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As new kinds of aggregation functions, overlap functions and semi overlap functions are widely applied to information fusion, approximation reasoning, data classification, decision science, etc. This paper extends the semi-overlap function on [0, 1] to the function on complete lattices and investigates the residual implication derived from it; then it explores the construction of a semi-overlap function on complete lattices and some fundamental properties. Especially, this paper introduces a more generalized concept of the 'semi-Θ-Ξ function', which innovatively unifies the semi-overlap function and semi-grouping function. Additionally, it provides methods for constructing and characterizing the semi-Θ-Ξ function. Furthermore, this paper characterizes the semi-overlap function on complete lattices and the semi-Θ-Ξ function on [0, 1] from an algebraic point of view and proves that the algebraic structures corresponding to the inflationary semi-overlap function, the inflationary semi-Θ-Ξ function, and residual implications derived by each of them are inflationary MTL algebras. This paper further discusses the properties of inflationary MTL algebra and its relationship with non-associative MTL algebra, and it explores the connections between some related algebraic structures. [ABSTRACT FROM AUTHOR]

In recent years, the global reduction in populations of the Apis mellifera species has generated a worrying deterioration in the production of essential foods for human consumption. This phenomenon threatens food security, as it reduces the pollination of vital crops, negatively affecting the health and stability of ecosystems. The three main factors generating the loss of the bee population are industrial agriculture, climate changes, and infectious diseases, mainly those of parasitic origin, such as the Varroa destructor mite. This article proposes an IoT system that uses accessible, efficient, low-cost devices for beekeepers in developing countries to monitor hives based on temperature, humidity, C O 2 , and TVOC. The proposed solution incorporates nine-feature aggregation as a data preprocessing strategy to reduce redundancy and efficiently manage data storage on hardware with limited capabilities, which, combined with a machine learning model, improves mite detection. Finally, an evaluation of the energy consumption of the solution in each of its nodes, an analysis of the data traffic injected into the network, an assessment of the energy consumption of each implemented classification model, and, finally, a validation of the solution with experts is presented. [ABSTRACT FROM AUTHOR]

As new kinds of aggregation functions, overlap functions and semi overlap functions are widely applied to information fusion, approximation reasoning, data classification, decision science, etc. This paper extends the semi-overlap function on [0, 1] to the function on complete lattices and investigates the residual implication derived from it; then it explores the construction of a semi-overlap function on complete lattices and some fundamental properties. Especially, this paper introduces a more generalized concept of the ‘semi-Θ-Ξ function’, which innovatively unifies the semi-overlap function and semi-grouping function. Additionally, it provides methods for constructing and characterizing the semi-Θ-Ξ function. Furthermore, this paper characterizes the semi-overlap function on complete lattices and the semi-Θ-Ξ function on [0, 1] from an algebraic point of view and proves that the algebraic structures corresponding to the inflationary semi-overlap function, the inflationary semi-Θ-Ξ function, and residual implications derived by each of them are inflationary MTL algebras. This paper further discusses the properties of inflationary MTL algebra and its relationship with non-associative MTL algebra, and it explores the connections between some related algebraic structures.

The purpose of the study is to propose a multi-class ensemble classifier using interval modeling dedicated to microarray datasets. An approach of creating the uncertainty intervals for the single prediction values of constituent classifiers and then aggregating the obtained intervals with the use of interval-valued aggregation functions is used. The proposed heterogeneous classification employs Random Forest, Support Vector Machines, and Multilayer Perceptron as component classifiers, utilizing cross-entropy to select the optimal classifier. Moreover, orders for intervals are applied to determine the decision class of an object. The applied interval-valued aggregation functions are tested in terms of optimizing the performance of the considered ensemble classifier. The proposed model's quality, superior to other well-known and component classifiers, is validated through comparison, demonstrating the efficacy of cross-entropy in ensemble model construction. [ABSTRACT FROM AUTHOR]

In recent years, the global reduction in populations of the Apis mellifera species has generated a worrying deterioration in the production of essential foods for human consumption. This phenomenon threatens food security, as it reduces the pollination of vital crops, negatively affecting the health and stability of ecosystems. The three main factors generating the loss of the bee population are industrial agriculture, climate changes, and infectious diseases, mainly those of parasitic origin, such as the Varroa destructor mite. This article proposes an IoT system that uses accessible, efficient, low-cost devices for beekeepers in developing countries to monitor hives based on temperature, humidity, CO2, and TVOC. The proposed solution incorporates nine-feature aggregation as a data preprocessing strategy to reduce redundancy and efficiently manage data storage on hardware with limited capabilities, which, combined with a machine learning model, improves mite detection. Finally, an evaluation of the energy consumption of the solution in each of its nodes, an analysis of the data traffic injected into the network, an assessment of the energy consumption of each implemented classification model, and, finally, a validation of the solution with experts is presented.

