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Extra info for Mathematical Models in the Social and Behavioral Sciences

Sample text

They propose that each case is a triplet (p, a, r) where p ∈ P (the set containing all problems), a ∈ A (the set of possible actions) and r ∈ R (the set containing all results). Casebased reasoning is concerned with the problems and how to classify them in comparison with each other. Gilboa and Schmeidler defined a similarity function between problems: S : P2 → [0, 1]. This function gives the distance between two problems. The decision maker can also use a utility function on the outcome: U = R → IR.

Adam CBR systems is the most important one. For instance, the set of cases must be able to grow to encapsulate any newly encountered case which does not fit existing cases. The system must also be able to deal efficiently with any unrecognisable case that is encountered. The issue of similarity between cases becomes a critical one, with the system having to properly assess the distance between any new case and one or several existing cases. Gilboa and Schmeidler (1995, 2000a) proposed a framework to formalise the relationship between case based reasoning and case-based decision making.

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