Re: Analogical reasoning with similarity measures


Subject: Re: Analogical reasoning with similarity measures
From: Dionis Boixader (boixader@ea.upc.es)
Date: Mon Nov 20 2000 - 17:40:40 MET


En/Na Chris Cornelis ha escrit:

> Hello,
>
> For my Ph.D. I am investigating the use of similarity measures in
> the inference step in fuzzy control/fuzzy expert systems. Starting from a
> rule
>
> if X is A then Y is B
>
> and an instance of data
>
> X is A'
>
> the object is to assess the similarity of A and A', on the basis of which
> we try to find a convenient modification B' of the consequence B
> ("reasoning by analogy", proposed by Turksen and Zhong).
>
> Does anybody know of any realistic implementations of this alternative to
> Zadeh's compositional rule of inference? Or, perhaps has done
> research/can give references on the suitability of certain similarity
> measures for this specific issue?
>
> Thanks in advance,
>
> Chris Cornelis
> Fuzziness and uncertainty modelling research unit
> University of Ghent, Belgium
>

Hello, Chris.
I think this topic is one of the most revisited ones in our field. I worked on it
in my PhD and what it happened to me was that I found many things were already
done. I'll bring some references to help you to avoid this kind of nasty
surprises. There must be lots of references that I don't know yet, so I wuold be
very happy if you or somebody else could bring some more.

Papers matching the idea you expose above:

Boixader & Jacas (1998)
Extensionality based approximate reasoning
Int. J. Approximate Reasoning vol 19 num 3-4 pg 221-230

Boixader & Jacas (1998)
Indistinguishability operators and Approximate Reasoning via CRI
in Fuzzy Sets, Logics and Knowledge Based Reasoning pg 277-290
Dubois, Prade & Klement eds.
Kluwer

Bouchon-Meunier, Valverde (1994)
Analogical Reasoning and Fuzzy Resemblance
Uncertainty in Intelligent Systems
Bouchon-Meunier et al. eds.
Elsevier Science Pub.

Godo, Jacas & Valverde (1991)
Fuzzy values in fuzzy logic

Kokzy & Hirota (1993)
Approximate Reasoning by linear rule interpolation and general approximation
Int. J. Approximate Reasoning 9, 197-225

Magrez & Smets (1989)
Fuzzy Modus Ponens: A New Model Suitable for Applications in Knowledge Based
Systems
Int. J. Intelligent Systems, Vol.4, 181-200

Papers related to the idea you expose above:

Bouchon-Meunier, Rifqi & Bothorel (1996)
General Measures of Comparation of Objects
Fuzzy Sets and Systems 84, 143-153

Dubois, Esteva, Garcia, Godo & Prade (1997)
A logical approach to interpolation based on similarity relations
Int.J.Approximate Reasoning 17, 1-36

Dubois & Prade
Similarity based approximate reasoning(1994)
Computational Intelligence Imitating Life
Zurada, Marles & Robinson eds.
IEEE press, New York.

Dubois & Prade
What are fuzzy rules and how to use them
Fuzzy Sets and Systems 84, 169-185

Esteva, Garcia & Godo (1994)
Relating and extending semantical approaches to possibilistic reasoning
Int.J.Approximate Reasoning 10, 311-344

Godo, Jacas & Valverde (1991)
Fuzzy values in fuzzy logic.
Int. J. Intelligent Systems vol6, 199-212

Klawonn & Castro (1995)
Similarity in Fuzzy Reasoning
Mathware & Soft Computing 2, 197-228

Klawonn & Kruse(1993)
Equality Relations as a basis for fuzzy control
Fuzzy Sets and Systems 54, 147-156

Zwick, Carlstein & Budescu (1987)
Measures of similarity between fuzzy concepts: A comparative analysis
Int.J.Approx. Reasoning 1

Furthermore, note that also papers on Case Based Reasoning in the setting of
Fuzzy Logic might contain information related to the analogical reasoning pattern
you are interested on.

And finally, don't forget the mother of all refernces in the topic:

Hume(1748)
An inquiry concerning human understanding
'from causes which appear similar, we expect similar effects.This is the sum of
all our experimental conclusions'

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