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Transitivity is a fundamental notion in preference modelling. In this work we study this property in the framework of additive fuzzy preference structures. In particular, we depart from a large preference relation that is transitive w.r.t. the nilpotent minimum t-norm and decompose it into an indifference and strict preference relation by means of generators based on t-norms, i. e. using a Frank t-norm as indifference generator. We identify the strongest type of transitivity these indifference and...

We analyze the existence of fuzzy sets of a universe that are convex with respect to certain particular classes of fusion operators that merge two fuzzy sets. In addition, we study aggregation operators that preserve various classes of generalized convexity on fuzzy sets. We focus our study on fuzzy subsets of the real line, so that given a mapping $F:[0,1]\times [0,1]\to [0,1]$, a fuzzy subset, say $X$, of the real line is said to be $F$-convex if for any $x,y,z\in ℝ$ such that $x\le y\le z$, it holds that ${\mu }_X\left(y\right)\ge F({\mu }_X\left(x\right),{\mu }_X\left(z\right))$, where ${\mu }_X:ℝ\to [0,1]$ stands here for the membership function...