Label prototypes for modelling with words

Abstract

This paper suggests a framework for modelling with words using label prototypes. The underlying methods are based on a random set label semantics together with the voting model interpretation of fuzzy sets. The potential of this methodology will be illustrated by its application to classification problems.

Classification and query evaluation using modelling with words

“…In the case where L 1 = small(s), L 2 = medium(m) and L 3 = large(l) with appropriateness degrees as defined in Example 2 then l medium^:large ðxÞ ¼ m x ðfs; mgÞ þ m x ðfmgÞ so that: l medium^:large ðxÞ ¼ Given this basic framework the following properties have been proven to hold (see [10]). From Proposition 1 we see that label semantics generates a functional calculus for appropriateness degrees that captures the standard min and max operations of fuzzy logic at the label level while also satisfying the law of excluded middle and the standard logical equivalences.…”

“…As well as classification, linguistic prototypes of this form can also be used to evaluate linguistic queries across a database. This utilises a new calculus for vague concepts based on random sets and label semantics [10].…”

Query evaluation from linguistic prototypes

“…Let the model attributes be random variables X i into Ω i for i n = 1, , L and let LA i be the label set for X i . Then a label prototype for object type In [3] we have described how linguistic prototypes of this kind can be used to estimate classification probabilities which can then be combined in a Naïve Bayes or Semi-Naïve Bayes classifier. In the following section we will outline how such prototypes can be used to evaluate a more general form of linguistic queries.…”

“…Here a linguistic prototype will represent an amalgam of objects of a certain type or class described in terms of the propensity for certain words to be used to label the attributes of the model for that class. The formal framework used will be label semantics ( [3] and [4]). The central idea is that a set of words is selected with a varying level of certainty, from some finite set, the label set, as appropriate labels for a given attribute value.…”