Brain tumor classification from magnetic resonance imaging (MRI) remains challenging in settings where only image-level labels are available and tumor classes exhibit overlapping visual characteristics. In this study, we consider the publicly available Brain Tumor MRI Dataset from Kaggle, a four-class dataset composed of 2D MRI slices belonging to the categories glioma, meningioma, pituitary tumor, and no tumor. Accordingly, the proposed framework is formulated as a slice-based multiclass classification approach rather than a volumetric 3D analysis pipeline. We propose a lightweight and interpretable framework that integrates handcrafted multiscale MRI descriptors, an artificial neural network (ANN), Bee Colony Optimization (BCO)-based neural architecture search, and fuzzy softmax confidence modeling. Each MRI slice is represented by a compact 9-dimensional feature vector derived from intensity, local entropy, and gradient magnitude computed globally and over non-overlapping spatial blocks. The ANN design problem is formulated as a discrete-continuous optimization task, where BCO is employed to optimize network architecture and training hyperparameters by maximizing validation macro- F1 . To quantify predictive reliability, the softmax outputs are interpreted as fuzzy class memberships and further analyzed using maximum membership, normalized entropy, decision margin, and ambiguity measures, enabling confidence-aware reliability assessment. These fuzzy confidence descriptors enable confidence-threshold-based selective classification and rejection of low-confidence predictions. Across repeated runs, the optimized BCO-ANN achieved a mean test accuracy of 0.781 +/- 0.009 , mean macro- F1 of 0.775 +/- 0.010 , mean Brier score of 0.319 +/- 0.012 , and mean Expected Calibration Error (ECE) of 0.0273 +/- 0.0080 , compared with 0.748 +/- 0.011 , 0.738 +/- 0.013 , 0.352 +/- 0.010 , and 0.0446 +/- 0.0071 for the baseline ANN, respectively. Under confidence-threshold-based rejection, selective macro- F1 increased to 0.820 +/- 0.009 at tau=0.55 and to 0.874 +/- 0.020 at tau=0.85 , with the expected reduction in coverage. These results indicate that the proposed framework provides a transparent and reproducible approach for optimization-aware and confidence-aware multiclass brain tumor MRI classification in a lightweight handcrafted feature setting.

In this paper, we present a new method of construction of the distance function between fuzzy numbers, i.e., the measure of difference between the two of them. This method is based on the application of some aggregation functions on differences of certain fuzzy number parameters and characteristics. Various types of mean values and measures of dispersion are characteristics that are relevant for determining the difference between two fuzzy numbers. To determine the distance (i.e., difference) between the two of them, in this paper we use some their known characteristics, and we define several new ones.

In this paper, we present a new method for solving a dual fuzzy linear system (DFLS), AX˜+C˜=BX˜+D˜, where the coefficient matrices A and B are arbitrary real m×n matrices and C˜ and D˜ are given fuzzy number vectors. A necessary and sufficient condition for the R-consistency of the associated system of linear equations is obtained. The straightforward method for solving m×n DFLS based on an arbitrary {1}-inverse of A−B is introduced. Also, as an application, we present the first algorithm for solving the fuzzy Stein matrix equations, based on {1}-inverses. Finally, these results are illustrated by examples.

This paper presents the construction of a new measuretype functions of a certain type, by applying aggregation functions on the initial sequence of measure-type functions of the same type. The measure-type functions considered in this paper are distance functions, metrics, fuzzy metrics, and fuzzy measures. The properties of the constructed new measure-type functions depend on the properties of applied aggregation functions, as well as the properties of the initial functions on which the aggregation function is applied.

For a given bipolar fuzzy number vector Y and a real matrix A, the system of equations AX = Y is called a bipolar fuzzy linear system, where X is an unknown bipolar fuzzy number vector. We present a new method for solving bipolar fuzzy linear systems with a unique solution and illustrate this new approach by an example.

