Obtaining contradiction measure on intuitionistic fuzzy sets from fuzzy connectives

In a previous paper, we proposed an axiomatic model for measuring self-contradiction in the framework of Atanassov fuzzy sets. This way, contradiction measures that are semicontinuous and completely semicontinuous, from both below and above, were defined. Although some examples were given, the problem of finding families of functions satisfying the different axioms remained open. The purpose of this paper is to construct some families of contradiction measures firstly using continuous t-norms and t-conorms, and secondly by means of strong negations. In both cases, we study the properties that they satisfy. These families are then classified according the different kinds of measures presented in the above paper.

Fuzzy min-max neural networks for categorical data: application to missing data imputation

The fuzzy min–max neural network classifier is a supervised learning method. This classifier takes the hybrid neural networks and fuzzy systems approach. All input variables in the network are required to correspond to continuously valued variables, and this can be a significant constraint in many real-world situations where there are not only quantitative but also categorical data. The usual way of dealing with this type of variables is to replace the categorical by numerical values and treat them as if they were continuously valued. But this method, implicitly defines a possibly unsuitable metric for the categories. A number of different procedures have been proposed to tackle the problem. In this article, we present a new method. The procedure extends the fuzzy min–max neural network input to categorical variables by introducing new fuzzy sets, a new operation, and a new architecture. This provides for greater flexibility and wider application. The proposed method is then applied to missing data imputation in voting intention polls. The micro data—the set of the respondents’ individual answers to the questions—of this type of poll are especially suited for evaluating the method since they include a large number of numerical and categorical attributes.

Contribución al estudio de dos conceptos básicos de la lógica fuzzy

La tesis doctoral CONTRIBUCIÓN AL ESTUDIO DE DOS CONCEPTOS BÁSICOS DE LA LÓGICA FUZZY constituye un conjunto de nuevas aportaciones al análisis de dos elementos básicos de la lógica fuzzy: los mecanismos de inferencia y la representación de predicados vagos. La memoria se encuentra dividida en dos partes que corresponden a los dos aspectos señalados. En la Parte I se estudia el concepto básico de «estado lógico borroso». Un estado lógico borroso es un punto fijo de la aplicación generada a partir de la regla de inferencia conocida como modus ponens generalizado. Además, un preorden borroso puede ser representado mediante los preórdenes elementales generados por el conjunto de sus estados lógicos borrosos. El Capítulo 1 está dedicado a caracterizar cuándo dos estados lógicos dan lugar al mismo preorden elemental, obteniéndose también un representante de la clase de todos los estados lógicos que generan el mismo preorden elemental. El Capítulo finaliza con la caracterización del conjunto de estados lógicos borrosos de un preorden elemental. En el Capítulo 2 se obtiene un subconjunto borroso trapezoidal como una clase de una relación de indistinguibilidad. Finalmente, el Capítulo 3 se dedica a estudiar dos tipos de estados lógicos clásicos: los irreducibles y los minimales. En el Capítulo 4, que inicia la Parte II de la memoria, se aborda el problema de obtener la función de compatibilidad de un predicado vago. Se propone un método, basado en el conocimiento del uso del predicado mediante un conjunto de reglas y de ciertos elementos distinguidos, que permite obtener una expresión general de la función de pertenencia generalizada de un subconjunto borroso que realice la función de extensión del predicado borroso. Dicho método permite, en ciertos casos, definir un conjunto de conectivas multivaluadas asociadas al predicado. En el último capítulo se estudia la representación de antónimos y sinónimos en lógica fuzzy a través de auto-morfismos. Se caracterizan los automorfismos sobre el intervalo unidad cuando sobre él se consideran dos operaciones: una t-norma y una t-conorma ambas arquimedianas. The PhD Thesis CONTRIBUCIÓN AL ESTUDIO DE DOS CONCEPTOS BÁSICOS DE LA LÓGICA FUZZY is a contribution to two basic concepts of the Fuzzy Logic. It is divided in two parts, the first is devoted to a mechanism of inference in Fuzzy Logic, and the second to the representation of vague predicates. «Fuzzy Logic State» is the basic concept in Part I. A Fuzzy Logic State is a fixed-point for the mapping giving the Generalized Modus Ponens Rule of inference. Moreover, a fuzzy preordering can be represented by the elementary preorderings generated by its Fuzzy Logic States. Chapter 1 contemplates the identity of elementary preorderings and the selection of representatives for the classes modulo this identity. This chapter finishes with the characterization of the set of Fuzzy Logic States of an elementary preordering. In Chapter 2 a Trapezoidal Fuzzy Set as a class of a relation of Indistinguishability is obtained. Finally, Chapter 3 is devoted to study two types of Classical Logic States: irreducible and minimal. Part II begins with Chapter 4 dealing with the problem of obtaining a Compa¬tibility Function for a vague predicate. When the use of a predicate is known by means of a set of rules and some distinguished elements, a method to obtain the general expression of the Membership Function is presented. This method allows, in some cases, to reach a set of multivalued connectives associated to the predicate. Last Chapter is devoted to the representation of antonyms and synonyms in Fuzzy Logic. When the unit interval [0,1] is endowed with both an archimedean t-norm and a an archi-medean t-conorm, it is showed that the automorphisms' group is just reduced to the identity function.

