Interval data driven construction of shadowed sets with application to linguistic word modelling

Abstract

The interval data from different surveyed persons for one linguistic word can reflect the intra- and inter-uncertainties of the word. This study shows how to construct shadowed set models for linguistic words based on the surveyed interval data. Firstly, corresponding to the popularly used fuzzy sets for linguistic words, four kinds of shadowed sets are introduced according to their shapes and named as the normal, the left-shoulder, the right-shoulder, and the non-cored shadowed sets. A data-driven approach that utilizes different statistics to determine the shapes and parameters of the shadowed set models is then proposed. The proposed data-driven approach includes two methods; the first is the tolerance limit method depending on the mean and standard deviation of the remaining interval data after pre-processing, whilst the other is the percentile method relying on the percentiles of the remaining interval data. Additionally, to evaluate the modelling performance, three novel indices are presented to measure the uncertainty-capture capability and accuracy of the constructed shadowed set models. Finally, the proposed approach is applied to two real-world problems. One is the modelling of 32 words in a codebook, and the other is the modelling of the thermal feeling words. The proposed methods are compared with other interval data driven methods, e.g. the enhanced interval approach and the fuzzy statistic method. Our results show that the proposed percentile method performs better in both applications. The proposed approach can also be applied to some other linguistic word modelling applications when it is reasonable to adopt shadowed sets as the words’ models.