Comparison Between Dsm And Minc Combination Rules

Both DSm and minC rules of combination endeavor to process conflicts among combined beliefs better. The nature of conflicts as well as their processing during the belief combination is sketched. An presentation of the minC combination, an alternative to Dempster’s rule of combination, follows. Working domains, structures and mechanisms of the DSm and minC combination rules are compared in the body of this chapter. Finally, some comparative examples are presented.

A generalization of the minC combination to DSm hyper-power sets is presented. Both the special formulas for static fusion or dynamic fusion without non-existential constraints and the quite general formulas for dynamic fusion with non-existential constraints are included. Examples of the minC combination on several different hybrid DSm models are presented. A comparison of the generalized minC combination with the hybrid DSm rule is discussed and explained on examples.

Dempster’s rule, non-normalized conjunctive rule, Yager’s rule and Dubois-Prade’s rule for belief functions combination are generalized to be applicable to hyper-power sets according to the DSm theory. A comparison of the rules with DSm rule of combination is presented. A series of examples is included.

This second volume dedicated to Dezert-Smarandache Theory (DSmT) in Information Fusion brings in new fusion quantitative rules (such as the PCR1-6, where PCR5 for two sources does the most mathematically exact redistribution of conflicting masses to the non-empty sets in the fusion literature), qualitative fusion rules, and the Belief Conditioning Rule (BCR) which is different from the classical conditioning rule used by the fusion community working with the Mathematical Theory of Evidence. Other fusion rules are constructed based on T-norm and T-conorm (hence using fuzzy logic and fuzzy set in information fusion), or more general fusion rules based on N-norm and N-conorm (hence using neutrosophic logic and neutrosophic set in information fusion), and an attempt to unify the fusion rules and fusion theories. The known fusion rules are extended from the power set to the hyper-power set and comparison between rules are made on many examples. One defines the degree of intersection of two sets, degree of union of two sets, and degree of inclusion of two sets which all help in improving the all existing fusion rules as well as the credibility, plausibility, and communality functions. The book chapters are written by Frederic Dambreville, Milan Daniel, Jean Dezert, Pascal Djiknavorian, Dominic Grenier, Xinhan Huang, Pavlina Dimitrova Konstantinova, Xinde Li, Arnaud Martin, Christophe Osswald, Andrew Schumann, Tzvetan Atanasov Semerdjiev, Florentin Smarandache, Albena Tchamova, and Min Wang.

Papers collected from researchers in fusion information, such as: Florentin Smarandache, Jean Dezert, Hongshe Dang, Chongzhao Han, Frederic Dambreville, Milan Daniel, Mohammad Khoshnevisan, Sukanto Bhattacharya, Albena Tchamova, Tzvetan Semerdjiev, Pavlina Konstantinova, Hongyan Sun, Mohammad Farooq, John J. Sudano, Samuel Corgne, Gregoire Mercier, Laurence Hubert-Moy, Anne-Laure Jousselme, Patrick Maupin and others on Dezert-Smarandache Theory of Plausible and Paradoxical Reasoning (DSmT).. The principal theories available until now for data fusion are the probability theory, the fuzzy set theory, the possibility theory, the hint theory and the theory of evidence. Since last two years J. Dezert and F. Smarandache are actively developing a new theory of plausible and paradoxical reasoning, called DSmT (acronym for Dezert-Smarandache Theory), for information fusion of uncertain and highly conflicting sources of information. The DSmT can be interpreted as a generalization of the Dempster-Shafer Theory (DST) but goes far beyond the DST. The free-DSmT model, which assumes that the ultimate refinement of the frame of discernment of the fusion problem is not accessible due to the intrinsic nature of its elements, is opposite to the Shafer's model (on which is based the DST) assuming the exhaustivity and exclusivity of all elements of the frame of discernment. The DSmT proposes a new theoretical framework for data fusion based on definition of hyper-power sets and a new simple commutative and associative rule of combination. Recently, it has been discovered, through a new DSm hybrid rule of combination, that DSmT can be also extended to problems involving hybrid-models (models including some exclusivity and/or non-existentially constraints). This new important theoretical result offers now to the DSmT a wider class of fusion applications and allows potentially to attack the next generation of complex dynamical/temporal fusion problems. DSmT can also provide a theoretical issue for the fusion of neutrosophic information (extension of fuzzy information proposed by F. Smarandache in nineties - see http://www.gallup.unm.edu/~smarandache/FirstNeutConf.htm for details about the neutrosophy logic and neutrosophy set theory).

In this chapter we present a class of fusion rules based on the redistribution of the conflicting or even non-conflicting masses to the subsets or to the complements of the elements involved in the conflict proportionally with respect to their masses or/and cardinals. At the end, these rules are presented in a more general theoretical way including explicitly the reliability of each source of evidence. Some examples are also provided.

In this chapter, we present and discuss a new generalized proportional conflict redistribution rule. The Dezert-Smarandache extension of the DempsterShafer theory has relaunched the studies on the combination rules especially for the management of the conflict. Many combination rules have been proposed in the last few years. We study here different combination rules and compare them in terms of decision on didactic example and on generated data. Indeed, in real applications, we need a reliable decision and it is the final results that matter. This chapter shows that a fine proportional conflict redistribution rule must be preferred for the combination in the belief function theory.

This volume has about 760 pages, split into 25 chapters, from 41 contributors. First part of this book presents advances of Dezert-Smarandache Theory (DSmT) which is becoming one of the most comprehensive and flexible fusion theory based on belief functions. It can work in all fusion spaces: power set, hyper-power set, and super-power set, and has various fusion and conditioning rules that can be applied depending on each application. Some new generalized rules are introduced in this volume with codes for implementing some of them. For the qualitative fusion, the DSm Field and Linear Algebra of Refined Labels (FLARL) is proposed which can convert any numerical fusion rule to a qualitative fusion rule. When one needs to work on a refined frame of discernment, the refinement is done using Smarandache¿s algebraic codification. New interpretations and implementations of the fusion rules based on sampling techniques and referee functions are proposed, including the probabilistic proportional conflict redistribution rule. A new probabilistic transformation of mass of belief is also presented which outperforms the classical pignistic transformation in term of probabilistic information content. The second part of the book presents applications of DSmT in target tracking, in satellite image fusion, in snow-avalanche risk assessment, in multi-biometric match score fusion, in assessment of an attribute information retrieved based on the sensor data or human originated information, in sensor management, in automatic goal allocation for a planetary rover, in computer-aided medical diagnosis, in multiple camera fusion for tracking objects on ground plane, in object identification, in fusion of Electronic Support Measures allegiance report, in map regenerating forest stands, etc.