The notion of decisive coalitions of voters with different grades of decisiveness is a part of the mathematical framework for many models in social choice theory. More generally, we study aggregation problems in which a subgroup of decision makers have the right to determine the properties of the aggregate. Then, we introduce property spaces and rights to properties and characterize aggregation operators that are consistent with rights to properties. Moreover, we define congruences in property spaces, and we propose a generalization of the Sugeno integral in our framework. [ABSTRACT FROM AUTHOR]

This paper provides a survey of apparent personality trait analysis based on multimodal trait prediction and optimization of multimodal output parameters. This paper analyzes, synthesizes, and compares the development of different methods of Personality computing based on the personality trait analysis within the Big Five model (OCEAN model) and based on audio, visual and textual inputs. The results of the trait analysis and detection are different for different methods, from trait extracted from handwriting with an accuracy of 62-83%, trait extracted from with 56-62%, trait extracted from audio with 70%, trait extracted from visual element images and videos 87-91%, from aggregation function min and max 52 - 81%, mean and median 85%, and methods based on robustness and Huber function 72 - 77 %. Trait analysis is a problem with numerous real-life applications. Accurate trait recognition and analysis of various human traits are tasks that have been studied for a very long time in the field of psychology and lately represent an important area of study in the field of computer science and computing. The best results in the field of apparent personality trait analysis were achieved with convolutional neural networks. Multimodal trait prediction will give a better prediction than prediction based on a single modality, and optimization with aggregation functions and robust methods can achieve a better prediction of the models.

In many domains of our daily life (e.g., agriculture, forestry, health, etc.), both laymen and experts need to classify entities into two binary classes (yes/no, good/bad, sufficient/insufficient, benign/malign, etc.). For many entities, this decision is difficult and we need another class called “maybe”, which contains a corresponding quantifiable tendency toward one of these two opposites. Human domain experts are often able to mark any entity, place it in a different class and adjust the position of the slope in the class. Moreover, they can often explain the classification space linguistically—depending on their individual domain experience and previous knowledge. We consider this human-in-the-loop extremely important and call our approach actionable explainable AI. Consequently, the parameters of the functions are adapted to these requirements and the solution is explained to the domain experts accordingly. Specifically, this paper contains three novelties going beyond the state-of-the-art: (1) A novel method for detecting the appropriate parameter range for the averaging function to treat the slope in the “maybe” class, along with a proposal for a better generalisation than the existing solution. (2) the insight that for a given problem, the family of t-norms and t-conorms covering the whole range of nilpotency is suitable because we need a clear “no” or “yes” not only for the borderline cases. Consequently, we adopted the Schweizer–Sklar family of t-norms or t-conorms in ordinal sums. (3) A new fuzzy quasi-dissimilarity function for classification into three classes: Main difference, irrelevant difference and partial difference. We conducted all of our experiments with real-world datasets.

Edge detection is a crucial process in numerous stages of computer vision. This field of study has recently gained momentum due to its importance in various applications. The uncertainty, among other characteristics of images, makes it difficult to accurately determine the edge of objects. Furthermore, even the definition of an edge is vague as an edge can be considered as the maximum boundary between two regions with different properties. Given the advancement of research in image discontinuity detection, especially using aggregation and pre-aggregation functions, and the lack of systematic literature reviews on this topic, this paper aims to gather and synthesize the current state of the art of this topic. To achieve this, this paper presents a systematic review of the literature, which selected 24 papers filtered from 428 articles found in computer databases in the last seven years. It was possible to synthesize important related information, which was grouped into three approaches: (i) based on both multiple descriptor extraction and data aggregation, (ii) based on both the aggregation of distance functions and fuzzy C-means, and (iii) based on fuzzy theory, namely type-2 fuzzy and neutrosophic sets. As a conclusion, this review provides interesting gaps that can be explored in future work. [ABSTRACT FROM AUTHOR]

The purpose of the study is to propose a multi-class ensemble classifier using interval modeling dedicated to microarray datasets. An approach of creating the uncertainty intervals for the single prediction values of constituent classifiers and then aggregating the obtained intervals with the use of interval-valued aggregation functions is used. The proposed heterogeneous classification employs Random Forest, Support Vector Machines, and Multilayer Perceptron as component classifiers, utilizing cross-entropy to select the optimal classifier. Moreover, orders for intervals are applied to determine the decision class of an object. The applied interval-valued aggregation functions are tested in terms of optimizing the performance of the considered ensemble classifier. The proposed model’s quality, superior to other well-known and component classifiers, is validated through comparison, demonstrating the efficacy of cross-entropy in ensemble model construction.

