In any computer vision task involving color images, a necessary step is classifying pixels according to color and segmenting the respective areas. However, the development of methods able to successfully complete this task has proven challenging, mainly due to the gap between human color perception, linguistic color terms, and digital representation. In this paper, we propose a novel method combining geometric analysis of color theory, fuzzy color spaces, and multi-label systems for the automatic classification of pixels according to 12 standard color categories (Green, Yellow, Light Orange, Deep Orange, Red, Pink, Purple, Ultramarine, Blue, Teal, Brown, and Neutral). Moreover, we present a robust, unsupervised, unbiased strategy for color naming based on statistics and color theory. ABANICCO was tested against the state of the art in color classification and with the standarized ISCC-NBS color system, providing accurate classification and a standard, easily understandable alternative for hue naming recognizable by humans and machines. We expect this solution to become the base to successfully tackle a myriad of problems in all fields of computer vision, such as region characterization, histopathology analysis, fire detection, product quality prediction, object description, and hyperspectral imaging.

Nowadays, many people worldwide suffer from brain disorders, and their health is in danger. So far, numerous methods have been proposed for the diagnosis of Schizophrenia (SZ) and attention deficit hyperactivity disorder (ADHD), among which functional magnetic resonance imaging (fMRI) modalities are known as a popular method among physicians. This paper presents an SZ and ADHD intelligent detection method of resting-state fMRI (rs-fMRI) modality using a new deep learning method. The University of California Los Angeles dataset, which contains the rs-fMRI modalities of SZ and ADHD patients, has been used for experiments. The FMRIB software library toolbox first performed preprocessing on rs-fMRI data. Then, a convolutional Autoencoder model with the proposed number of layers is used to extract features from rs-fMRI data. In the classification step, a new fuzzy method called interval type-2 fuzzy regression (IT2FR) is introduced and then optimized by genetic algorithm, particle swarm optimization, and gray wolf optimization (GWO) techniques. Also, the results of IT2FR methods are compared with multilayer perceptron, k-nearest neighbors, support vector machine, random forest, and decision tree, and adaptive neuro-fuzzy inference system methods. The experiment results show that the IT2FR method with the GWO optimization algorithm has achieved satisfactory results compared to other classifier methods. Finally, the proposed classification technique was able to provide 72.71% accuracy.

Noname manuscript No. (will be inserted by the editor) Abstract This paper proposes a distributed weighted regularized lea st squares algorithm (DWRLS) with radial basis functions to tackle spherical data that are stored acr oss numerous local servers and cannot be shared with each other. Via developing a novel integral operator approa ch based on spherical quadrature rules, we succeed in deriving optimal approximation rates for DWRLS and theor etically demonstrate that DWRLS performs similarly as running a weighted regularized least squares algo rithm on the whole data stored on a large enough machine. This interesting finding implies that distributed learning is capable of sufficiently exploiting potential values of distributively stored spherical data, even thoug h local servers cannot access the whole data. Keywords Distributed learning Scattered data approximation Sphere Integral operator 1 Introduction In geophysics, solar system, climate prediction, environm ent governance and meteorology, and image rendering, samples formed as input-output pairs are collected over spheres [13, 15, 49], such as the surface of the earth and the direction of radiance. Due to the storage bo ttleneck and data privacy, these spherical data are often distributively stored across numerous computati onal servers.

The present paper comes across the main steps that laid from Zadeh's fuzziness ana Atanassov's intuitionistic fuzzy sets to Smarandache's indeterminacy and to Molodstov's soft sets. Two hybrid methods for assessment and decision making respectively under fuzzy conditions are also presented through suitable examples that use soft sets and real intervals as tools. The decision making method improves an earlier method of Maji et al. Further, it is described how the concept of topological space, the most general category of mathematical spaces, can be extended to fuzzy structures and how to generalize the fundamental mathematical concepts of limit, continuity compactness and Hausdorff space within such kind of structures. In particular, fuzzy and soft topological spaces are defined and examples are given to illustrate these generalizations.

The Interval-valued intuitionistic fuzzy sets (IVIFSs) based on the intuitionistic fuzzy sets combines the classical decision method is in its research and application is attracting attention. After comparative analysis, there are multiple classical methods with IVIFSs information have been applied into many practical issues. In this paper, we extended the classical EDAS method based on cumulative prospect theory (CPT) considering the decision makers (DMs) psychological factor under IVIFSs. Taking the fuzzy and uncertain character of the IVIFSs and the psychological preference into consideration, the original EDAS method based on the CPT under IVIFSs (IVIF-CPT-MABAC) method is built for MAGDM issues. Meanwhile, information entropy method is used to evaluate the attribute weight. Finally, a numerical example for project selection of green technology venture capital has been given and some comparisons is used to illustrate advantages of IVIF-CPT-MABAC method and some comparison analysis and sensitivity analysis are applied to prove this new methods effectiveness and stability.

