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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]

Note that Θ – Ξ functions and aggregation functions are two interrelated concepts rather than mutually inclusive ones. On the other hand, 0-overlap functions and 1-grouping functions are common subsets of these two broader categories. Although the homogeneity and quasi-homogeneity properties of 0-overlap functions and 1-grouping functions have been thoroughly described through existing research on aggregation functions, it is noteworthy that our approach offers a direct proof of their homogeneity, rather than treating them as a mere special case of quasi-homogeneity. Then the pseudo-homogeneity of these functions is extended to aggregation functions with continuous diagonals, and the necessary and sufficient conditions for such aggregation functions are obtained by utilizing the pseudo-inverses of unary functions. Finally, by exploring the structures of the Θ – Ξ functions, which serve as a unified representation of 0-overlap functions and 1-grouping functions, the homogeneity, quasi-homogeneity, and pseudo-homogeneity of Θ – Ξ functions are comprehensively characterized. Our findings are further illustrated through examples, providing a clear understanding of these functions and their properties. [ABSTRACT FROM AUTHOR]

Functional equations involving certain generalized forms of the so-called 'laws of sciences' are considered. The resolution of these equations is linked to the concept of comparison meaningfulness that appears in measurement theory and dimension theory. The results obtained are stated without assuming any topological requirement. [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]

How to expand the variable domain and monotonicity of aggregation functions to generate new aggregation functions is an important research content in aggregation functions. In this work, the concept of interval-valued pre-(quasi-)grouping functions is given by relaxing the interval monotonicity of interval-valued (quasi-)grouping functions to interval directional monotonicity. Then, some basic properties of interval-valued pre-(quasi-)grouping functions and the relationship between interval-valued pre-(quasi-)grouping functions and pre-(quasi-)grouping functions are presented. Accordingly, several construction methods of interval-valued pre-(quasi-)grouping functions are proposed. Finally, the concept of (I G , IN) -interval-valued directional monotonic fuzzy implications and QL -interval-valued directional monotonic operations are introduced on the basis of interval-valued pre-(quasi-)grouping functions I G , interval-valued overlap functions IO and interval-valued fuzzy negations IN. In addition, related studies were conducted on the basic properties of (I G , IN) -interval-valued directional monotonic fuzzy implications and QL -interval-valued directional monotonic operations. [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.

As significant carriers of the application of fuzzy set theories, fuzzy systems have been widely used in many fields. However, selecting fuzzifications, fuzzy reasoning engines, and defuzzifications is subjective for Mamdani fuzzy systems, and the fuzzy rule of Takagi-Sugeno-Kang fuzzy systems is less of a linguistic interpretation. Regarding these shortcomings, this paper proposes a fuzzy system based on vague partitions processing information directly from the fuzzy rule base, in which fuzzy rules have explicit semantics. Firstly, the n-dimensional vague partition of the n-dimensional universe is defined based on 1-dimensional vague partitions and the aggregation function, and its properties are discussed. Based on these, we design the new fuzzy system, and investigate its approximation properties which is the theoretical guarantee for applying the fuzzy system. As an application, we combine the fuzzy system with PID control system to deal with autonomous vehicle path tracking control problems. A series of experiments are constructed, and experimental results indicate that the fuzzy system based on vague partitions makes the fuzzy PID control system strong robustness, and has obvious advantages compared with other traditional fuzzy systems for path tracking control problems. [ABSTRACT FROM AUTHOR]

In literature, for the four usual classes of uninorms, the modularity equation has been solved except for the kind of ones having continuous underlying functions. This paper is devoted to solving the modularity equation involving two uninorms with continuous underlying functions. We discuss this modularity equation in detail by dividing the main section into two parts. The structure characterization of the two uninorms is almost completely obtained and it is found that they are equal in the unit square except in a subdomain. [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 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.

A characterization of what we call pseudo-projective aggregation functions is shown, thus generalizing existing recent results in the literature. The approach followed is then applied to obtain certain characterizations of projective and pseudo-projective aggregation operators as well as to develop a social choice voting model. [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. [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]

In this contribution, we fully characterize one- and two-dimensional positively homogeneous aggregation functions and provide a method of checking non-decreasingness of positively homogeneous functions in higher dimensions. We also examine the interaction of positive homogeneity with super-addivity and sub-additivity of functions and link it to the concavity and convexity, respectively, of their generalized opposite diagonal functions. Some remarks on the computation of a linear super-additive transformation of aggregation functions are added. [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]

This paper introduces a novel method for stress-constrained topology optimization in which the stress constraint is a differentiable approximation of the maximum element stress violation in the structure. The element stress violation is given by a differentiable rectifier function. A key feature of the proposed method is its ability to render designs that satisfy the stress limit without renormalization of the constraint, as in some existing aggregation approaches. Numerical experiments demonstrate that the proposed technique exhibits better convergence and is less sensitive to the aggregation parameter than aggregation methods that employ renormalization. The effectiveness of the proposed method is demonstrated by several examples. [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.

