Draft Papers
Authors: J. Lawry, J. Recasens, I. Gonzalez Rodrıguez
Title: A Similarity Approach to Evidence Combination in Dempster-Shafer Theory
Abstract: Combination operators for fusing different sources of evidence are investigated from the perspective of maximising proximity or similarity to a consistent solution. Operators are defined as the composition of an extension function and a normalisation method where the former identifies a unique joint belief assignment from two marginals and the latter redistributes mass associated with the empty set to other pairs of focal sets. This definition motivates an initial study into normalisation methods followed by a related examination of extension functions. The normalisation of a joint belief assignment is taken to be the closest or most similar consistent assignment according to a predefined metric. A range of distance and similarity metrics are considered and their associated normalisation methods are then identified. Extension functions are based on identifying the joint belief assignment with the required marginals that are closest to a consistent assignment. In effect this means finding the assignments which are closest to their normalised assignment. Issues of uniqueness are discussed and a number of operators are identified on the basis of extension functions and normalisation methods derived from particular metrics. Finally, we attempt to justify this approach by arguing that the very decision to intersect two sources of evidence carries with it an implicit assumption of consistency, rather than an assumption of independence as in Dempster’s rule.
Description: Unpublished paper investigating how different fusion operators in Dempster-Shafer theory can be justified in terms of similarity.
File: simcomb3.pdf
Title: A Similarity Approach to Evidence Combination in Dempster-Shafer Theory
Abstract: Combination operators for fusing different sources of evidence are investigated from the perspective of maximising proximity or similarity to a consistent solution. Operators are defined as the composition of an extension function and a normalisation method where the former identifies a unique joint belief assignment from two marginals and the latter redistributes mass associated with the empty set to other pairs of focal sets. This definition motivates an initial study into normalisation methods followed by a related examination of extension functions. The normalisation of a joint belief assignment is taken to be the closest or most similar consistent assignment according to a predefined metric. A range of distance and similarity metrics are considered and their associated normalisation methods are then identified. Extension functions are based on identifying the joint belief assignment with the required marginals that are closest to a consistent assignment. In effect this means finding the assignments which are closest to their normalised assignment. Issues of uniqueness are discussed and a number of operators are identified on the basis of extension functions and normalisation methods derived from particular metrics. Finally, we attempt to justify this approach by arguing that the very decision to intersect two sources of evidence carries with it an implicit assumption of consistency, rather than an assumption of independence as in Dempster’s rule.
Description: Unpublished paper investigating how different fusion operators in Dempster-Shafer theory can be justified in terms of similarity.
File: simcomb3.pdf
Authors: J. Lawry
Title: Machines Can’t Think (Or Make Decisions)!
Description: Unpublished essay about how the language we use around cognition and decision making can lead us to confuse agency and responsibility in AI.
File: machinesdontthink.pdf
Title: Machines Can’t Think (Or Make Decisions)!
Description: Unpublished essay about how the language we use around cognition and decision making can lead us to confuse agency and responsibility in AI.
File: machinesdontthink.pdf