Linguistic modelling and information coarsening based on prototype theory and label semantics.

*(English)*Zbl 1191.68699Summary: The theory of prototypes provides a new semantic interpretation of vague concepts. In particular, the calculus derived from this interpretation results in the same calculus as label semantics proposed by Lawry. In the theory of prototypes, each basic linguistic label \(L\) has the form ‘about P’, where \(P\) is a set of prototypes of \(L\) and the neighborhood size of the underlying concept is described by the word ‘about’ which represents a probability density function \(\delta \) on \([0,+\infty \)). In this paper we propose an approach to vague information coarsening based on the theory of prototypes. Moreover, we propose a framework for linguistic modelling within the theory of prototypes, in which the rules are concise and transparent. We then present a linguistic rule induction method from training data based on information coarsening and data clustering. Finally, we apply this linguistic modelling method to some benchmark time series prediction problems, which show that our linguistic modelling and information coarsening methods are potentially powerful tools for linguistic modelling and uncertain reasoning.

##### MSC:

68T37 | Reasoning under uncertainty in the context of artificial intelligence |

##### Keywords:

linguistic modelling; prototype theory; knowledge extraction; information coarsening; linguistic IF-THEN rules; Gaussian-type density function; label semantics; prototype-based clustering; mackey-glass time series prediction; sunspots time series prediction
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\textit{Y. Tang} and \textit{J. Lawry}, Int. J. Approx. Reasoning 50, No. 8, 1177--1198 (2009; Zbl 1191.68699)

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