International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper we extend some previously established links between the derivation operators used in formal concept analysis and some mathematical morphology operators to fuzzy concept analysis. We also propose to use mathematical morphology to navigate in a fuzzy concept lattice and perform operations on it. Links with other lattice-based for malisms such as rough sets and F-transforms are also established. This paper proposes a discussion and new results on such links and their potential interest.

Wearable devices have promoted the application of Human Activity Recognition to the development of techniques for the assessment or diagnosing of illnesses and seizures, among other applications. For instance, the use of tri-axial accelerometry (3DACM) to detect abnormal and sudden movements has been introduced in the epileptic seizure recognition. In a previous research, Fuzzy Rule Based Classifiers (FRBC) have been found valid for the detection of epileptic convulsions; however, Ant Colony Systems learned FRBC performed with a high variability depending on the training data. In this study, we cope with this problem by the selection of a suitable partitioning method that has been extended to generate Fuzzy partitions. The comparison with the previous obtained results shows the fuzzy partitioning does not improve the overall performance in terms of error but highly reduces the variability in the performance of the obtained models, which allows us to obtain general models.

Although image retrieval for e-commerce field has a huge commercial potential, e-commerce oriented content-based image retrieval is still very raw. Modern online shopping systems have certain limitations. In particular, they use conventional tag-based retrieval and lack making use of visual content. The paper presents a methodology to retrieve images of shopping items based on fuzzy dominant colors. People regard color as an aesthetic issue, especially when it comes to choosing the colors of their clothing, apartment design and other objects around. No doubt, color inuences purchasing behavior — to a certain extent, it is a reection of human's likes and dislikes. The fuzzy color model that we are proposing represents the collection of fuzzy sets, providing the conceptual quantization of crisp HSI space having soft boundaries. The proposed method has two parts: assigning a fuzzy colorimetric profile to the image and processing the user query. We also use underlying mechanisms of attention from a theory of visual attention, like perceptual categorization. Subjectivity and sensitivity of humans in color perception and bridging the semantic gap between low-level color visual features and high-level concepts are major issues that we plan to tackle in this research.

Spanish primary and secondary school curricula comprise several contents, learning outcomes and assessment criteria directly related with probability and approximate calculus. Some of them refer to situations modeled by the students, which entail not only uncertainty but also imprecision. For this reason, different techniques including fuzzy logic and fuzzy sets theory could be applied when dealing with this kind of situations in the classroom. Several teaching situations handling imprecise concepts in primary and secondary schools are suggested from a theoretical point of view. These more exible ways of reasoning could be combined with the traditional probability approach, allowing to tackle more general problems and not only those involving exact calculations or specific numerical assignments. Moreover, this type of approaches will provide the students with tools to manage imprecision as a mathematical tool in their personal life.

Opinions have a relevant inuence on people’s behavior. The Internet and the Web have made it possible for people to share their opinions and for other people and organizations find out more about opinions and experiences from individuals. Still, opinions involve sentiments that are vague and imprecise textual descriptions. Hence, due to the nature of the data, Fuzzy Logic can be a promising approach. This paper proposes a method to automatically build a fuzzy system, based on features extracted and selected from documents, to perform classification of sentiment in opinions across different domains. Almost 60 features were extracted from documents and multiple feature selection algorithms were applied. Over the selected features, the Wang-Mendel (WM) method was used to generate fuzzy rules and classify documents. Variations on fuzzy set modeling, on the use of weights in the rules and on fuzzy inference mechanisms were considered. The classifier fuzzy system based achieved 71,25% of accuracy in a 10-fold cross-validation, comparable to a SVM classifier.

In this paper we present an extension of the action language Golog that allows for using fuzzy notions in non-deterministic argument choices and the reward function in decision-theoretic planning. Often, in decision-theoretic planning, it is cumbersome to specify the set of values to pick from in the non-deterministic-choice-of-argument statement. Also, even for domain experts, it is not always easy to specify a reward function. Instead of providing a finite domain for values in the non-deterministic-choice-of-argument statement in Golog, we now allow for stating the argument domain by simply providing a formula over linguistic terms and fuzzy uents. In Golog’s forward-search DT planning algorithm, these formulas are evaluated in order to find the agent’s optimal policy. We illustrate this in the Diner Domain where the agent needs to calculate the optimal serving order.

Hesitant fuzzy sets represent a useful tool in many areas such as decision making or image processing. Finite interval-valued hesitant fuzzy sets are a particular kind of hesitant fuzzy sets that generalize fuzzy sets, interval-valued fuzzy sets or Atanassov’s intuitionistic fuzzy sets, among others. Partitioning is a long-standing open problem due to its remarkable importance in many areas such as clustering. Thus, many different partitioning approaches have been developed for crisp and fuzzy sets. This work presents a partitioning method for the so-called finite interval-valued hesitant fuzzy sets. The definition of this partitioning method involves a definition of an ordering relation for finite interval-valued fuzzy sets membership degrees, i.e, finitely generated sets, as well as the definitions of t-norm and t-conorm for these kinds of sets.

Iterative OWA (ItOWA) as proposed by Dujmovic, is a two-stage procedure for computing the weighting vector by a double nested iteration: (i) weights at step h are computed as limit to infinity of a matrix power, (ii) the result is used to start the computation at step h + 1, until the OWA operator arity n is reached. Thereafter Dujmovic suggested a computational solution based on the conjecture that the limit exists, and numerical simulations have being supported the hypothesis that the conjecture is correct. In this paper, we prove that the limit actually exists and we provide an analytical solution to the procedure, so the weighting vector can be computed directly instead of an iterative time-consuming procedure. This theoretical result enables a faster computation of the weighting vector and characterization in terms of weights values, attitudinal character and entropy.