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Sometimes we have to work with L-fuzzy context sequences where one or more values are missing. These sequences can represent, among other things, the evolution in time of an L-fuzzy context. The studies of tendencies that we have done so far used tools that are not valid when the L-fuzzy context has unknown values. In this work we address such situations and we propose new methods to tackle the problem. Besides, we use the study of tendencies to analyse relations between the objects and the attributes of L-fuzzy contexts and to replace the absent values taking into account the behaviour of the sequence. [ABSTRACT FROM AUTHOR]

Gradient maps are common intermediate representations in image processing, with extensive use in both classical and state-of-the-art algorithms. Most of the research on gradient map extraction has been devoted to the definition of gradient extraction operators or filters, normally by optimizing certain criteria. In this context, we find a rather limited literature in gradient map extraction using multiscale information. In this work, we develop the idea of producing a gradient map by fusing the gradient maps obtained at different scales. We first analyze the Gaussian Scale Space and the behaviour of gradients when images are projected into it; second, we propose two classes of self-adapting vector fusion operators, which are inspired by the focus-selective nature of the human visual system; third, we present a framework for multiscale boundary detection based on the use of such classes of operators for multiscale gradient fusion. We experimentally test our boundary detection framework to illustrate the validity of our vector fusion operators. [ABSTRACT FROM AUTHOR]

The necessity of dealing with uncertainty in real world problems has been a long-term research challenge which has originated different methodologies and theories. Recently, the concept of Hesitant Fuzzy Sets (HFSs) has been introduced to model the uncertainty that often appears when it is necessary to establish the membership degree of an element and there are some possible values that make to hesitate about which one would be the right one. Many researchers have paid attention on this concept who have proposed diverse extensions, relationships with other types of fuzzy sets, different types of operators to compute with this type of information, applications on information fusion and decision-making, etc. Nevertheless, some of these proposals are questionable, because they are straightforward extensions of previous works or they do not use the concept of HFSs in a suitable way. Therefore, this position paper studies the necessity of HFSs and provides a discussion about current proposals including a guideline that the proposals should follow and some challenges of HFSs. [ABSTRACT FROM AUTHOR]

In the evaluation of boundary detection methods it is common to use as ground truth a set of boundary images that are hand-made by human experts. This work proposes a novel representation of this ground truth. More specifically, we propose to combine the hand-made boundary images into a set-based consensus, which is constructed from the concordances and discordances among the images. We study the theoretical and visual properties of this consensus and present an application to boundary image quality evaluation. [ABSTRACT FROM AUTHOR]

Intervals are a popular way to represent the uncertainty related to data, in which we express the vagueness of each observation as the width of the interval. However, when using intervals for this purpose, we need to use the appropriate set of mathematical tools to work with. This can be problematic due to the scarcity and complexity of interval-valued functions in comparison with the numerical ones. In this work, we propose to extend a generalization of the Sugeno integral to work with interval-valued data. Then, we use this integral to aggregate interval-valued data in two different settings: first, we study the use of intervals in a brain-computer interface; secondly, we study how to construct interval-valued relationships in a social network, and how to aggregate their information. Our results show that interval-valued data can effectively model some of the uncertainty and coalitions of the data in both cases. For the case of brain-computer interface, we found that our results surpassed the results of other interval-valued functions. [ABSTRACT FROM AUTHOR]

In this work we present an image reduction algorithm based on averaging aggregation functions. We axiomatically define the concepts of image reduction operator and local reduction operator. We study the construction of the latter by means of averaging functions and we propose an image reduction algorithm (image reduction operator). We analyze the properties of several averaging functions and their effect on the image reduction algorithm. Finally, we present experimental results where we apply our algorithm in two different applications, analyzing the best operators for each concrete application. [ABSTRACT FROM AUTHOR]

