This paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy set. It also presents basic ideas on fuzzy integrals defined using these fuzzy measures. Definitions of new types of fuzzy measures and integrals are motivated by our research on generalized quantifiers. Several useful properties of fuzzy measures and fuzzy integrals are stated and proved. Definitio...

Recently we proposed a new type of fuzzy integrals defined over complete residuated lattices. These integrals are intended for the modeling of type ⟨1, 1⟩ fuzzy quantifiers. An interesting theoretical question is, how to introduce various notions of convergence of this type of fuzzy integrals. In this contribution, we would like to present some results on strong and pointwise convergence of the...

We describe in this paper a new approach for pattern recognition using modular neural networks with a fuzzy logic method for response integration. We proposed a new architecture for modular neural networks for achieving pattern recognition in the particular case of human faces and fingerprints. Also, the method for achieving response integration is based on the fuzzy Sugeno integral with some m...

An important limitation of fuzzy integrals for information fusion is the exponential growth of coefficients for an increasing number of information sources. To overcome this problem a variety of fuzzy measure identification algorithms has been proposed. HLMS is a simple gradient-based algorithm for fuzzy measure identification which suffers from some convergence problems. In this paper, two pro...

In this work we review some recent results on the integration of information from multiple sources when it is represented by means of numerical values. In particular, these methods are adequate to combine membership degrees in fuzzy sets (i.e., values in [0,1]).

Morphological tools can provide transformations suitable for real projective images, but the camera and objects to be analyzed have to be positioned in such a manner that a regular mesh on the objects projects a regular mesh on the image. A morphological modification of the image is thus the projection of an equivalent operation on the object. Otherwise, due to perspective effects, a morphologi...

Using order relations on the space of fuzzy numbers, we define the levels of fuzzy number valued mappings and we present some topologicals and geometrics properties. We use this concept to locate points and the set of points that solve a problem of fuzzy optimization. Consequently we obtain a necessary condition, for means of fuzzy integrals, for fuzzy global optimality.

This paper shows the detection of textures by analysing the image by stochastic properties. Different parts of the composed stochastic properties are fused by a decision directed method. The stochastic is mapped on a fuzzy measure and a fuzzy function. The fusion of the so represented stochastic information is achieved by the fuzzy integral. The result of the fuzzy integral is used for a new fu...

A new inequality for the universal integral on abstract spaces is obtained in a rather general form. As two corollaries, Minkowski’s and Chebyshev’s type inequalities for the universal integral are obtained. The main results of this paper generalize some previous results obtained for special fuzzy integrals, e.g., Choquet and Sugeno integrals. Furthermore, related inequalities for seminormed in...