Color is a powerful feature for image analysis but it is usually not used in image classification schemes. We propose a method to combine fuzzy color information with the result obtained from a One-Versus-All classifier (OVA) trained with Bag-of-features. This method consists in weighting the outputs of the OVA classifier based on the distances between the new image to be classified and the classes. Experimental results show that our approach improves OVA classifier performance.

Feature aggregation is a crucial step in many methods of image classification, like the Bag-of-Words (BoW) model or the Convolutional Neural Networks (CNN). In this aggregation step, usually known as spatial pooling, the descriptors of neighbouring elements within a region of the image are combined into a local or a global feature vector. The combined vector must contain relevant information, while removing irrelevant and confusing details. Maximum and average are the most common aggregation functions used in the pooling step. To improve the aggregation of relevant information without degrading their discriminative power for classification in this work we propose the use of Ordered Weighted operators. We provide an extensive evaluation that shows that the final result of the classification using OWA aggregation is always better than average pooling and better than maximum pooling when dealing with small dictionary sizes.

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.

In this paper, we will present a wider view on the relationship between interval-valued fuzzy sets and interval type-2 fuzzy sets, where we will show that interval-valued fuzzy sets are a particular case of the interval type-2 fuzzy sets. For this reason, both concepts should be treated in a different way. In addition, the view presented in this paper will allow a more general perspective of interval type-2 fuzzy sets, which will allow representing concepts that could not be presented by interval-valued fuzzy sets.

In this work we analyze the competitiveness of fuzzy rule-based systems in comparison with black box models like support vector machines to deal with fingerprint classification problems. With this aim, we carry out an experimental study applying different feature extraction models (covering almost every kind of features that are usually considered in this problem) and three fingerprint databases of different qualities. The obtained results show the good behavior of fuzzy rule-based classification systems. Observing these results, new future lines are outlined, which could improve the classification performance achieved with the current models.

An important problem in working with fuzzy sets is the correct construction of the membership functions that represent the objects of the system. Different experts construct different membership functions to represent the same object. In this paper, we construct an interval type-2 fuzzy set (IT2FS) with different fuzzy sets such that the length of the (membership) interval represents the uncertainty of the expert with respect to the choice of the membership function. We analyze this problem in the context of image segmentation. We propose a new version of the classical fuzzy thresholding algorithm, in which an expert can select multiple membership functions, to avoid the problem of selecting only one to represent the image. From these membership functions, we construct an IT2FS, and by minimizing its entropy, we find a threshold with which to binarize the image. We present experimental results that show that it is advisable to use this methodology when it is not known which membership function is the most suitable.

In this paper, we propose new aggregation functions for the pairwise comparison of alternatives in fuzzy preference modeling. More specifically, we introduce the concept of a grouping function, i.e., a specific type of aggregation function that combines two degrees of support (weak preference) into a degree of information or, say, a degree of comparability between two alternatives, and we relate this new concept to that of incomparability. Grouping functions of this type complement the existing concept of overlap functions in a natural way, since the latter can be used to turn two degrees of weak preference into a degree of indifference. We also define the so-called generalized bientropic functions that allow for a unified representation of overlap and grouping functions. Apart from analyzing mathematical properties of these types of functions and exploring relationships between them, we elaborate on their use in fuzzy preference modeling and decision making. We present an algorithm to elaborate on an alternative preference ranking that penalizes those alternatives for which the expert is not sure of his/her preference.

In this work we present a new image thresholding algorithm for the segmentation of MRI brain images into two classes: gray matter and white matter. The proposed algorithm is based on the concept of incomparability proposed by Fodor and Roubens for fuzzy preference relations. We test our algorithm for local and global segmentation of brain images. We proof that global segmentation performs better results than local segmentation and improves the results obtained by other thresholding algorithm.

In this paper we introduce the concept of Generalized Atanassov's Intuitionistic Fuzzy Index. We characterize it in terms of fuzzy implication operators and propose a construction method with order automorphisms. Finally, we obtain, by means of special aggregation functions applied to the generalized Atanassov's intuitionistic fuzzy index, the Atanassov's intuitionistic fuzzy entropy given by Burillo and Bustince.

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 K(α) 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.

The edge detection process can be broken down into four basic transformations, modifying the image from the original presentation to the final edges one. The adoption of this framework makes the process far more understandable, and offers an starting point for the combination and comparison of different edge detection methods. In this work we analyze the role of the third of the transformations, the blending, where the edge features are combined to obtain the edginess values. This work studies the use of quasi-aritmethic means for the combination of the edge features. Moreover, we show results obtained with different operators on real images, in order to illustrate the importance of the blending phase in the edge detection process. Results will show the impact of the function selection in the final results.

In this work an ignorance-based fuzzy clustering algorithm is presented. The algorithm is based on the entropy-based clustering algorithm proposed by Yao et al.[14]In our proposal, we calculate the total ignorance instead of using the entropy at each data point to select the cluster centers. The experimental results show that the ignorance-based clustering improves the data classification made by the EFC in image segmentation.

In this work an ignorance-based fuzzy clustering algorithm is presented. The algorithm is based on the entropy-based clustering algorithm proposed by Yao et al.. In our proposal, we calculate the total ignorance instead of using the entropy at each data point to select the data point as the first cluster center. The experimental results show that the ignorance-based clustering improves the data classification made by the EFC in image segmentation.

In this paper we study in depth certain properties of interval type 2 fuzzy sets. In particular we recall a method to construct different interval type 2 fuzzy connectives starting from an operator. We further study the law of contradiction and the law of excluded middle for these sets. Furthermore we analyze the properties: idempotency, absorption, and distributiveness.

The problem of segmentation in spite of all the work over the last decades is still an important research field. Moreover, during the past years, fuzzy logic theory has been successfully applied to image thresholding. Considering that for segmentation purposes, in most cases, image pixels have an inherent ambiguity in the predicate that they must fulfill to belong to an object, which results in the experts uncertainty in assigning the pixel to that object, Atanassovpsilas intuitionistic fuzzy sets (A-IFSs) are a relevant and interesting extension since, uncertainty is one of the underlying ideas behind this theory. In this paper we describe a thresholding technique using A-IFSs. This approach uses Atanassov's intuitionistic index values for representing the uncertainty of the expert when assigning the pixel to the background or to the object. The general framework of this approach and its natural extension to multilevel thresholding are presented. Segmentation results and their performance evaluation are presented.

In this paper we present a method for constructing a special case of interval type 2 fuzzy sets from a grayscale image. We use properties that are exclusive of these sets in order to represent the changes in intensity in the image and so create what in image processing is known as false edges.

Starting from the definitions of the weak fuzzy subsethood measure (V.R. Young, Fuzzy subsethood. Fuzzy Sets and Systems, 77 (1996) 371–384) and of strong fuzzy inclusion, (D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, New York, Academic Press, 1980) we define weak fuzzy S-subsethood measures. We analyze their axiomatization and present various constructions obtained by aggregating implication operators with special properties. We conclude by presenting the conditions under which we can construct fuzzy entropies and overlap indices from these measures.