Catálogo de publicaciones - libros

Traditional data processing in science and engineering starts with computing the basic statistical characteristics such as the population mean and population variance:

The CESTAC method and its implementation known as CADNA software have been created to estimate the accuracy of the solution of real life problems when these solutions are obtained from numerical methods implemented on a computer. The method takes into account uncertainties on data and round-off errors. On another hand a theoretical model for this method in which operands are gaussian variables called stochastic numbers has been developed. In this paper numerical examples based on the Lagrange polynomial interpolation and polynomial computation have been constructed in order to demonstrate the consistency between the CESTAC method and the theory of stochastic numbers. Comparisons with the interval approach are visualized.

In the present paper we propose a novel approach for modeling friction, by using fuzzy differential equations under the strongly generalized differentiability concept. The key point is a continuous fuzzyfication of the signum function. The lack of the uniqueness for the solutions of a fuzzy differential equation allows us to choose the solution which better reflects the behavior of the modeled real-world system, so it allows us to incorporate expert’s knowledge in our model. Numerical solutions of the fuzzy differential equations modeling dry friction are proposed. In order to show how the expert’s knowledge can be incorporated in the system, we study the dry friction equation with different additional assumptions.

In interval computations, at each intermediate stage of the computation, we have intervals of possible values of the corresponding quantities. In our previous papers, we proposed an extension of this technique to , where on each stage, in addition to intervals of possible values of the quantities, we also keep sets of possible values of pairs (triples, etc.). In this paper, we show that in several practical problems, such as estimating statistics (variance, correlation, etc.) and solutions to ordinary differential equations (ODEs) with given accuracy, this new formalism enables us to find estimates in feasible (polynomial) time.

This paper continues investigation of systems of fuzzy interval logics based on the Checklist Paradigm semantics of Bandler and Kohout [1] [2]. While the early papers dealt with checklist paradigm based interval systems containing commutative AND and OR, this paper is the fifth in the series of papers in which we have been describing the systems in which these connective types are non-commutative. In the present paper we investigate non-commutative interval system generated from implication operators based on the Checklist Paradigm measure of Bandler and Kohout. This system includes the well-known Early Zadeh implication operator (PLY) which is not contrapositive. While the commutative systems can be sufficiently characterized by an 8-element group of transformations, the non-commutative systems require the 16 element group .

The algebra of truth values for fuzzy sets of type-2, due to Zadeh, contains as subalgebras those of type-1 and of interval-valued fuzzy sets. It also contains many other interesting subalgebras, some of which could possibly serve as a basis of a useful fuzzy set theory. This paper is about one such subalgebra which we call the subalgebra of points, and which generalizes type-1. We investigate it as an algebra, and determine its automorphism group. In particular, we show that is it a characteristic subalgebra and that its automorphisms are exactly those induced by automorphisms of the containing truth value algebra of fuzzy sets of type-2.

In this paper we show that Atanassov’s Intuitionistic Fuzzy sets can be viewed as a classification model, that can be generalized in order to take into account more classes than the three classes considered by Atanassov’s (membership, non-membership and non-determinacy). This approach will imply, on one hand, to change the meaning of these classes, so each one will have a positive definition. On the other hand, this approach implies the possibility of a direct generalization for alternative logics and additional valuation states, being consistent with Atanassov’s focuss. From this approach we shall stress the absence of any structure within those three valuation states in Atanassov’s model. In particular, we consider this is the main cause of the dispute about Atanassov’s model: acknowledging that the name is not appropriate, once we consider that a crisp direct graph is defined in the valuation space, formal differences with other three-state models will appear.

The classical classification problem with nominal data is considered. First, to make the problem practically tractable, some transformation into a numerical (real) domain is performed using a frequency based analysis. Then, the use of a fuzzy sets based, and – in particular - an intuitionistic fuzzy sets based technique is proposed. To better explain the procedure proposed, the analysis is heavily based on an example. Importance of the results obtained for other areas exemplified by decision making and case based reasoning is mentioned.

This paper proposes an automated approach for constructing the intuitionistic fuzzy histograms (-histograms) of a gray-scale digital image, based on the notion of intuitionistic fuzzy numbers (-numbers). A method for constructing parametric -numbers from their fuzzy counterparts using intuitionistic fuzzy generators (IFGs) is also presented, using an entropic optimization criterion. Finally, experimental results demonstrate the ability of the proposed approach to obtain efficiently the -histograms of gray-scale images.

Atanassov’s intuitionistic fuzzy sets (A-IFSs) have been used recently to determine the optimal threshold value for gray-level image segmentation [1]. Atanassov’s intuitionistic fuzzy index values are used for representing the unknowledge/ignorance of an expert on determining whether a pixel of the image belongs to the background or the object of the image. This optimal global threshold of the image is computed automatically, regardless of the actual image analysis process.

Although global optimal thresholding techniques give good results under experimental conditions, when dealing with real images having several objects and the segmentation purpose is to point out some application-specific information, one should use heuristic techniques in order to obtain better thresholding results.

This paper introduces an evolution of the above mentioned technique intended for use with such images. The proposed approach takes into account the image and segmentation specificities by using a two-step procedure, with a restricted set of the image gray-levels.

Preliminary experimental results and comparison with other methods are presented.