We propose a method to perform regression on partially labeled data, which is based on SSFCM (Semi-Supervised Fuzzy C-Means), an algorithm for semi-supervised classification based on fuzzy clustering. The proposed method, called SSFCM-R, precedes the application of SSFCM with a relabeling module based on target discretization. After the application of SSFCM, regression is carried out according to one out of two possible schemes: (i) the output corresponds to the label of the closest cluster; (ii) the output is a linear combination of the cluster labels weighted by the membership degree of the input. Some experiments on synthetic data are reported to compare both approaches.

Crowd analysis from drones has attracted increasing attention in recent times, thanks to the ease of deployment and affordable cost of these devices. However, how this technology can provide a solution to crowd flow detection is still an explored research question. In this paper, we contribute by proposing a crowd flow detection method for video sequences shot by a drone. The method is mainly based on a Fully Convolutional Network model for crowd density estimation, which aims to provide a good compromise between effectiveness and efficiency, and clustering algorithms aimed at detecting the centroids of high-density areas in density maps. The method was tested on the VisDrone Crowd Counting dataset-characterized not by still images but by video sequences-providing promising results. This direction may open up new ways of analyzing high-level crowd behavior from drones.1

Abstract We study the impact of fuzziness on the behavior of Fuzzy Rule-Based Classifiers (FRBCs) defined by trapezoidal fuzzy sets forming Strong Fuzzy Partitions. In particular, if an FRBC selects the class related to the rule with the highest activation (so-called Winner-Takes-All approach), then fuzziness, as quantified by the slope of the membership functions, has no impact in classifying data in regions of the input space where rules dominate. On the other hand, fuzziness affects the behaviour of the FRBC in regions where the confidence in classification is low. As a consequence, in the context of Explainable Artificial Intelligence, fuzziness is profitable in FRBCs only if classification is accompanied by an explanation of the confidence of the provided outputs.

Fuzzy Rule-Based Systems (FRBSs) are endowed with a knowledge base that can be used to provide model and outcome explanations. Usually, FRBSs are acquired from data by applying some learning methods: it is expected that, when modeling the same phenomenon, the FRBSs resulting from the application of a learning method should provide almost the same explanations. This requires a stability in the description of the knowledge bases that can be evaluated through the proposed measure of Descriptive Stability. The measure has been applied on three methods for generating FRBSs based on three benchmark datasets. The results show that, under same settings, different methods may produce FRBSs with varying stability, which impacts on their ability to provide trustful explanations.

Data counting is non-trivial when data are uncertain. In the case of uncertainty due to incompleteness, possibility theory can be used to define a granular counting model. Two algorithms were proposed in literature to compute granular counting: exact granular counting, with quadratic time complexity, and approximate granular counting, with linear time complexity. However, both algorithms require that all data are available before counting. This paper presents an incremental granular counting algorithm which provides an efficient and exact computation of the granular count without the need of having all data available, thus opening the door to applications involving data streams.

Crowd analysis is receiving an increasing attention in the last years because of its social and public safety implications. One of the building blocks of crowd analysis is crowd counting and the associated crowd density estimation. Several commercially available drones are equipped with onboard cameras and embed powerful GPUs, making them an excellent platform for real-time crowd counting tools. This paper proposes a light-weight and fast fully-convolutional neural network to learn a regression model for crowd counting in images acquired from drones. A robust model is derived by training the network from scratch on a subset of the very challenging VisDrone dataset, which is characterized by a high variety of locations, environments, perspectives and lighting conditions. The derived model achieves an MAE of 8.86 and an RMSE of 15.07 on the test images, outperforming models developed by state-of-the-art light-weight architectures, that are MobileNetV2 and YOLOv3.

JFML is an open source Java library aimed at facilitating interoperability of fuzzy systems by implementing the IEEE Std 1855-2016 - the IEEE Standard for Fuzzy Markup Language (FML) that is sponsored by the IEEE Computational Intelligence Society. We developed a Python wrapper for JFML that enables to use all the functionalities of JFML through a Python 3.x module. The bridge between Python and Java is accomplished through the use of the Py4J framework. As a result, the possibility of using the IEEE standard for representing fuzzy systems is enlarged to a wider community of developers and knowledge engineers, with minimal code redundancy. Experiments show full interoperability between Python programs and JFML without any tangible overhead. We illustrate the use of Py4JFML in a beer style classification case study.