Fuzzy sets are a mathematical notion that allows us to represent uncertainty by assigning a degree of membership to a value in a range. This degree of membership represents the degree to which a particular value belongs to the fuzzy set. Fuzzy numbers are fuzzy sets that satisfy specific conditions, and can be applied in the interpretation of the behavior of neural networks. In many real-world problems, the output of a neural network may not be a precise numerical value, but rather a range of values that are subject to uncertainty. In the context of neural networks, fuzzy numbers can be used to represent uncertainty in the output of the network. Fuzzy numbers are used in applications where the representation of ambiguity and uncertainty in numerical data is explicitly desired. This paper will consider discretizations and defuzzifications triangular fuzzy numbers with the use of MATLAB® software. MATLAB® functions were applied to the analysis of kidney images, where the fuzzy numbers represent the tendency value of the degree of redness, which serves as an indicator for classifying the image as normal or abnormal based on different characteristics.

This paper is a review of recent research on image fuzzy segmentation using the fuzzy c-means clustering algorithm based on a distance function constructed by applying the aggregation function on the sequence of the initial distance functions and pixel descriptors. In image segmentation algorithms, distance functions compare pixels and represent a decision criterion for the classification of pixels into image segments. Determination of the segmentation criterion is based on the information fusion process, where the application of the appropriated aggregation function enables the adjustment of the segmentation criteria according to the intuitively expected decision. Initial distance functions represents the basic criteria which are relevant for segmentation, and applied aggregation function represent a model for this basic criteria fusion into one final decision criteria. With regards to a new distance function construction by applying aggregation functions, in this article we present relevant properties of the following aggregation functions: minimum, maximum, weighted arithmetic mean, generalized means, product of powers, weighted arithmetic mean of powers and OWA aggregation functions. Beside the pixel color or color components, other pixel descriptors are important for image segmentation and other image processing tasks. For experimental verification of the methodology used in image segmentation, the fuzzy c-means clustering algorithm is used.

This paper considers image segmentation relied on aggregated distance function using either aggregation of only distance functions or distance functions which are also and fuzzy metrics. In image segmentation algorithms, distance functions compare either two pixels or pixel with segments, and may be used to make decision regarding belongingness of image pixels. Choice of suitable distance function within the segmentation criterion is based on information fusion process. Application of the appropriate aggregation function enables to adjust the segmentation criteria according to intuitively expected decision. Aggregation function is applied on distance functions representing the basic criteria relevant for segmentation. In this paper, the fuzzy c-means clustering algorithm is used for image segmentation and experimental verification of used methodology for such a distance function construction. The quality of the performed segmentation with proposed distance functions is compared with the segmentation quality obtained by using the standard Euclidean metric.

In this paper we introduce notions of distortion function and aggregated distortion function. Applying some extended aggregation function on the triangle of distortion functions, a new extended aggregation function is obtained. Properties of the aggregation function constructed in this way depend on the properties of applied aggregation function and the distortion functions used. Its properties as continuity, convexity, concavity, subadditivity and superadditivity are investigated.

In this paper we present construction of new fuzzy measures by applying extended aggregation function on a sequence of fuzzy measures. According to properties of applied aggregation function and properties of initial fuzzy measures, some properties of constructed fuzzy measure are proved. Additionally, one new extended aggregation function named extended weighted arithmetic mean of distorted arguments is introduced, and its relevant properties are proved. It is shown that this extended aggregation function, with appropriated parameters, can be suitable for construction of new fuzzy measures. Other types of non-additive measures can be constructed in the same way, by applying aggregation function on the initial sequence of non-additive measures.

In this paper we construct two extended aggregation functions, extended powers product and extended weighted arithmetic mean of powers.Their basic properties are examined, as well as certain properties of distance functions constructed by them.In addition, one pixel descriptor, which is motivated by Local Binary Pattern family of descriptors (LBPs), is introduced.We give an application of the introduced extended aggregation functions and descriptor, by a construction of a new distance function, used in Fuzzy c-Means Clustering Algorithm (FCM) for image segmentation.