Abstract This article develops a novel approach for multi-objective optimization on the basis of ratio analysis plus the full multiplicative form (MULTIMOORA) using spherical fuzzy sets (SFSs) to obtain proper evaluations. SFSs surpass Pythagorean and intuitionistic fuzzy sets in modeling human cognition since the degree of hesitation is expressed explicitly in a three-dimensional space. In the spherical fuzzy environment, the implementation of the MULTIMOORA encounters two major problems in the aggregation operators and the distance measures that might lead to erroneous results. The extant aggregation operators in some cases can result in a biased evaluation. Therefore, two aggregation functions for SFSs are proposed. These functions guarantee balanced evaluation and avoid false ranking. In the reference point technique, when comparing SFSs, being closer to the ideal solution does not necessarily imply an SFS with a better score. To make up for this drawback, two reference points are employed instead of one, and the distance is not expressed as a crisp value but as an SFS instead. To overcome the disadvantages of the dominance theory in large-scale applications, the results of the three techniques are aggregated to get the overall utility on which the ranking is based. The illustration and validation of the proposed spherical fuzzy MULTIMOORA are examined through two applications, personnel selection, and energy storage technologies selection. The results are compared with the results of other methods to explicate the adequacy of the proposed method and validate the results.

There are distinct techniques to generate fuzzy implication functions. Despite most of them using the combination of associative aggregators and fuzzy negations, other connectives such as (general) overlap/grouping functions may be a better strategy. Since these possibly non-associative operators have been successfully used in many applications, such as decision making, classification and image processing, the idea of this work is to continue previous studies related to fuzzy implication functions derived from general overlap functions. In order to obtain a more general and flexible context, we extend the class of implications derived by fuzzy negations and t-norms, replacing the latter by general overlap functions, obtaining the so-called (GO , N) -implication functions. We also investigate their properties, the aggregation of (GO , N) -implication functions, their characterization and the intersections with other classes of fuzzy implication functions. [ABSTRACT FROM AUTHOR]

Several important classes of aggregation functions defined on a bounded lattice form a lattice with respect to the pointwise operations of join and meet, respectively. The lattice structure of such classes is usually very complex; thus, it is very useful to characterize them by some appropriate sets of functions. In this paper, we focus on the three important classes of aggregation functions, namely the lattice of all aggregation functions, the lattice of idempotent aggregation functions, and the lattice of Sugeno integrals (defined on distributive lattices) and characterize their lattices by means of join-dense subsets. Moreover, the minimality of these sets is discussed. [ABSTRACT FROM AUTHOR]

This article develops a novel approach for multi-objective optimization on the basis of ratio analysis plus the full multiplicative form (MULTIMOORA) using spherical fuzzy sets (SFSs) to obtain proper evaluations. SFSs surpass Pythagorean and intuitionistic fuzzy sets in modeling human cognition since the degree of hesitation is expressed explicitly in a three-dimensional space. In the spherical fuzzy environment, the implementation of the MULTIMOORA encounters two major problems in the aggregation operators and the distance measures that might lead to erroneous results. The extant aggregation operators in some cases can result in a biased evaluation. Therefore, two aggregation functions for SFSs are proposed. These functions guarantee balanced evaluation and avoid false ranking. In the reference point technique, when comparing SFSs, being closer to the ideal solution does not necessarily imply an SFS with a better score. To make up for this drawback, two reference points are employed instead of one, and the distance is not expressed as a crisp value but as an SFS instead. To overcome the disadvantages of the dominance theory in large-scale applications, the results of the three techniques are aggregated to get the overall utility on which the ranking is based. The illustration and validation of the proposed spherical fuzzy MULTIMOORA are examined through two applications, personnel selection, and energy storage technologies selection. The results are compared with the results of other methods to explicate the adequacy of the proposed method and validate the results. [ABSTRACT FROM AUTHOR]

