In the statistical literature, truncated distributions can be used for modeling real data. Due to error of measurement in truncated continuous data, choosing a crisp trimmed point caucuses a fault inference, so using fuzzy sets to define a threshold pointmay leads us more efficient results with respect to crisp thresholds. Arellano-Valle et al. [2] defined a selection distribution for analysis of truncated data with crisp threshold. In this paper, we define fuzzy multivariate selection distribution...

This work explores commutative semi-uninorms on finite chains by means of strictly increasing unary functions and the usual addition. In this paper, there are three families of additively generated commutative semi-uninorms. We not only study the structures and properties of semi-uninorms in each family but also show the relationship among these three families. In addition, this work provides the characterizations of uninorms in ${𝒰}_{min}$ and ${𝒰}_{max}$ that are generated by additive generators.

A uni-nullnorm is a special case of 2-uninorms obtained by letting a uninorm and a nullnorm share the same underlying t-conorm. This paper is mainly devoted to solving the distributivity equation between uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms and some binary operators, such as, continuous t-norms, continuous t-conorms, uninorms, and nullnorms. The new results differ from the previous ones about the distributivity in the class of 2-uninorms, which have not yet...