Virtual Learning Environments (VLE) offer a wide range of courses and learning supports for students. Such innovative learning platforms generate daily a huge quantity of data, regarding the interactions among the students and the VLE. To analyze these big educational data a new research branch called educational data mining (EDM) has emerged, that puts together computer scientists and pedagogues researchers' expertise. So far, educational data have been studied as stationary data by traditional machine learning methods. Rather, educational data are non-stationary in nature and can be better analyzed as data streams. In this paper we investigate the use of an adaptive fuzzy clustering algorithm called DISSFCM (Dynamic Incremental Semi-Supervised FCM) to process educational data as data streams and predict the students' outcomes to one exam module. Numerical experiments on the Open University Learning Analytics Dataset (OULAD) show the reliability of DISSFCM in creating good classification models of educational data.

We propose a method to extract and integrate fuzzy information granules from a populated OWL ontology. The purpose of this approach is to represent imprecise knowledge within an OWL ontology, as motivated by the fact that the Semantic Web is full of imprecise and uncertain information coming from p erceptual data, incomplete data, data with errors, etc. In particular, we focus on Fuzzy Set Theory as a means for representing and processing information granules corresponding to imprecise concepts usually expressed by linguistic terms. The method applies to numerical data properties. The values of a property are first clustered to form a collection of fuzzy sets. Then, for each fuzzy set, the relative σ-count is computed and compared with a number of predefined fuzzy quantifiers, which are therefore used to define new assertions that are added to the original ontology. In this way, the extended ontology provides both a punctual view and a granular view of individuals w.r.t. the selected property. We use a real-world ontology concerning hotels and populated with data of the Italian city of Pisa, to illustrate the method and to test its implementation. We show that it is possible to extract granular properties that can be described in natural language and smoothly integrated in the original ontology by means of annotated assertions.

DC∗ is a method for generating interpretable fuzzy information granules from pre-classified data. It is based on the subsequent application of LVQ1 for data compression and an ad-hoc procedure based on A∗ to represent data with the minimum number of fuzzy information granules satisfying some interpretability constraints. While being efficient in tackling several problems, the A∗ procedure included in DC∗ may happen to require a long computation time because the A∗ algorithm has exponential time complexity in the worst case. In this paper, we approach the problem of driving the search process of A∗ by suggesting a close-to-optimal solution that is produced through a Genetic Algorithm (GA). Experimental evaluations show that, by driving the A∗ algorithm embodied in DC∗ with a GA solution, the time required to perform data granulation can be reduced by at least 45% and up to 99%.

BACKGROUND: When the reads obtained from high-throughput RNA sequencing are mapped against a reference database, a significant proportion of them - known as multireads - can map to more than one reference sequence. These multireads originate from gene duplications, repetitive regions or overlapping genes. Removing the multireads from the mapping results, in RNA-Seq analyses, causes an underestimation of the read counts, while estimating the real read count can lead to false positives during the detection of differentially expressed sequences. RESULTS: We present an innovative approach to deal with multireads and evaluate differential expression events, entirely based on fuzzy set theory. Since multireads cause uncertainty in the estimation of read counts during gene expression computation, they can also influence the reliability of differential expression analysis results, by producing false positives. Our method manages the uncertainty in gene expression estimation by defining the fuzzy read counts and evaluates the possibility of a gene to be differentially expressed with three fuzzy concepts: over-expression, same-expression and under-expression. The output of the method is a list of differentially expressed genes enriched with information about the uncertainty of the results due to the multiread presence. We have tested the method on RNA-Seq data designed for case-control studies and we have compared the obtained results with other existing tools for read count estimation and differential expression analysis. CONCLUSIONS: The management of multireads with the use of fuzzy sets allows to obtain a list of differential expression events which takes in account the uncertainty in the results caused by the presence of multireads. Such additional information can be used by the biologists when they have to select the most relevant differential expression events to validate with laboratory assays. Our method can be used to compute reliable differential expression events and to highlight possible false positives in the lists of differentially expressed genes computed with other tools.

When approaching real-world problems with intelligent systems, an interaction with user is often expected. However, data-driven models are usually evaluated only in terms of accuracy, thus not involving users. In literature several works have been proposed for defining measures for interpretability assessment, however, such measures are mostly based on a structural evaluation. For this reason, we investigated a new methodology for assessing interpretability based on semantic cointension. The objective of this work is to provide empirical evidence about the usefulness of semantic cointension in facing a medical problem, namely the prediction of prognosis in Immunoglobulin A Nephropathy. An experimental session has been conducted, where fuzzy rule-based classifiers have been modeled, which are highly interpretable from the structural viewpoint. Results show that through the notion of semantic cointension it is possible to perform a semantic-driven assessment of interpretability, which also takes into account the overall fuzzy inference schema.