In many domains of our daily life (e.g., agriculture, forestry, health, etc.), both laymen and experts need to classify entities into two binary classes (yes/no, good/bad, sufficient/insufficient, benign/malign, etc.). For many entities, this decision is difficult and we need another class called "maybe", which contains a corresponding quantifiable tendency toward one of these two opposites. Human domain experts are often able to mark any entity, place it in a different class and adjust the position of the slope in the class. Moreover, they can often explain the classification space linguistically—depending on their individual domain experience and previous knowledge. We consider this human-in-the-loop extremely important and call our approach actionable explainable AI. Consequently, the parameters of the functions are adapted to these requirements and the solution is explained to the domain experts accordingly. Specifically, this paper contains three novelties going beyond the state-of-the-art: (1) A novel method for detecting the appropriate parameter range for the averaging function to treat the slope in the "maybe" class, along with a proposal for a better generalisation than the existing solution. (2) the insight that for a given problem, the family of t-norms and t-conorms covering the whole range of nilpotency is suitable because we need a clear "no" or "yes" not only for the borderline cases. Consequently, we adopted the Schweizer–Sklar family of t-norms or t-conorms in ordinal sums. (3) A new fuzzy quasi-dissimilarity function for classification into three classes: Main difference, irrelevant difference and partial difference. We conducted all of our experiments with real-world datasets. [ABSTRACT FROM AUTHOR]

The notion of decisive coalitions of voters with different grades of decisiveness is a part of the mathematical framework for many models in social choice theory. More generally, we study aggregation problems in which a subgroup of decision makers have the right to determine the properties of the aggregate. Then, we introduce property spaces and rights to properties and characterize aggregation operators that are consistent with rights to properties. Moreover, we define congruences in property spaces, and we propose a generalization of the Sugeno integral in our framework.

The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric n-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we continue developing this topic, this time focusing on another generalization, called general pseudo-overlap functions on lattices, which in a given classification system measures the degree of overlapping of several classes and for any given object where symmetry is an unnecessarily restrictive condition. Moreover, we also provide some methods of constructing these functions, as well as a characterization theorem for them. Also, the notions of pseudo-t-norms and pseudo-t-conorms are used to generalize the concepts of additive and multiplicative generators for the context of general pseudo-quasi-overlap functions on lattices and we explore some related properties. [ABSTRACT FROM AUTHOR]

Brain–computer interface (BCI) technologies are popular methods of communication between the human brain and external devices. One of the most popular approaches to BCI is motor imagery (MI). In BCI applications, the electroencephalography (EEG) is a very popular measurement for brain dynamics because of its noninvasive nature. Although there is a high interest in the BCI topic, the performance of existing systems is still far from ideal, due to the difficulty of performing pattern recognition tasks in EEG signals. This difficulty lies in the selection of the correct EEG channels, the signal-to-noise ratio of these signals, and how to discern the redundant information among them. BCI systems are composed of a wide range of components that perform signal preprocessing, feature extraction, and decision making. In this article, we define a new BCI framework, called enhanced fusion framework, where we propose three different ideas to improve the existing MI-based BCI frameworks. First, we include an additional preprocessing step of the signal: a differentiation of the EEG signal that makes it time invariant. Second, we add an additional frequency band as a feature for the system: the sensorimotor rhythm band, and we show its effect on the performance of the system. Finally, we make a profound study of how to make the final decision in the system. We propose the usage of both up to six types of different classifiers and a wide range of aggregation functions (including classical aggregations, Choquet and Sugeno integrals, and their extensions and overlap functions) to fuse the information given by the considered classifiers. We have tested this new system on a dataset of 20 volunteers performing MI-based brain–computer interface experiments. On this dataset, the new system achieved 88.80% accuracy. We also propose an optimized version of our system that is able to obtain up to 90.76%. Furthermore, we find that the pair Choquet/Sugeno integrals and overlap functions are the ones providing the best results. [ABSTRACT FROM AUTHOR]

In this work, by considering a class of matrix valued fuzzy controllers and using a (κ , ς) -Cauchy–Jensen additive functional equation ( (κ , ς) -CJAFE), we apply the Radu–Mihet method (RMM), which is derived from an alternative fixed point theorem, and obtain the existence of a unique solution and the H–U–R stability (Hyers–Ulam–Rassias) for the homomorphisms and Jordan homomorphisms on Lie matrix valued fuzzy algebras with ς members (ς -LMVFA). With regards to each theorem, we consider the aggregation function as a matrix value fuzzy control function and investigate the results obtained. [ABSTRACT FROM AUTHOR]