In this paper, we psropose a novel method for construction of a distance function and demonstrate its application in image segmentation. In algorithms for image segmentation, distance functions represent a criterion which divides pixels into groups of segments. We introduce two extended aggregation functions, extended powers product and extended weighted arithmetic mean of powers . Their relevant properties are examined, as well as certain resulting properties of distance functions, which are constructed by an application of mentioned aggregation functions. In addition, one pixel descriptor, which is motivated by Local Binary Pattern family of descriptors ( LBP s), is introduced and discussed. In the experimental section, we present an application of the introduced extended aggregation functions and descriptor, by a construction of a new distance function, used in Fuzzy c-Means Clustering Algorithm ( FCM ) for image segmentation.

In this paper, some features of the aggregation operators min, max and generalized means, that are relevant for the construction of new distance functions by applying aggregation operator on sequence of some given distance functions, are examined and presented. The features of the constructed distance function depend on the characteristics of the applied aggregation operator. AMS Mathematics Subject Classification (2010): 47S40, 32F45

The main result of this paper is a generalization of Portmanteau Theorem for a sequence of interval-valued pseudo-probability measures. The classical Lebesgue integral from Probability Theory had been substituted with the pseudo-integral of a real-valued function with respect to an interval-valued ⊕-measure.

In this paper we present construction of new distance functions by using aggregation operators of median type on given sequence of distance functions. Depending on characteristics of the given distance functions, features of new constructed function are analyzed. Also, one application on image segmentation is presented. AMS Mathematics Subject Classification (2010): 47S40, 68U10, 32F45

A necessary and sufficient condition for the existence of a non-trivial factorization of an arbitrary bivariate polynomial with integer coefficients was presented in [2]. In this paper we develop an efficient algorithm for factoring bivariate polynomials with integer coefficients. Also, we shall give a proof of the optimality of the algorithm. For a given codeword, formed by mixing up two codewords, the algorithm recovers those codewords directly by factoring corresponding bivariate polynomial. Our algorithm determines uniquely the given polynomials which are used in forming the mixture of two codewords.

In this paper, we propose a new method for construction of distance functions and metrics, by applying aggregation operators on some given distance functions and metrics. For some types and examples of aggregation operators, we analyze which properties of the given distance functions and metrics are preserved by such construction. We also present one possible application of the distance functions constructed in such way in image segmentation by fuzzy c-means algorithm. Other similar applications in image processing are also possible.

Teorija mera i integrala je jedna od kapitalnih oblasti matematike, i odavno formirana i bogata teorija vidi npr. [1]. U drugoj polovini 20-og veka se formirala i teorija raznih vrsta fazi-mera koja je našla bogatu primenu u raznim naukama, vidi npr. [2, 3]. U sekcijama 2 i 4 su razmotreni samo neki tipovi fazi-mera. Operatori agregacije su jedan tip fazi-operacija, koje su našle veliku primenu u informatičkim i drugim naukama. Osnovne definicije i primeri operatora agregacije su dati u sekciji 3. U sekciji 4 su izložene neke nove ideje, pristupi i primeri konstrukcije mera i fazi-mera primenom operatora agregacije na niz polaznih mera i fazi-mera.

The concentrations of isopropyl alcohol were monitored during the working time (8 hours) in three different printing plants (two sheet-fed offset and one digital) in Novi Sad, Serbia, using portable gas chromatograph. The concentration levels were below the recommended limits by the U.S. National Institute for Occupational Safety and Health. Unequal presence of isopropyl alcohol in printing plants involved a multiple linear regression analysis of microclimate parameters using program ORIGIN 5.0. The results of multiple linear regression confirmed that the microclimate conditions in the digital printing plant generate the lowest values of isopropyl alcohol concentrations due to the installed ventilation fans in comparison with other two sheet- fed offset printing plants. Multiple regression models can be evaluated to predict the values for total isopropyl alcohol concentrations due to the humidity, temperature and light intensity.