

One of the most important open issues is that the classical conflict coefficient in D-S evidence theory (DST) cannot correctly determine the conflict degree between two pieces of evidence. This…

An In-Depth Look at Quantitative Information Fusion Rules

- Computer Science
- 2016

The author proposes a Unification of Fusion Theories extending the power and hyper-power sets from previous theories to a Boolean algebra obtained by the closures of the frame of discernment under union, intersection, and complement of sets.

An In-Depth Look at Information Fusion Rules & the Unification of Fusion Theories

- Computer ScienceArXiv
- 2004

This paper introduces the degree of union and degree of inclusion with respect to the cardinal of sets not with the fuzzy set point of view, besides that of intersection, many fusion rules can be improved.

DSmT: A new paradigm shift for information fusion

- Computer ScienceArXiv
- 2006

The theory of plausible and paradoxical reasoning, known as DSmT (Dezert-Smarandache Theory) in literature, developed for dealing with imprecise, uncertain and potentially highly conflicting sources of information.

## References

SHOWING 1-10 OF 32 REFERENCES

Proportional Conflict Redistribution Rules for Information Fusion

- Computer Science
- 2004

Five versions of a Proportional Conflict Redistribution rule (PCR) for information fusion together with several examples are proposed and improved PCR rules are proposed in this paper.

Information fusion based on new proportional conflict redistribution rules

- Computer Science, Mathematics2005 7th International Conference on Information Fusion
- 2005

This paper proposes anew family of fusion rules for the combination of uncertainty and conflicting information, based on new Proportional Conflict Redistributions (PCR) allowing us to deal with highly conflicting sources for static and dynamic fusion applications.

Strategies for combining conflicting dogmatic beliefs

- Computer ScienceSixth International Conference of Information Fusion, 2003. Proceedings of the
- 2003

Proposals for combining dogmatic or highly conpicting beliefs and how they handle cases when the beliefs are conflicting and dogmatic are described.

Associativity in combination of belief functions; a derivation of minC combination

- Computer Science, MathematicsSoft Comput.
- 2003

A new approach to understanding contradictions is employed and an original notion of potential contradiction is introduced: an associative combination of generalized belief functions – minC combination and its derivation – is presented as part of the new approach.

Combination of Evidence in Dempster-Shafer Theory

- Computer Science
- 2002

This report surveys a number of possible combination rules for Dempster-Shafer structures and provides examples of the implementation of these rules for discrete and interval-valued data.

Data fusion in the transferable belief model

- MathematicsProceedings of the Third International Conference on Information Fusion
- 2000

When Shafer introduced his theory of evidence based on the use of belief functions, he proposed a rule to combine belief functions induced by distinct pieces of evidence. Since then, theoretical…

Representation and combination of uncertainty with belief functions and possibility measures

- Mathematics, Computer ScienceComput. Intell.
- 1988

The framework of belief functions in terms of expressive power for knowledge representation is examined and it is indicated that combination rules issued from fuzzy set and possibility theory look more flexible than Dempster rule because many variants exist, and their numerical stability seems to be better.

A mathematical theory of evidence

- Computer Science
- 1976

This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.

On the Justification of Dempster's Rule of Combination

- Mathematics, Computer ScienceArtif. Intell.
- 1991

Abstract In Dempster-Shafer theory it is claimed that the pooling of evidence is reflected by Dempster's rule of combination, provided certain requirements are met. The justification of this claim is…

Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem

- Mathematics, Computer ScienceInt. J. Approx. Reason.
- 1993

The Bayes’ theorem is generalized within the transferable belief model framework and the DRC and GBT and their uses for belief propagation in directed belief networks are analysed.