Wastewater is a complex mixture of organic and inorganic impurities, suspended solids, nutrients, saprotrophic and disease-causing bacteria and other microbes. When untreated wastewater is discharged into the rivers, seas, or oceans, it causes harm to human and aquatic life. Therefore, it is necessary to monitor the wastewater quality before diverting it into receiving water. The main aim of this study was the selection of an appropriate aggregation function to propose the wastewater quality index (WWQI) which is suitable for monitoring the spatial and seasonal variations of wastewater quality in the stormwater flow channel (SWF) located in Kolkata, India. Two different aggregation functions, i.e., weighted geometric mean function and weighted arithmetic mean function, were tested and analysed with primary data. Twelve wastewater quality parameters were selected. And, sampling was done seasonally for a 1-year period from December 2018 to December 2019 at eight selected locations along the SWF channel. The relative weights of each parameter were calculated based on their relative significance. Sub-index rating curves were generated to each parameter for WWQI calculations. The results revealed that weighted arithmetic mean function produced higher values of WWQI than geometric mean function. Furthermore, sensitivity analysis was carried out to evaluate the aggregation function that best suits the data of the SWF channel. The sensitivity analysis also revealed that weighted arithmetic mean function, being linear and free from ambiguity and less eclipsing, was more appropriate for measuring the WWQI for the SWF channel. Therefore, the study concluded that weighted arithmetic mean function was the most suitable aggregation function to calculate the WWQI for the SWF channel. [ABSTRACT FROM AUTHOR]

The tortuosity assessment of vessels and nerve fibres in ophthalmic images has drawn substantial attention, for its potentials in assisting various medical diagnoses. Numerous morphological tortuosity measures have been leveraged to quantify tortuosity from various perspectives, which warrants the simultaneous use of multiple measures with an aim to produce a robust and accurate assessment. This paper proposes an approach for the automated assessment of curvilinear structures' tortuosity. Starting with the generation of clusters of tortuosity density for each individual measure, labelled fuzzy sets are then extracted that enhances the readability of subsequent operations. Finally, results from multiple measures are aggregated by a nearest neighbour guided approach where weights are generated in a data-driven manner to explain the derived aggregations. Experimental results on both ophthalmic vessel and nerve images demonstrate the superior performance of the proposed method over those where measurements are used independently or aggregated using conventional averaging operators.

Edge detection is a crucial process in numerous stages of computer vision. This field of study has recently gained momentum due to its importance in various applications. The uncertainty, among other characteristics of images, makes it difficult to accurately determine the edge of objects. Furthermore, even the definition of an edge is vague as an edge can be considered as the maximum boundary between two regions with different properties. Given the advancement of research in image discontinuity detection, especially using aggregation and pre-aggregation functions, and the lack of systematic literature reviews on this topic, this paper aims to gather and synthesize the current state of the art of this topic. To achieve this, this paper presents a systematic review of the literature, which selected 24 papers filtered from 428 articles found in computer databases in the last seven years. It was possible to synthesize important related information, which was grouped into three approaches: (i) based on both multiple descriptor extraction and data aggregation, (ii) based on both the aggregation of distance functions and fuzzy C-means, and (iii) based on fuzzy theory, namely type-2 fuzzy and neutrosophic sets. As a conclusion, this review provides interesting gaps that can be explored in future work.

In this paper, we devoted a design under uncertainty of a four-echelon supply chain network including multiple suppliers, multiple plants, multiple distributors and multiple customers. The proposed model is a bi-objective mixed integer linear programming which considers several constraints and aims to minimize the total costs including the procurement, production, storage and distribution costs as well as to maximize on-time deliveries (OTD). To bring the model closer to real-world planning problems, the objective function coefficients (e.g. procurement cost, production cost, inventory holding and transport costs) and other parameters (e.g., demand, production capacity and safety stock level), are all considered triangular fuzzy numbers. Besides, a hybrid mathematical model-based on credibility approach is constructed for the problem, i.e., expected value and chance constrained models. Moreover, to build the crisp equivalent model, we use different property of the credibility measure. The resulted crisp equivalent model is a bi-objective mixed integer linear programs (BOMILP). To transform this crisp BOMILP into a single objective mixed integer linear programs (MILP) model, we apply three different aggregation functions. Finally, numerical results are reported for a real case study to demonstrate the efficiency and applicability of the proposed model. [ABSTRACT FROM AUTHOR]

