We extend the concept of fuzzy integral based on ⊕-decomposable measure from nonnegative fuzzy measurable function to extended real-valued fuzzy measurable function. Further investigations of fuzzy integrals based on pseudo-additive decomposable measure are carried out. Meanwhile, the space (S(μ),σ(·,·)) of all fuzzy measurable function will be proved to be a pseudo-metric space. Finally, as an...

in this paper, some results of the chebyshev type integral inequality for the pseudo-integral are proven. the obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. finally, we applied our results  to the case of comonotone functions.

The original aim of this research was the introduction of a compositive measure of information (see e.g. [5]) on a class (an algebra) of fuzzy subsets of an universe f2. However, there is a bijection between the class of compositive informations and the class of decomposable measures (see e.g. [2]). Therefore, we restated our problem as the one of the construction of a decomposable measure over...

In this paper we compare the WOWA operator (an aggregation operator that generalizes both the weighted mean and the OWA operator) with the Choquet integral. We show that the Sugeno λ-measure and the decomposable fuzzy measures are particular cases of the measure implicit in the WOWA operator.

In this paper some types of decomposable signed fuzzy measures have been presented. We discuss properties of 6-and ⊕decomposable signed fuzzy measures. We consider their relationship with bi-capacities.

The systems represented by the Choquet or the multi-linear fuzzy integral with respect to fuzzy measure is equivalently decomposable into hierarchically sub-systems through the use of Inclusion-Exclusion Covering (IEC) (Theorem 4.1,4.2) . Hence, IEC is one of very useful concepts/indexes for structural analysis of the fuzzy integral systems (short for: the systems represented by the Choquet or ...

The fuzzy entropy h(T) of a dynamical system has been introduced in [5] (see also [1, 3, 8, 10]). Generalizing the notion of a fuzzy partition Mesiar and Rybarik have studied the p-entropy (see [7, 10, 11]) based on the Pap y-calculus ([9]). The notion is based on an increasing bijective function g : [0,oo] —> [0, oo], such that #(0) = 0 and #(1) = 1. The choice g(x) = x leads to the fuzzy entr...

In this paper we consider some properties of intuitionistic fuzzy preference relations. We pay attention to preservation of intuitionistic fuzzy preference relations by aggregation operations. In particular, we know, that a special kind of aggregation operations (lattice operations) do not preserve intuitionistic fuzzy preference relations. We describe the operations which preserve intuitionist...

We consider the problem of choosing an alternative in a set A = {A1, A2, ..., Am} of alternatives, given a set D = {d1, d2, ..., dh} of decision makers and a set Ω = {O1, O2, ..., On} of objectives. We assume that any decision maker dk assigns to any pair (alternative Ai, objective Oj) a number aijk that measures to what extent Ai satisfies Oj . We assume that Ω is a subset of a universal set U...