Abstract: Content-aware, edge-preserving smoothing techniques have gained visibility in recent years. However, they have had a rather limited impact on the edge detection literature compared to content-unaware (linear) techniques, often based on Gaussian filters. In this work, we focus on Anisotropic Diffusion, covering its initial definition by Perona and Malik and subsequent extensions. A visual case study is used to illustrate their features. We perform a quantitative evaluation of the performance of the Canny method for edge detection when substituting linear Gaussian smoothing filters by Anisotropic Diffusion. [Copyright &y& Elsevier]

Abstract: The human vision is usually considered a multiscale, hierarchical knowledge extraction system. Inspired by this fact, multiscale techniques for computer vision perform a sequential analysis, driven by different interpretations of the concept of scale. In the case of edge detection, the scale usually relates to the size of the region where the intensity changes are measured or to the size of the regularization filter applied before edge extraction. Multiscale edge detection methods constitute an effort to combine the spatial accuracy of fine-scale methods with the ability to deal with spurious responses inherent to coarse-scale methods. In this work we introduce a multiscale method for edge detection based on increasing Gaussian smoothing, the Sobel operators and coarse-to-fine edge tracking. We include visual examples and quantitative evaluations illustrating the benefits of our proposal. [Copyright &y& Elsevier]

In this paper we stress the relevance of a particular family of fuzzy sets, where each element can be viewed as the result of a classification problem. In particular, we assume that fuzzy sets are defined from a well-defined universe of objects into a valuation space where a particular graph is being defined, in such a way that each element of the considered universe has a degree of membership with respect to each state in the valuation space. The associated graph defines the structure of such a valuation space, where an ignorance state represents the beginning of a necessary learning procedure. Hence, every single state needs a positive definition, and possible queries are limited by such an associated graph. We then allocate this family of fuzzy sets with respect to other relevant families of fuzzy sets, and in particular with respect to Atanassov''s intuitionistic fuzzy sets. We postulate that introducing this graph allows a natural explanation of the different visions underlying Atanassov''s model and interval valued fuzzy sets, despite both models have been proven equivalent when such a structure in the valuation space is not assumed. [Copyright &y& Elsevier]

• We analyze boundary evaluation methods, focusing on those based on (a) boundary matching and (b) analysis of confusion matrices, which are the current most popular trend. • We review literature in boundary matching, describing the constraints and goals holding for different tasks. • We propose a taxonomy for boundary matching methods in the context of boundary evaluation. • We design a novel experimental framework to compare the potential differences between boundary image comparison methods (in general), and boundary matching strategies (in particular). • We carry out extensive experiments to quantitatively and qualitatively analyze the similarities and divergences in the results by different boundary matching methods. Most of the strategies for boundary image evaluation involve the comparison of computer-generated images with ground truth solutions. While this can be done in different manners, recent years have seen a dominance of techniques based on the use of confusion matrices. That is, techniques that, at the evaluation stage, interpret boundary detection as a classification problem. These techniques require a correspondence between the boundary pixels in the candidate image and those in the ground truth; that correspondence is further used to create the confusion matrix, from which evaluation statistics can be computed. The correspondence between boundary images faces different challenges, mainly related to the matching of potentially displaced boundaries. Interestingly, boundary image comparison relates to many other fields of study in literature, from object tracking to biometrical identification. In this work, we survey all existing strategies for boundary matching, we propose a taxonomy to embrace them all, and perform a usability-driven quantitative analysis of their behaviour. [ABSTRACT FROM AUTHOR]