Homogeneity, as one type of invariantness, means that an aggregation function is invariant with respect to multiplication by a constant, and quasi-homogeneity, as a relaxed version, reflects the original output as well as the constant. In this paper, we characterize all homogeneous/quasi-homogeneous n-ary aggregation functions and present several methods to generate new homogeneous/quasi-homogeneous n-ary aggregation functions by aggregation of given ones. [ABSTRACT FROM AUTHOR]

There are distinct techniques to generate fuzzy implication functions. Despite most of them using the combination of associative aggregators and fuzzy negations, other connectives such as (general) overlap/grouping functions may be a better strategy. Since these possibly non-associative operators have been successfully used in many applications, such as decision making, classification and image processing, the idea of this work is to continue previous studies related to fuzzy implication functions derived from general overlap functions. In order to obtain a more general and flexible context, we extend the class of implications derived by fuzzy negations and t-norms, replacing the latter by general overlap functions, obtaining the so-called (GO,N)-implication functions. We also investigate their properties, the aggregation of (GO,N)-implication functions, their characterization and the intersections with other classes of fuzzy implication functions.

Several important classes of aggregation functions defined on a bounded lattice form a lattice with respect to the pointwise operations of join and meet, respectively. The lattice structure of such classes is usually very complex; thus, it is very useful to characterize them by some appropriate sets of functions. In this paper, we focus on the three important classes of aggregation functions, namely the lattice of all aggregation functions, the lattice of idempotent aggregation functions, and the lattice of Sugeno integrals (defined on distributive lattices) and characterize their lattices by means of join-dense subsets. Moreover, the minimality of these sets is discussed.

Ordered Weighted Averaging (OWA) operators have been integrated in Convolutional Neural Networks (CNNs) for image classification through the OWA layer. This layer lets the CNN integrate global information about the image in the early stages, where most CNN architectures only allow for the exploitation of local information. As a side effect of this integration, the OWA layer becomes a practical method for the determination of OWA operator weights, which is usually a difficult task that complicates the integration of these operators in other fields. In this paper, we explore the weights learned for the OWA operators inside the OWA layer, characterizing them through their basic properties of orness and dispersion. We also compare them to some families of OWA operators, namely the Binomial OWA operator, the Stancu OWA operator and the exponential RIM OWA operator, finding examples that are currently impossible to generalize through these parameterizations. [ABSTRACT FROM AUTHOR]

Rapid deployment of IT brings about new issues with software usability measurement. Usability is based on users’ experience and is strongly subjective, having a qualitative character. The users’ comfort is usually collected by surveys in their daily work. The present article stems from an experimental study related to the evaluation of the usability of tools by a rule-based system. The work suggests a robust computational model that will be able to avoid the main problems arising from the experimental study (a large and less-legible rule base) and to deal with the vagueness of IT user experience, different levels of skills and various numbers of filled questionnaires in different departments. The computational model is based on three hierarchical levels of aggregation supported by fuzzy logic. Choices for the most suitable aggregation functions in each level are advocated and illustrated with examples. The number of questions and granularity of answers in this approach can be adjusted to each user group, which could reduce the response burden and errors. Finally, the paper briefly describes further possibilities of the suggested approach.

Matrix algebra is an efficient way to represent the relationship between different concepts in the multiple criteria decision analysis theory. The main purpose of this paper is to provide a compact and systematic representation of the capacities and nonlinear integrals based decision theory and models from the perspective of matrices or vectors. We first investigate the forms and properties of the matrix representation of some equivalent transformations of capacities and introduce some new types of equivalent representations. Then we represent respectively the specified conditions corresponding to several particular families of capacities as well as the calculation formulas of three types of nonlinear integrals in terms of vectors and matrices without the process of presorting the integrand values. Finally, we discuss the applications of the matrix representations in the capacity identification models and illustrate them through a multiple criteria decision making problem. The use of matrix-vector formalism facilitates formulation of the relevant optimization problems and their solutions in capacity based decision analysis can be easily programmed and implemented by means of standard software tools and libraries in the environments such as R and Matlab.

