Preservation of structures under aggregation functions is an active area research with applications in many fields. Among such structures, min-subgroups play important role, for instance, mathematical morphology, where they can be used to model translation invariance. Aggregation has only been studied binary functions. However, results concerning preservation the min-subgroup structure aggregat...

Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with 13 some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic submeasures and more general semi-copula-based probabilistic submeasures. Some algebraic properties of classes of such submeasures are also studied. 15 © 2012 Else...

The modeling of a utility function’s forms is a very interesting part of modern decision making theory. We apply a basic concept of the personal utility theory on determination of minimal net and maximal gross annual premium in general insurance. We introduce specific values of gross annual premium on the basis of a personal utility function, which is determined empirically by a short personal ...

We present an overview of the meaningful aggregation functions mapping ordinal scales into an ordinal scale. Three main classes are discussed, namely order invariant functions, comparison meaningful functions on a single ordinal scale, and comparison meaningful functions on independent ordinal scales. It appears that the most prominent meaningful aggregation functions are lattice polynomial fun...

The paper introduces a new class of functions from [0,1]n to [0,n] called d-Choquet integrals. These are generalization the “standard” Choquet integral obtained by replacing difference in definition usual dissimilarity function. In particular, all integrals encompasses but use dissimilarities provides higher flexibility and generality. We show that some aggregation/pre-aggregation/averaging/fun...

Z. Takáč in [16] introduced the aggregation operators on any subalgebra of M (set of all fuzzy membership degrees of the type-2 fuzzy sets, that is, the functions from [0,1] to [0,1]). Furthermore, he applied the Zadeh’s extension principle (see [24]) to obtain in [16, 17] a set of aggregation operators on L* (the strongly normal and convex functions of M). In this paper, we introduce the aggre...

Convexity is one of the most important geometric properties sets and a useful concept in many fields mathematics, like optimization. As there are also applications making use fuzzy optimization, it obvious that studies convexity frequent. In this paper we have extended notion for hesitant order to fulfill some necessary properties. Namely, found an appropriate definition on any ordered universe...