A key feature for machine intelligence is the ability of learning knowledge from past experiences. Furthermore, in a human-centric environment, the acquired knowledge must fulfill comprehensibility requirements so as to be shared by human users. In literature, several approaches have been proposed to acquire comprehensible knowledge from data by preserving a number of interpretability constraints, especially for Fuzzy Rule-Based Classifiers (FRBCs). As a general result, accuracy and interpretability emerge as conflicting features, so that a tradeoff is often required. In consequence of this tradeoff, the resulting FRBCs are provided with a knowledge base expressed in natural language but, as a matter of fact, the semantics embedded by the linguistic structures might not be cointensive with the explicit semantics defined in the knowledge base. As an alternative approach, in this paper we propose a technique to design FRBCs from data with the specific aim of maximizing interpretability in the sense of semantic cointension. The most important result of this approach is to control cointension so as to select models that possess knowledge bases that users can understand on the basis of their natural language description. This enables the use of the FRBC in a human-centric environment. Experimental sessions are performed on benchmark classification problems to show the effectiveness of the proposed approach.

In recommender systems, the task of automatically deriving user profiles, encoding the actual preferences of users, covers a fundamental role. In this paper, we propose a strategy for learning and updating user profiles by using fuzzy sets that reveal to be a valid tool to model the vague and imprecise nature of preferences as well as the items to be recommended. The proposed adaptation strategy resembles a competitive learning process in which the user profile is continuously updated in order to make its components as similar as possible to the description of the accessed items. On the same time a mechanism to forget outdated user preferences is proposed in order to describe changes in user interests over time. The strategy was applied on the MovieLens dataset and the obtained results show its effectiveness to learn user profiles reflecting the current preferences of users.

Recommender systems are systems capable of assisting users by quickly providing them with relevant resources according to their interests or preferences. The efficacy of a recommender system is strictly connected with the possibility of creating meaningful user profiles, including information about user preferences, interests, goals, usage data and interactive behavior. In particular, analysis of user preferences is important to predict user behaviors and make appropriate recommendations. In this paper, we present a fuzzy framework to represent, learn and update user profiles. The representation of a user profile is based on a structured model of user cognitive states, including a competence profile, a preference profile and an acquaintance profile. The strategy for deriving and updating profiles is to record the sequence of accessed resources by each user, and to update preference profiles accordingly, so as to suggest similar resources at next user accesses. The adaption of the preference profile is performed continuously, but in earlier stages it is more sensitive to updates (plastic phase) while in later stages it is less sensitive (stable phase) to allow resource recommendation. Simulation results are reported to show the effectiveness of the proposed approach.

Interpretability represents the most important driving force behind the implementation of fuzzy logic-based systems. It can be directly related to the system's knowledge base, with reference to the human user's easiness experienced while reading and understanding the embedded pieces of information. In this paper, we present a preliminary study on interpretability conditions for fuzzy rule-based classifiers on the basis of an innovative approach that relies on the concept of semantic cointension. The approach adopted in this study consists in analysing the components of a fuzzy classifiers so that inference is carried out with the respect of logical properties. As a result, we derive some sufficient conditions and basic requirements to be verified by a fuzzy classifier in order to be tagged as interpretable in the semantic sense.

Item recommendation depends on metadata describing items as well as users through their profiles. Most currently used technologies use precise metadata because of the efficiency of the recommendation process. Nonetheless fuzzy metadata can be useful because of their ability to deal with imprecision and gradedness, two features pervading real-world applications. Fuzzy metadata can have both possibilistic and veristic interpretations, which are complementary and can simultaneously occur in a recommendation context. In this paper we describe a preliminary approach to deal with this double interpretation proposing an extension of the theory of veristic variables, that is specifically suited for item recommendation. Fuzzy metadata are used to calculate the interestingness of an item for a user computing possibility and necessity measures, which enable the ranking of items. As described in the illustrative examples, this approach effectively provides for semantically significant results that are useful for item recommendation with fuzzy metadata.