The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric n-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we continue developing this topic, this time focusing on another generalization, called general pseudo-overlap functions on lattices, which in a given classification system measures the degree of overlapping of several classes and for any given object where symmetry is an unnecessarily restrictive condition. Moreover, we also provide some methods of constructing these functions, as well as a characterization theorem for them. Also, the notions of pseudo-t-norms and pseudo-t-conorms are used to generalize the concepts of additive and multiplicative generators for the context of general pseudo-quasi-overlap functions on lattices and we explore some related properties.

Classic adaptive binarization methodologies threshold pixels intensity with respect to adjacent pixels exploiting integral images. In turn, integral images are generally computed optimally by using the summed-area-table algorithm (SAT). This document presents a new adaptive binarization technique based on fuzzy integral images. Which, in turn, this technique is supported by an efficient design of a modified SAT for generalized Sugeno fuzzy integrals. We define this methodology as FLAT (Fuzzy Local Adaptive Thresholding). Experimental results show that the proposed methodology produced a better image quality thresholding than well-known global and local thresholding algorithms. We proposed new generalizations of different fuzzy integrals to improve existing results and reaching an accuracy ≈ 0. 94 on a wide dataset. Moreover, due to high performances, these new generalized Sugeno fuzzy integrals created ad hoc for adaptive binarization, can be used as tools for grayscale processing and more complex real-time thresholding applications. • Generalized Sugeno fuzzy thresholding algorithms are used for image binarization. • Fuzzy integrals methods outperform traditional adaptive thresholding. • Fuzzy integral adaptive algorithms are used for fast image binarization. [ABSTRACT FROM AUTHOR]

In this work, by considering a class of matrix valued fuzzy controllers and using a (κ,ς)-Cauchy–Jensen additive functional equation ((κ,ς)-CJAFE), we apply the Radu–Mihet method (RMM), which is derived from an alternative fixed point theorem, and obtain the existence of a unique solution and the H–U–R stability (Hyers–Ulam–Rassias) for the homomorphisms and Jordan homomorphisms on Lie matrix valued fuzzy algebras with ς members (ς-LMVFA). With regards to each theorem, we consider the aggregation function as a matrix value fuzzy control function and investigate the results obtained.

Four different types of convolutions of aggregation functions (the upper, the lower, the super-, and the sub-convolution) are examined in the setting of both sub- and super-decomposition integrals defined on a finite space. Examples of the results of the paper are provided. As a by-product, the super-additive transformation of sub-decomposition integrals and the sub-additive transformation of super-decomposition integrals are fully characterized. Possible applications are indicated.

• We make a revision of recent generalizations of the Choquet integral that appear in the literature. • We show some of the most relevant theoretical features of these extensions. • We also discuss some applications where these extensions have provided good results. In 2013, Barrenechea et al. used the Choquet integral as an aggregation function in the fuzzy reasoning method (FRM) of fuzzy rule-based classification systems. After that, starting from 2016, new aggregation-like functions generalizing the Choquet integral have appeared in the literature, in particular in the works by Lucca et al. Those generalizations of the Choquet integral, namely C T -integrals (by t-norm T), C F -integrals (by a fusion function F satisfying some specific properties), CC -integrals (by a copula C), C F 1 F 2 -integrals (by a pair of fusion functions (F 1 , F 2) under some specific constraints) and their generalization gC F 1 F 2 -integrals, achieved excellent results in classification problems. The works by Lucca et al. showed that the aggregation task in a FRM may be performed by either aggregation, pre-aggregation or just ordered directional monotonic functions satisfying some boundary conditions, that is, it is not necessary to have an aggregation function to obtain competitive results in classification. The aim of this paper is to present and discuss such generalizations of the Choquet integral, offering a general panorama of the state of the art, showing the relations and intersections among such five classes of generalizations. First, we present them from a theoretical point of view. Then, we also summarize some applications found in the literature. [ABSTRACT FROM AUTHOR]

