A Probabilistic Framework for Interval Type-2 Fuzzy Linguistic Summarization

Many studies on linguistic summarization have addressed the use of ordinary fuzzy set [type-1 fuzzy set (T1FS)] for modeling words; however, few of them have exploited interval type-2 fuzzy set (IT2FS), although IT2FS is better able to deal with the uncertainty associated with words. The existing studies on linguistic summarization using IT2FS have focused on scalar cardinality based degree of truth. In this paper, for the first time, we propose a probabilistic framework based on the idea of interval mass assignment to evaluate interval type-2 fuzzy linguistic summaries based on the type-II quantified sentences and the semi-fuzzy quantifiers as an alternative method to the scalar cardinality based methods. We implement a real case study on linguistic summarization of time series data of Europe Brent Spot Price, as well as a comparison of the results obtained with our approach and those of the existing approaches.