Catálogo de publicaciones - libros

In the formal and fully graded setting of Fuzzy Class Theory (or higher-order fuzzy logic) we make an initial investigation into basic notions of fuzzy topology. In particular we study graded notions of fuzzy topology regarded as a fuzzy system of open or closed fuzzy sets and as a fuzzy system of fuzzy neighborhoods. We show their basic graded properties and mutual relationships provable in Fuzzy Class Theory and give some links to the traditional notions of fuzzy topology.

A genuine fuzzy approach to fuzzy mathematics consists in constructing axiomatic theories over suitable systems of formal fuzzy logic. The features of formal fuzzy logics (esp. the invalidity of the law of contraction) entail certain differences in form between theories axiomatized in fuzzy logic and usual theories known from classical mathematics. This paper summarizes the most important differences and presents guidelines for constructing new theories, defining new notions, and proving new theorems in formal fuzzy mathematics.

This work presents a new method to compare two Temporal Fuzzy Chains (TFCs). The TFCs comparison is used to compare the temporal evolution of two dynamical systems (TFCs). Firstly, the two TFCs that represent the two DSs are obtained. After that, the two obtained TFCs are compared, so the of the two TFCs is obtained. This is done by using linguistic labels.

T-norm properties for left-continuous, increasing [0,1]→[0,1] functions can be fully described in terms of contour lines. For a left-continuous t-norm , the rotation-invariance property comes down to the continuity of its contour line . However, contour lines are inadequate to investigate the geometrical structure of these rotation-invariant t-norms. Enforced with the companion and zooms it is possible to totally reconstruct  by means of its contour line and its -zoom, with the unique fixpoint of .

With an exponent-type membership function serving as conduct fuzzy value, the author builds a model in fuzzy reversed posynomial geometric programming with its dual programming developed. In the application process of fuzzy reversed posynomial geometric programming , he consequently discovers that the former can be changed into a convex parameter geometric programming with respect to ,. Therefore, he can get many nice properties like fuzzy posynomial geometric programming. Besides,he advances a dual theory and algorithm in fuzzy reversed posynomial geometric programming. And finally he uses numerical examples to testify the built model and its method effectively.

In this paper, the concept and type of posynomial fuzzy relation geometric programming is introduced, some basic theories of posynomial fuzzy relation geometric programming is presented, and then a solution procedure is expatiated to solving such a programming based on structure of feasible region. And finally, two practical examples are given for illustration purpose.

Comparing the similarity between two fuzzy sets (FSs) is needed in many applications. The focus herein is linguistic approximation using type-1 (T1) FSs, i.e. associating a T1 FS with a linguistic label from a vocabulary. Because each label is represented by an T1 FS , there is a need to compare the similarity of and to find the most similar to . In this paper, a vector similarity measure (VSM) is proposed for T1 FSs, whose two elements measure the similarity in shape and proximity, respectively. A comparative study shows that the VSM gives best results. Additionally, the VSM can be easily extended to interval type-2 FSs.

The type-2 fuzzy sets was extended of original fuzzy sets and there are many researches related to type-2 fuzzy sets and fuzzy logic systems (FLS), recently. The paper deals with the approximate presentation of type-2 fuzzy sets and operations by using triangulated irregular networks (TIN). TIN usually used to represent approximate 3-D surfaces with applications in computer graphics. By using TINs and half-edge structure, authors proposed representation and operations of type-2 fuzzy sets based on this approach. Some results compared with original approaches are shown to confirm the approach be good and correctly.

This paper focuses on the control of wheeled mobile robot under bounded torque disturbances. Hybrid tracking controller for the mobile robot was developed by considering its kinematic model and Euler-Lagrange dynamics. The procedure consist in minimizing the stabilization error of the kinematic model through genetic algorithm approach while attenuation to perturbed torques is made through type-2 Fuzzy Logic Control (FLC) via backstepping methodology. Type-2 fuzzy logic is proposed to synthesize the controller for the overall system which is claimed to be a robust tool for related applications. The theoretical results are illustrated through computer simulations of the closed-loop system.

The combination of Soft Computing techniques allows the improvement of intelligent systems with different hybrid approaches. In this work we consider two parts of a Modular Neural Network for image recognition, where a Type-2 Fuzzy Inference System (FIS 2) makes a great difference. The first FIS 2 is used for feature extraction in training data, and the second one to find the ideal parameters for the integration method of the modular neural network. Once again Fuzzy Logic is shown to be a tool that can help improve the results of a neural system, when facilitating the representation of the human perception.