Case-Based Approximate Reasoning (Theory and Decision by Eyke Hüllermeier

By Eyke Hüllermeier

Making use of other frameworks of approximate reasoning and reasoning below uncertainty, particularly probabilistic and fuzzy set-based strategies, this e-book develops formal types of the above inference precept, that's basic to CBR. The case-based approximate reasoning equipment hence received specially emphasize the heuristic nature of case-based inference and elements of uncertainty in CBR.

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Example text

In interpretative CBR, for instance, the focus is on arguing whether a new situation should be treated in the same way as a previous one [80]. Again, the similarity between the two situations plays a crucial role. Needless to say, a clear differentiation between problem solving CBR and interpretative CBR is often not possible in practice. In fact, most CBR systems combine aspects of both types. Integration with other techniques. Hybrid representations combining different paradigms belong to the relatively recent developments in intelligent systems research.

The value λı defines the level of importance of the ı-th attribute. As can be seen, λı = 1 corresponds to full importance, whereas λı = 0 means that the ı-th attribute is completely ignored. 21) preserves reflexivity, symmetry, and transitivity. So-called ordered weighted averaging (OWA) operators, which generalize several well-known operators, such as the average and the minimum, have also been proposed as aggregation operators in the context of case-based reasoning [409]. Another interesting aggregation operator (apparently not yet considered in connection with similarity evaluation) is the Choquet integral [67, 180].

The so-called local-global principle makes the following assumption: There are local similarity measures σı : Aı × Aı −→ R≥0 and a composition function f : (R≥0 )n −→ R≥0 such that σ(a, a ) = f σ1 (a1 , a1 ), . . 19) for all a = (a1 , . . , an ), a = (a1 , . . 19). For example, the global monotonicity axiom states that σ(a, a ) < σ(a, a ) ⇒ ∃ ı ∈ {1, . . , n} : σı (aı , aı ) < σı (aı , aı ). for all a, a , a ∈ A. 2. Commonly used similarity measures are often derived from the weighted Euclidean metric 1/2 n ∆ : (a, a ) → ωı · (aı − aı ) 2 .

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