On the Notion of Similarity in Case-Based Reasoning
Published 1 January 1995
Michael M. Richter
Citations27
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TL;DR
The semantics of similarity measures is studied and reduced to the evidence theory of Dempster and Shafer and applications are given for classification and configuration.
Abstract
The semantics of similarity measures is studied and reduced to the evidence theory of Dempster and Shafer. Applications are given for classification and configuration, the latter uses utility theory in addition.
Keywords
Computer ScienceDecision Sciences
Psychological ReviewFeatures of similarity.
7,287 Citations1977Amos Tversky
The metric and dimensional assumptions that underlie the geometric representation of similarity are questioned on both theoretical and empirical grounds and a set of qualitative assumptions are shown to imply the contrast model, which expresses the similarity between objects as a linear combination of the measures of their common and distinctive features.
The Annals of Mathematical StatisticsUpper and Lower Probabilities Induced by a Multivalued Mapping
5,972 Citations1967A. P. Dempster
Studies in fuzziness and soft computingUpper and Lower Probabilities Induced by a Multivalued Mapping
5,299 Citations2008Arthur P. Dempster
A distinctive feature of the present approach is a rule for conditioning, or more generally, arule for combining sources of information, as discussed in Sects.
International Journal of Approximate ReasoningDecision analysis using belief functions
149 Citations1990Thomas M. Strat
A probabilistic interpretation of a simple assumption is offered that disambiguates decision problems represented with belief functions and it is proved that it yields expected values identical to those obtained by a Probabilistic analysis that makes the same assumption.
Lecture notes in economics and mathematical systemsA Mathematical Theory of Hints
139 Citations1995Jürg Kohlas, Paul-André Monney
Artificial IntelligenceDempster's rule of combination is #P-complete
106 Citations1990Pekka Orponen
It is proved that, given as input a set of tables representing basic probability assignments m 1, …, m n over a frame of discernment Θ, and a set A ⊆ Θ , the problem of computing the combined basic probability value (m 1 … ⊕ m n )(A) is # P -complete.
Automated reasoning seriesSimilarity, Uncertainty and Case-Based Reasoning in Patdex
55 Citations1991Michael M. Richter, Stefan Weß
This paper describes Patdex from a principal point of view and embed its main concepts into a theoretical framework and describes its use of cases for knowledge acquisition.
Mathematical Methods of Operations ResearchTheory of evidence ? A survey of its mathematical foundations, applications and computational aspects
43 Citations1994J. Kohlas, Paul-André Monney
Evidence theory has been used to represent uncertainty in expert systems, especially in the domain of diagnostics, and it can be applied to decision analysis and it gives a new perspective for statistical analysis.
European Journal of Operational ResearchModeling uncertainty with belief functions in numerical models
16 Citations1989Jürg Kohlas
A new approach for the representation and the analysis of uncertain, incomplete, partial information in numerical models is introduced, based on Shafer's mathematical theory of evidence, which allows a more flexible and realistic description and formalization of the available information.
Topics in Case-Based Reasoning: First European Workshop, EWCBR-93, Kaiserslautern, Germany, November 1-5, 1993. Selected Papers
13 Citations1994Stefan Weß, Klaus‐Dieter Althoff +2 more
A priori selection of mesh densities for adaptive finite element analysis, using a case-based reasoning approach and a reflective architecture for integrated memory-based learning and reasoning are described.