Indistinguishability relations in Dempster-Shafer theory of evidence

Abstract Each theory or model implicitly defines its inherent notion of equality for the objects in question. In turn, this equality, and its counterpart, the mathematical concept of equivalence, provides the basis on which to establish classification mechanisms for the domain at hand. Nevertheless, equivalence relations have not been proved to be sufficiently suited to capturing the underlying structure when dealing with domains pervaded with uncertainty. Therefore, the need for a more flexible definition of equality brings the concept of T-indistinguishability operator on to the scene. In this paper, we study the notion of indistinguishability within the context of the Dempster–Shafer theory of evidence and provide effective definitions and procedures for computing the T-indistinguishability operator associated with a given body of evidence. We also show how these procedures could also be adapted in order to provide a new method for tackling the problem of belief function approximation based on the concept of T-preorder.

[1]  Ronald R. Yager,et al.  A class of fuzzy measures generated from a Dempster-Shafer belief structure , 1999, Int. J. Intell. Syst..

[2]  Mathias Bauer,et al.  Approximation algorithms and decision making in the Dempster-Shafer theory of evidence - An empirical study , 1997, Int. J. Approx. Reason..

[3]  Didier Dubois,et al.  Consonant approximations of belief functions , 1990, Int. J. Approx. Reason..

[4]  Frans Voorbraak,et al.  A Computationally Efficient Approximation of Dempster-Shafer Theory , 1988, Int. J. Man Mach. Stud..

[5]  L. Valverde.  On the structure of F-indistinguishability operators , 1985 .

[6]  H. Poincaré.  La science et l'hypothèse , 1968 .

[7]  Henri Prade,et al.  Fuzzy sets and probability: misunderstandings, bridges and gaps , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

[8]  M. Sugeno.  FUZZY MEASURES AND FUZZY INTEGRALS—A SURVEY , 1993 .

[9]  J. Recasens,et al.  Maps between indistinguishability operators , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[10]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[11]  Alessandro Saffiotti,et al.  The Transferable Belief Model , 1991, ECSQARU.

[12]  Ronald R. Yager.  Fuzzy set and possibility theory : recent developments , 1982 .

[13]  J. Jacas.  On the generators of T-indistinguishability operator. , 1988 .

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

[15]  J. Recasens,et al.  Fuzzy T-transitive relations: eigenvectors and generators , 1995 .

[16]  David Harmanec,et al.  Faithful Approximations of Belief Functions , 1999, UAI.

[17]  Bjørnar Tessem,et al.  Approximations for Efficient Computation in the Theory of Evidence , 1993, Artif. Intell..

[18]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[19]  M. Gupta,et al.  FUZZY INFORMATION AND DECISION PROCESSES , 1981 .

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

[21]  Ton Sales.  Fuzzy sets as set classes. , 1982 .

[22]  George J. Klir,et al.  Minimal information loss possibilistic approximations of random sets , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.