See-and-avoid quadcopter using fuzzy control optimized by cross-entropy

In this work we present an optimized fuzzy visual servoing system for obstacle avoidance using an unmanned aerial vehicle. The cross-entropy theory is used to optimise the gains of our controllers. The optimization process was made using the ROS-Gazebo 3D simulation with purposeful extensions developed for our experiments. Visual servoing is achieved through an image processing front-end that uses the Camshift algorithm to detect and track objects in the scene. Experimental flight trials using a small quadrotor were performed to validate the parameters estimated from simulation. The integration of crossentropy methods is a straightforward way to estimate optimal gains achieving excellent results when tested in real flights.

Multi-argument fuzzy measures on lattices of fuzzy sets

In this paper, we axiomatically introduce fuzzy multi-measures on bounded lattices. In particular, we make a distinction between four different types of fuzzy set multi-measures on a universe X, considering both the usual or inverse real number ordering of this lattice and increasing or decreasing monotonicity with respect to the number of arguments. We provide results from which we can derive families of measures that hold for the applicable conditions in each case.

Extending the expressiveness of fuzzy logic languages

En el trabajo que aquí presentamos se incluye la base teórica (sintaxis y semántica) y una implementación de un framework para codificar el razonamiento de la representación difusa o borrosa del mundo (tal y como nosotros, seres humanos, entendemos éste). El interés en la realización de éste trabajo parte de dos fuentes: eliminar la complejidad existente cuando se realiza una implementación con un lenguaje de programación de los llamados de propósito general y proporcionar una herramienta lo suficientemente inteligente para dar respuestas de forma constructiva a consultas difusas o borrosas. El framework, RFuzzy, permite codificar reglas y consultas en una sintaxis muy cercana al lenguaje natural usado por los seres humanos para expresar sus pensamientos, pero es bastante más que eso. Permite representar conceptos muy interesantes, como fuzzificaciones (funciones usadas para convertir conceptos no difusos en difusos), valores por defecto (que se usan para devolver resultados un poco menos válidos que los que devolveríamos si tuviésemos la información necesaria para calcular los más válidos), similaridad entre atributos (característica que utilizamos para buscar aquellos individuos en la base de datos con una característica similar a la buscada), sinónimos o antónimos y, además, nos permite extender el numero de conectivas y modificadores (incluyendo modificadores de negación) que podemos usar en las reglas y consultas. La personalización de la definición de conceptos difusos (muy útil para lidiar con el carácter subjetivo de los conceptos borrosos, donde nos encontramos con que cualificar a alguien de “alto” depende de la altura de la persona que cualifica) es otra de las facilidades incluida. Además, RFuzzy implementa la semántica multi-adjunta. El interés en esta reside en que introduce la posibilidad de obtener la credibilidad de una regla a partir de un conjunto de datos y una regla dada y no solo el grado de satisfacción de una regla a partir de el universo modelado en nuestro programa. De esa forma podemos obtener automáticamente la credibilidad de una regla para una determinada situación. Aún cuando la contribución teórica de la tesis es interesante en si misma, especialmente la inclusión del modificador de negacion, sus multiples usos practicos lo son también. Entre los diferentes usos que se han dado al framework destacamos el reconocimiento de emociones, el control de robots, el control granular en computacion paralela/distribuída y las busquedas difusas o borrosas en bases de datos. ABSTRACT In this work we provide a theoretical basis (syntax and semantics) and a practical implementation of a framework for encoding the reasoning and the fuzzy representation of the world (as human beings understand it). The interest for this work comes from two sources: removing the existing complexity when doing it with a general purpose programming language (one developed without focusing in providing special constructions for representing fuzzy information) and providing a tool intelligent enough to answer, in a constructive way, expressive queries over conventional data. The framework, RFuzzy, allows to encode rules and queries in a syntax very close to the natural language used by human beings to express their thoughts, but it is more than that. It allows to encode very interesting concepts, as fuzzifications (functions to easily fuzzify crisp concepts), default values (used for providing results less adequate but still valid when the information needed to provide results is missing), similarity between attributes (used to search for individuals with a characteristic similar to the one we are looking for), synonyms or antonyms and it allows to extend the number of connectives and modifiers (even negation) we can use in the rules. The personalization of the definition of fuzzy concepts (very useful for dealing with the subjective character of fuzziness, in which a concept like tall depends on the height of the person performing the query) is another of the facilities included. Besides, RFuzzy implements the multi-adjoint semantics. The interest in them is that in addition to obtaining the grade of satisfaction of a consequent from a rule, its credibility and the grade of satisfaction of the antecedents we can determine from a set of data how much credibility we must assign to a rule to model the behaviour of the set of data. So, we can determine automatically the credibility of a rule for a particular situation. Although the theoretical contribution is interesting by itself, specially the inclusion of the negation modifier, the practical usage of it is equally important. Between the different uses given to the framework we highlight emotion recognition, robocup control, granularity control in parallel/distributed computing and flexible searches in databases.