Offline reinforcement learning (RL), which refers to decision-making from a previously-collected dataset of interactions, has received significant attention over the past years. Much effort has focused on improving offline RL practicality by addressing the prevalent issue of partial data coverage through various forms of conservative policy learning. While the majority of algorithms do not have finite-sample guarantees, several provable conservative offline RL algorithms are designed and analyzed within the single-policy concentrability framework that handles partial coverage. Yet, in the nonlinear function approximation setting where confidence intervals are difficult to obtain, existing provable algorithms suffer from computational intractability, prohibitively strong assumptions, and suboptimal statistical rates. In this paper, we leverage the marginalized importance sampling (MIS) formulation of RL and present the first set of offline RL algorithms that are statistically optimal and practical under general function approximation and single-policy concentrability, bypassing the need for uncertainty quantification. We identify that the key to successfully solving the sample-based approximation of the MIS problem is ensuring that certain occupancy validity constraints are nearly satisfied. We enforce these constraints by a novel application of the augmented Lagrangian method and prove the following result: with the MIS formulation, augmented Lagrangian is enough for statistically optimal offline RL. In stark contrast to prior algorithms that induce additional conservatism through methods such as behavior regularization, our approach provably eliminates this need and reinterprets regularizers as "enforcers of occupancy validity" than "promoters of conservatism."

Rational approximations are introduced and studied in granular graded rough sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between granularity, mereology and approximations in the context. In addition, a framework for rational approximations is introduced by her in the mentioned paper(s). Granular approximations constructed as per the procedures of variable precision rough sets (VPRS) are likely to be more rational than those constructed from a classical perspective under certain conditions. This may continue to hold for some generalizations of the former. However, a formal characterization of such conditions is not available in the previously published literature. In this research, theoretical aspects of the problem are critically examined, uniform generalizations of granular VPRS are introduced, new connections with granular graded rough sets are proved, appropriate concepts of substantial parthood are introduced, their extent of compatibility with the framework is accessed, and the framework is extended. Basic assumptions are explained in detail, and additional examples are constructed for readability. Furthermore, meta applications to cluster validation, image segmentation and dynamic sorting are invented. Extensions to direct generalizations of VPRS such as probabilistic rough sets are a natural consequence of the work.

When the fuzzy relation equations have a solution, we first propose an algorithm to find all minimal solutions of the fuzzy relation equations and also supply an algorithm to find all maximal solutions of the fuzzy relation equations, which will be illustrated, respectively, by numeral examples. Then we prove that every solution of the fuzzy relation equations is between a minimal solution and a maximal one, so that we describe the solution set of the fuzzy relation equations completely.

A fuzzy inference system was developed for predicting the heat index from temperature and relative humidity data. The effectiveness of fuzzy logic in using imprecise mapping of input to output to encode interconnectedness of system variables was exploited to uncover a linguistic model of how the temperature and humidity conditions impact the heat index in a growth room. The developed model achieved an R2 of 0.974 and a RMSE of 0.084 when evaluated on a test set, and the results were statistically significant (F1,5915 = 222900.858, p < 0.001). By providing the advantage of linguistic summarization of data trends as well as high prediction accuracy, the fuzzy logic model proved to be an effective machine learning method for heat control problems.

An important constraint of Fuzzy Inference Systems (FIS) is their structured rules defined based on evaluating all input variables. Indeed, the length of all fuzzy rules and the number of input variables are equal. However, in many decision-making problems evaluating some conditions on a limited set of input variables is sufficient to decide properly (unstructured rules). Therefore, this constraint limits the performance, generalization, and interpretability of the FIS. To address this issue, this paper presents a neuro-fuzzy inference system for classification applications that can select different sets of input variables for constructing each fuzzy rule. To realize this capability, a new fuzzy selector neuron with an adaptive parameter is proposed that can select input variables in the antecedent part of each fuzzy rule. Moreover, in this paper, the consequent part of the Takagi-Sugeno-Kang FIS is also changed properly to consider only the selected set of input variables. To learn the parameters of the proposed architecture, a trust-region-based learning method (General quasi-Levenberg-Marquardt (GqLM)) is proposed to minimize cross-entropy in multiclass problems. The performance of the proposed method is compared with some related previous approaches in some real-world classification problems. Based on these comparisons the proposed method has better or very close performance with a parsimonious structure consisting of unstructured fuzzy.