Oppositions in Fuzzy Linguistic Summaries

An important aspect of interpretability in Fuzzy Linguistic Summaries (FLS) is the absence of opposition therein, which is not guaranteed by the the current approaches used for their generation, possibly leading to confusion for the end-user. In this paper, we first introduce a 3-level hierarchy to organise the models of opposition starting from simpler sentences, then enriched with generalised quantifiers and thirdly considering the several negation operators allowed by fuzzy logic. We then introduce a general model of opposition for FLS sentences, which we propose to represent as a 4-dimensional cube. We additionally discuss the antonym property in this analysis framework and prove it for general protoforms.