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Information cells and information cell mixture models for concept modelling. (English) Zbl 1259.68118
Summary: By combining the prototype theory and random set theory interpretations of vague concepts, a novel structure named information cell and a combined structure named information cell mixture model are proposed to represent the semantics of vague concepts. An information cell \(L_i\) on the domain \(\Omega\) has a transparent cognitive structure ‘\(L_i =\text{about} P_i\)’ which is mathematically formalized by a 3-tuple \(\langle P_i ,d_i ,\delta_i \rangle\); comprising a prototype set \(P_i\) (\(\subseteq \Omega \)), a distance function \(d_i\) on \(\Omega\) and a density function \(\delta_i\) on \([0,+\infty)\). An information cell mixture model on domain \(\Omega\) is actually a set of weighted information cells \(L_i\)s. A positive neighborhood function of the information cell mixture model is introduced in this paper to reflect the belief distribution of positive neighbors of the underlying concept. An information cellularization algorithm is also proposed to learn the information cell mixture model from a training data set, which is a direct application of the \(k\)-means and EM algorithms. Information cell mixture models provide some tools for information coarsening and concept modelling, and have potential applications in uncertain reasoning and classification.
68Q55 Semantics in the theory of computing
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