Aranzazu Jurio

Medical diagnosis of cardiovascular diseases using an interval-valued fuzzy rule-based classification system

This work was partially supported by the Spanish Ministry of Science and Technology under project TIN2010-15055 and the Research Services of the Universidad Publica de Navarra.

Some properties of overlap and grouping functions and their application to image thresholding

In this paper we study under which conditions overlap and grouping functions satisfy some commonly demanded properties such as migrativity or homogeneity. We also recall that the convex combination of overlap (grouping) functions is a new overlap (grouping) function. This property allows us to achieve a consensus between different methods that solve certain problems by means of these functions. We also show one application of this property in image processing.

An alternative to fuzzy methods in decision-making problems

In this work we present a construction method for Atanassovs intuitionistic fuzzy preference relations starting from fuzzy preference relations and taking into account the ignorance of the expert in the construction of the latter. Moreover, we propose two generalizations of the weighted voting strategy to work with Atanassovs intuitionistic fuzzy preference relations. An advantage of these algorithms is that they start from fuzzy preference relations and their results can be compared with those of any other decision-making algorithm based on fuzzy sets theory. We verify that our proposal is able to provide a unique solution in some cases in which the voting strategy is not able to order the alternatives.

Image Magnification Using Interval Information

In this paper, a simple and effective image-magnification algorithm based on intervals is proposed. A low-resolution image is magnified to form a high-resolution image using a block-expanding method. Our proposed method associates each pixel with an interval obtained by a weighted aggregation of the pixels in its neighborhood. From the interval and with a linear Kα operator, we obtain the magnified image. Experimental results show that our algorithm provides a magnified image with better quality (peak signal-to-noise ratio) than several existing methods.

Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions

In this paper we present a generalization of the weighted voting method used in the exploitation phase of decision making problems represented by preference relations. For each row of the preference relation we take the aggregation function (from a given set) that provides the value which is the least dissimilar with all the elements in that row. Such a value is obtained by means of the selected penalty function. The relation between the concepts of penalty function and dissimilarity has prompted us to study a construction method for penalty functions from the well-known restricted dissimilarity functions. The development of this method has led us to consider under which conditions restricted dissimilarity functions are faithful. We present a characterization theorem of such functions using automorphisms. Finally, we also consider under which conditions we can build penalty functions from Kolmogoroff and Nagumo aggregation functions. In this setting, we propose a new generalization of the weighted voting method in terms of one single variable functions. We conclude with a real, illustrative medical case, conclusions and future research lines.

QL-operations and QL-implication functions constructed from tuples (O,G,N) and the generation of fuzzy subsethood and entropy measures

Abstract Considering the important role played by overlap and grouping functions in several applications in which associativity is not demanded, in this paper we introduce the notion of QL-operations constructed from tuples ( O , G , N ) , where overlap functions O, grouping functions G and fuzzy negations N are used for the generalization of the implication p → q ≡ ¬ p ∨ ( p ∧ q ) , which is defined in quantum logic (QL). We also study under which conditions QL-operations constructed from tuples ( O , G , N ) are fuzzy implication functions, presenting a general form for obtaining QL-implication functions, and particular forms of such fuzzy implication functions according to specific properties of O and G. We analyze the main properties satisfied by QL-operations and QL-implication functions, establishing under which conditions of O, G and N, the derived QL-operations (implication functions) satisfy the different known properties for fuzzy implication functions. We show that QL-implication functions constructed from tuples ( O , G , N ) are richer than QL-implication functions constructed from t-norms and positive t-conorms. We provide a comparative study of QL-implication functions and other classes of fuzzy implication functions constructed from fuzzy negations, overlap and grouping functions, analyzing the intersections among such classes. Finally, we present the application of both QL-operations and QL-implication functions constructed from tuples ( O , G , N ) to the generation of fuzzy subsethood and derived entropy measures, which are useful for several practical applications.

Decision making with an interval-valued fuzzy preference relation and admissible orders

Graphical abstractDisplay Omitted In this paper we analyze under which conditions we must use interval-valued fuzzy relations in decision making problems. We propose an algorithm to select the best alternative from a set of solutions which have been calculated with the nondominance algorithm using intervals and different linear orders among them. Based on the study made by Orlovsky in his work about nondominance, we study a characterization of weak transitive and 0.5-transitive interval-valued fuzzy relations, as well as the conditions under which transitivity is preserved by some operators on those relations. Next, we study the case of interval-valued reciprocal relations. In particular, we describe the preservation of reciprocity by different operators and analyze the transitivity properties for these interval-valued reciprocal relations. Finally, we propose to use, in the nondominance algorithm, linear interval orders generated by means of operators which preserve transitivity.

Hierarchical fuzzy logic based approach for object tracking

In this paper a novel tracking approach based on fuzzy concepts is introduced. A methodology for both single and multiple object tracking is presented. The aim of this methodology is to use these concepts as a tool to, while maintaining the needed accuracy, reduce the complexity usually involved in object tracking problems. Several dynamic fuzzy sets are constructed according to both kinematic and non-kinematic properties that distinguish the object to be tracked. Meanwhile kinematic related fuzzy sets model the objects motion pattern, the non-kinematic fuzzy sets model the objects appearance. The tracking task is performed through the fusion of these fuzzy models by means of an inference engine. This way, object detection and matching steps are performed exclusively using inference rules on fuzzy sets. In the multiple object methodology, each object is associated with a confidence degree and a hierarchical implementation is performed based on that confidence degree.

A construction method of Atanassov's intuitionistic fuzzy sets for image processing

In this work we introduce a new construction method of Atanassovs intuitionistic fuzzy sets (A-IFSs) from fuzzy sets. We use A-IFSs in image processing. We propose a new image magnification algorithm using A-IFSs. This algorithm is characterized by its simplicity and its efficiency.

A construction method of interval-valued Fuzzy Sets for image processing

In this work we present a new construction method of IVFSs from Fuzzy Sets. We use these IVFSs for image processing. Concretely, in this contribution we introduce a new image magnification algorithm using IVFSs. This algorithm is based on block expansion and it is characterized by its simplicity.