In this paper we propose a new version of penalty-based aggregation functions, the Multi Cost Aggregation choosing functions (MCAs), in which the function to minimize is constructed using a convex combination of two relaxed versions of restricted equivalence and dissimilarity functions instead of a penalty function. We additionally suggest two different alternatives to train a MCA in a supervised classification task in order to adapt the aggregation to each vector of inputs. We apply the proposed MCA in a Motor Imagery-based Brain–Computer Interface (MI-BCI) system to improve its decision making phase. We also evaluate the classical aggregation with our new aggregation procedure in two publicly available datasets. We obtain an accuracy of 82.31% for a left vs. right hand in the Clinical BCI challenge (CBCIC) dataset, and a performance of 62.43% for the four-class case in the BCI Competition IV 2a dataset compared to a 82.15% and 60.56% using the arithmetic mean. Finally, we have also tested the goodness of our proposal against other MI-BCI systems, obtaining better results than those using other decision making schemes and Deep Learning on the same datasets. • We develop relaxed versions of Restricted Equivalence Functions. • We aggregate information from different classifiers trained on different wave bands. • The new aggregations learn from the input data to discriminate between classes. • The novel aggregation functions can be adapted to the original data. [ABSTRACT FROM AUTHOR]

Ordered Weighted Averaging (OWA) operators are a profusely applied class of averaging aggregation functions, i.e. operators that always yield a value between the minimum and the maximum of the inputs. The orness measure was introduced to classify the behavior of the OWA operators depending on the weight vectors. Defining a suitable orness measure is an arduous task when we deal with OWA operators defined over more intricate spaces, such us intervals or lattices. In this work we propose a suitable definition for the orness measure to classify OWA operators defined on the set of m-dimensional intervals taking real values in [ 0 , 1 ]. The orness measure is applied to decide which is the best partition of a continuous range that should be divided into four linguistic labels. This example shows the good behavior of the proposed orness measure. [ABSTRACT FROM AUTHOR]

Fuzzy set theory has developed a prolific armamentarium of mathematical tools for each of the topics that has fallen within its scope. One of such topics is data comparison, for which a range of operators has been presented in the past. These operators can be used within the fuzzy set theory, but can also be ported to other scenarios in which data are provided in various representations. In this work, we elaborate on notions for type-2 fuzzy sets, specifically for the comparison of type-2 fuzzy membership degrees, to create function comparison operators. We further apply these operators to hyperspectral imaging, in which pixelwise data are provided as functions over a certain energy spectra. The performance of the functional comparison operators is put to the test in the context of in-laboratory hyperspectral image segmentation. [ABSTRACT FROM AUTHOR]

Abstract Ordered weighted average (OWA) operators are commonly used to aggregate information in multiple situations, such as decision making problems or image processing tasks. The great variety of weights that can be chosen to determinate an OWA operator provides a broad family of aggregating functions, which obviously give different results in the aggregation of the same set of data. In this paper, some possible classifications of OWA operators are suggested when they are defined on m -dimensional intervals taking values on a complete lattice satisfying certain local conditions. A first classification is obtained by means of a quantitative orness measure that gives the proximity of each OWA to the OR operator. In the case in which the lattice is finite, another classification is obtained by means of a qualitative orness measure. In the present paper, several theoretical results are obtained in order to perform this qualitative value for each OWA operator. [ABSTRACT FROM AUTHOR]

In this paper we propose an algorithm to solve group decision making problems using n -dimensional fuzzy sets, namely, sets in which the membership degree of each element to the set is given by an increasing tuple of n elements. The use of these sets has naturally led us to define admissible orders for n -dimensional fuzzy sets, to present a construction method for those orders and to study OWA operators for aggregating the tuples used to represent the membership degrees of the elements. In these conditions, we present an algorithm and apply it to a case study, in which we show that the exploitation phase which appears in many decision making methods can be omitted by just considering linear orders between tuples. [ABSTRACT FROM AUTHOR]

This paper deals with OWA (ordered weighted average) operators defined on any complete lattice endowed with a t-norm and a t-conorm and satisfying a certain finiteness local condition. A parametrization of these operators is suggested by introducing a quantitative orness measure for each OWA operator, based on its proximity to the OR operator. The meaning of this measure is analyzed for some concrete OWA operators used in color image reduction, as well as for some OWA operators used in a medical decision making process. [ABSTRACT FROM AUTHOR]

Abstract: In this work we present a construction method for Atanassov’s 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 Atanassov’s 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. [Copyright &y& Elsevier]