Estimating linguistic summaries on the unit interval data

The results of flexible referendum votings and classifications by ordinal sums or uninorms are in the unit interval, i.e., covering “Yes”, “No” and “Maybe” with the inclinations towards the extremes. This raises questions of effectively distilling relevant summaries for informing (for instance, from voting), i.e., "approx. 20% voters very significantly incline to No", and re-adjusting properties of functions in ordinal sums and uninorms (for classification). A larger number of votes and classification experiments together with a vocabulary of linguistic terms require an effective and understandable estimation. To avoid calculation of matching degrees, the unit interval is divided into equi-length subintervals. To tackle these challenges, this work proposes enhancing estimation based on subintervals’ cardinalities by interval valued fuzzy sets and linguistic summaries. Next, the quality of agreement and its deviation are adjusted to reveal the relevant summaries covering subsets of data. By this approach, we can mine the key sentences expressing flexible voting among wards and classification behaviour. The obtained theoretical results are discussed and illustrated on examples. The paper provides a framework for the future experiments with a large representative sample of voters in the autumn 2022 referendum in Switzerland, in which the interpretation of flexible voting results against the background of a real-life referendum will be evaluated.