Abstract: The purpose of this paper is to discuss the properties of regularity and strong regularity of fuzzy measure on metric spaces following the previous results. Some properties are defined with the help of nulladditivity such as inner\outer regularity and the regularity of fuzzy measure. We define the strong regularity of fuzzy measures and show our result that the null-additive fuzzy mea...

In last years, a variety of papers on fuzzy sets and other fuzzy topics was concerned with set-algebraic operations for and properties of fuzzy sets. However, only few remarks are devoted to fuzzy cardinals. In classical set theory the cardinality of a set is a measure of its size or "power". In the fuzzy case one has to differentiate: there are measures of fuzziness and measures of power. Here...

We consider the aggregation operators which are ⊕-additive for commonotone functions. The main result is that any operator is expressed by a kind of general fuzzy integral which uses a family of fuzzy measures connected by a ⊕-additive Cauchy’s equations. In particular, the family of fuzzy measures can be obtained by a ⊕-fitting pseudomultiplication. In this case, the aggregation operator is ex...

Hellinger distance is a distance between two additive measures defined in terms of the RadonNikodym derivative of these two measures. This measure proposed in 1909 has been used in a large variety of contexts. In this paper we define an analogous measure for fuzzy measures. We discuss them for distorted probabilities and give two examples.

Many people suuer from a continuous strong pain which is caused solely by the malfunction of the pain mechanism itself. One way to ease their pain is to electrically stimulate the spinal cord. Since the equations of pain are not known, we must use heuristic methods to nd the optimal pain relief stimulation. In this paper, we show how fuzzy measures and similar nonlinear models can be used in pa...

In the present communication, two exponential fuzzy information measures are introduced and characterized axiomatically. To show the effectiveness of the proposed measure, it is compared with the existing measures. Two fuzzy discrimination and symmetric discrimination measures are defined and their validity are checked. Important properties of new measures are studied. Their applications in pat...

In this paper, we tackle the study of so-called supplementarity measures. They are introduced axiomatically and are then related to incompatibility measures by antonyms. To do this, we have to establish what we mean by antonymous measure. We then prove that, under certain conditions, supplementarity and incompatibility measures are antonymous. Besides, with the aim of constructing antonymous me...

The family of k-additive measures has been introduced as a midterm between probabilities and general fuzzy measures and finds a wide number of applications in practice. However, its structure is different from other families of fuzzy measures and is certainly more complex (for instance, its vertices are not always {0, 1}valued), so it has not been yet fully studied. In this paper we present som...