Optimal Selection of Proportional Bounding Quantifiers in Linguistic Data Summarization

Proportional bounding quantifiers like “Between p1 and p2 percent” are potentially useful for expressing linguistic summaries of data. Given p1, p2, existing methods for data summarization based on fuzzy quantifiers can be used to assign a quality score to the summary. However, the problem remains how the optimal choice of p1, p2 in the range 0≤ p1 ≤ p2 ≤ 100% can be established. Moreover, the proposed quality indicators are rather heuristic in nature. The paper presents a method for computing the optimal bounding quantifier which best summarizes the given data. Specifically, the most specific quantifier will be chosen which results in the highest validity score of the summary given a constraint on the the percentage range p2− p1. The method not only assigns validity scores to the quantifiers of interest but also determines the best choice of quantifier in O(N logm) time, where N is the size of the base set and m the number of different membership grades in the fuzzy arguments.