Adaptive software systems are systems that tailor their behavior to each user on the basis of a personalization process. The efficacy of this process is strictly connected with the possibility of an automatic detection of preference profiles, through the analysis of the users' behavior during their interactions with the system. The definition of such profiles should take into account imprecision and gradedness, two features that justify the use of fuzzy sets for their representation. This paper proposes a model for representing preference profiles through fuzzy sets. The model's strategy for adapting profiles to user preferences is to record the sequence of accessed resources by each user, and to update preference profiles accordingly so as to suggest similar resources at next user accesses. Profile adaption is performed continuously, but in earlier stages it is more sensitive to updates (plastic phase) while in later stages it is less sensitive (stable phase) to allow resource suggestion. Simulation results are reported to show the effectiveness of the proposed approach.

In this paper we present an approach for extracting interpretable information granules for classification. The approach, called DCγ(double clustering with genetic algorithms) is based on two clustering steps. The first step uses LVQ1 to identify cluster prototypes in the multidimensional data space so as to represent hidden relationships among data. In the second step a genetic algorithm is applied to the projections of these prototypes with the objective of finding a minimal number of fuzzy information granules that verify some interpretability constraints. The key feature of DCγis the efficiency of the minimization process carried out in the second step. Experimental results on two medical diagnosis problems show the effectiveness of the proposed approach in terms of accuracy, interpretability and efficiency.

In this paper we describe an approach for mining interpretable diagnostic rules through a fuzzy information granulation process. Specifically, this process is performed by the DC* algorithm (Double Clustering with A*), which is aimed at mining from data a set of fuzzy information granules that satisfy a number of interpretability constraints. Such granules can be labelled with linguistic terms and used as building blocks for deriving diagnostic rules. The DC* is based on two clustering steps. The first step applies the LVQ1 algorithm to find a number of prototypes in the input space, which represent hidden relationships among data. The second clustering step .based on the A* search. takes place on the projections of such prototypes, and is aimed at finding an optimal number of granules that verify interpretability constraints. The application of DC* to two well-known medical datasets provided a set of intelligible rules with satisfactory accuracy.

Data Mining, a central step in the broader overall process of Knowledge Discovery from Databases, concerns with discovering useful properties, called patterns, from data. Understandability is an essential — yet rarely tackled — feature that makes resulting patterns accessible by end users. In this paper we argue that the adoption of Fuzzy Logic for Data Mining can improve understandability of derived patterns. Indeed, Fuzzy Logic is able to represent concepts in a “human-centric” way. Hence, Data Mining methods based on Fuzzy Logic may potentially meet the so-called “Comprehensibility Postulate”, which characterizes the blurry notion of understandability. However, the mere adoption of Fuzzy Logic for Data Mining is not enough to achieve understandability. This paper describes and comments a number of issues that need to be addressed to provide for understandable patterns. A careful consideration of all such issues may end up in a systematic methodology to discover comprehensible knowledge from data.

In this paper we present a multi-level approach for extracting well-defined and semantically sound information granules from numerical data. The approach is based on the Double Clustering framework (DC/), which performs two main clustering steps on the data space in order to extract granules qualitatively described in terms of fuzzy sets that meet a number of interpretability constraints. While DC/ can extract information granules with a fixed level of granulation, its multi-level extension, called ML-DC (Multi-Level Double Clustering), can perform granulation of data at different levels, in a hierarchical fashion. At the first level, the whole dataset is granulated. At the second level, data embraced in each first-level granule are further granulated taking into account the context generated by that granule. The hierarchical collection of granules derived via ML-DC is then used to construct a committee of fuzzy inference systems that can approximate any I/O mapping with a good balance between accuracy and interpretability.

The paper proposes a new Empirical Risk Functional as cost function for training neuro-fuzzy classifiers. This cost function, called Approximate Differentiable Empirical Risk Functional (ADERF), provides a differentiable approximation of the misclassification rate so that the Empirical Risk Minimization Principle formulated in Vapnik's Statistical Learning Theory can be applied. Also, based on the proposed ADERF, a learning algorithm is formulated. Experimental results on a number of benchmark classification tasks are provided and comparison to alternative approaches given.

In this paper an approach for automatic discovery of transparent diagnostic rules from data is proposed. The approach is based on a fuzzy clustering technique that is defined by three sequential steps. First, our Crisp Double Clustering algorithm is applied on available symptoms measurements, to provide a set of representative multidimensional prototypes that are further clustered onto each one-dimensional projection. The resulting clusters are used in the second step, where a set of fuzzy relations are defined in terms of transparent fuzzy sets. As a final step, the derived fuzzy relations are employed to define a set of fuzzy rules, which establish the knowledge base of a fuzzy inference system that can be used for fuzzy diagnosis. The approach has been applied to the Aachen Aphasia dataset as a real-world benchmark and compared with related work.