• A new approach to Z-numbers, called mixed-discrete Z-numbers, is introduced. • The second component of mixed-discrete Z-numbers is managed as a discrete fuzzy number. • The computational complexity of the operations is greatly reduced with this approach. • An application to reach a decision from a group of experts is presented. One of the main goals of computing with words is the accurate modeling of natural language. In this direction, Z-numbers were introduced by Zadeh in 2011 as a pair of fuzzy numbers, (A, B), where A is interpreted as a fuzzy restriction on the values of a variable, while B is interpreted as a measure of certainty or sureness of A. This structure allows to model many imprecise sentences of the natural language, but has the drawback of the complexity and hight computational cost of their operations, because the second component is usually considered from a probabilistic point of view. Since the computational problems are caused by the second component, we present in this paper a new approach called mixed-discrete Z-numbers. In this new approach the first component will be managed as a usual fuzzy number, and the second one as a discrete fuzzy number with support in a finite chain. That is, the second component B of a Z -number is modeled as a linguistic valuation based on a discrete fuzzy number and the operations on these second components are managed through aggregation functions on discrete fuzzy numbers. Understanding B as a measure of certainty and not as a measure of probability, greatly improves experts' flexibility, allows to model situations where no probability distribution is known, and reduces greatly the computational complexity of Z -numbers operations. After studying these new Z-numbers and their operations, an application to reach a decision from a group of experts is presented in order to show the potential of this approach. [ABSTRACT FROM AUTHOR]

The 2019 coronavirus disease outbreak, caused by the severe acute respiratory syndrome type-2 virus (SARS-CoV-2), was declared a pandemic in March 2020. Since its emergence to the present day, this disease has brought multiple countries to the brink of health care collapse during several waves of the disease. One of the most common tests performed on patients is chest x-ray imaging. These images show the severity of the patient's illness and whether it is indeed covid or another type of pneumonia. Automated assessment of this type of imaging could alleviate the time required for physicians to treat and diagnose each patient. To this end, in this paper we propose the use of Convolutional Neural Networks (CNNs) to carry out this process. The aim of this paper is twofold. Firstly, we present a pipeline adapted to this problem, covering all steps from the preprocessing of the datasets to the generation of classification models based on CNNs. Secondly, we have focused our study on the modification of the information fusion processes of this type of architectures, in the pooling layers. We propose a number of aggregation theory functions that are suitable to replace classical processes and have shown their benefits in past applications, and study their performance in the context of the x-ray classification problem. We find that replacing the feature reduction processes of CNNs leads to drastically different behaviours of the final model, which can be beneficial when prioritizing certain metrics such as precision or recall. • Convolutional Neural Networks are effective for detecting SARS-CoV-2 on x-ray images. • Intermediate extracted features can be fused through different aggregation functions. • Grouping functions are harder to train but can offer better classification accuracy. • An early restart policy eases training models which make use of grouping functions. [ABSTRACT FROM AUTHOR]

Ordered Weighted Averaging (OWA) operators have been integrated in Convolutional Neural Networks (CNNs) for image classification through the OWA layer. This layer lets the CNN integrate global information about the image in the early stages, where most CNN architectures only allow for the exploitation of local information. As a side effect of this integration, the OWA layer becomes a practical method for the determination of OWA operator weights, which is usually a difficult task that complicates the integration of these operators in other fields. In this paper, we explore the weights learned for the OWA operators inside the OWA layer, characterizing them through their basic properties of orness and dispersion. We also compare them to some families of OWA operators, namely the Binomial OWA operator, the Stancu OWA operator and the exponential RIM OWA operator, finding examples that are currently impossible to generalize through these parameterizations.

Rapid deployment of IT brings about new issues with software usability measurement. Usability is based on users' experience and is strongly subjective, having a qualitative character. The users' comfort is usually collected by surveys in their daily work. The present article stems from an experimental study related to the evaluation of the usability of tools by a rule-based system. The work suggests a robust computational model that will be able to avoid the main problems arising from the experimental study (a large and less-legible rule base) and to deal with the vagueness of IT user experience, different levels of skills and various numbers of filled questionnaires in different departments. The computational model is based on three hierarchical levels of aggregation supported by fuzzy logic. Choices for the most suitable aggregation functions in each level are advocated and illustrated with examples. The number of questions and granularity of answers in this approach can be adjusted to each user group, which could reduce the response burden and errors. Finally, the paper briefly describes further possibilities of the suggested approach. [ABSTRACT FROM AUTHOR]

Aggregation functions are extensively used in decision making processes to combine available information. Arithmetic mean and weighted mean are some of the most used ones. In order to use a weighted mean, we need to define its weights. The Analytical Hierarchy Process (AHP) is a well known technique used to obtain weights based on interviews with experts. From the interviews we define a matrix of pairwise comparisons of the importance of the weights. We call these AHP-like matrices absolute preferences of weights. We propose another type of matrix that we call a relative preference matrix. We define this matrix with the same goal—to find the weights for weighted aggregators. We discuss how it can be used for eliciting the weights for the weighted mean and define a similar approach for the Choquet integral.