Buckling failure mainly occurs in slender rod structure under pressure, which incurs great concern and should be addressed in topology optimization (TO). However, due to the internal defects of material and the external environment interference of engineering system, the practical engineering structure inevitably produces many uncertain factors in the manufacturing and service stages. Therefore, a reliability‐based topology optimization (RBTO) model under buckling and compliance constraints is established to operate the structural lightweight design considering reliability and stability requirements. To reduce the number of probabilistic constraints, the Kreisselmeier–Steinhauser aggregation function is adopted for combining the multiple constraints into a single smooth and differentiable constraint. Then, a single‐loop approach combining modified chaos control strategy is applied to guarantee the robustness, effectiveness, and computational efficiency of RBTO. In addition, the sensitivities of the probabilistic constraint with respect to design and random variables are deduced, and the accuracy of sensitivities is verified by finite difference method. Finally, the validity of the RBTO method is verified by comparing with deterministic TO, in which three numerical examples are employed to demonstrate the robustness and computational accuracy. [ABSTRACT FROM AUTHOR]

Overlap functions are a class of aggregation functions that measure the overlapping degree between two values. They have been successfully applied as a fuzzy conjunction operation in several problems in which associativity is not required, such as image processing and classification. Interval-valued overlap functions were defined as an extension to express the overlapping of interval-valued data, and they have been usually applied when there is uncertainty regarding the assignment of membership degrees, as in interval-valued fuzzy rule-based classification systems. In this context, the choice of a total order for intervals can be significant, which motivated the recent developments on interval-valued aggregation functions and interval-valued overlap functions that are increasing to a given admissible order, that is, a total order that refines the usual partial order for intervals. Also, width preservation has been considered on these recent works, in an intent to avoid the uncertainty increase and guarantee the information quality, but no deeper study was made regarding the relation between the widths of the input intervals and the output interval, when applying interval-valued functions, or how one can control such uncertainty propagation based on this relation. Thus, in this paper we: (i) introduce and develop the concepts of width-limited interval-valued functions and width limiting functions, presenting a theoretical approach to analyze the relation between the widths of the input and output intervals of bivariate interval-valued functions, with special attention to interval-valued aggregation functions; (ii) introduce the concept of (a , b) -ultramodular aggregation functions, a less restrictive extension of one-dimension convexity for bivariate aggregation functions, which have an important predictable behaviour with respect to the width when extended to the interval-valued context; (iii) define width-limited interval-valued overlap functions, taking into account a function that controls the width of the output interval and a new notion of increasingness with respect to a pair of partial orders (≤ 1 , ≤ 2) ; (iv) present and compare three construction methods for these width-limited interval-valued overlap functions, considering a pair of orders (≤ 1 , ≤ 2) , which may be admissible or not, showcasing the adaptability of our developments. [ABSTRACT FROM AUTHOR]

Conditional distributivity (also called restricted distributivity) is a form of relaxed distributivity on the restricted domain. There are three options for conditional distributivity in literature. In this paper, we focus on type-III conditional distributivity equation involving nullnorms over uninorms. Firstly, we show that it can be transformed into the other two types of conditional distributivity equations involving t-norms/t-conorms over uninorms. Secondly, type-I and type-II conditional distributivity equations involving t-norms/t-conorms over uninorms that are related to our study and remain unknown are investigated. Finally, we show that this new perspective results in not only all known solutions, but new solutions as well. [ABSTRACT FROM AUTHOR]

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 article, a new fully fuzzy approach is developed for the evaluation based on distance from average solution (EDAS) for multi-criteria decision-making (MCDM) using spherical fuzzy sets (SFSs). The proposed approach avoids the current limitations and drawbacks of distance-based methods in general and the EDAS method in particular using spherical fuzzy information namely, early defuzzification, the flaws of distance measures, and the undefined spherical fuzzy subtraction and division operations. First, the approach employs the score function only in the final step for ranking. Second, the concept of the spherical fuzzy difference is introduced to make up for the subtraction operation which is the backbone of EDAS and as a substitute for distance measures. The spherical fuzzy difference is utilized to indicate any increase or decrease in the membership degree, the non-membership degree, and the hesitancy degree in the performance of an alternative for a criterion than that of its peer in the average solution. Then, the weighted spherical differences are calculated. The total weighted spherical differences from the average solution of each alternative for the assessment criteria are aggregated in the appraisal score. Due to a flaw in the extant aggregation operators, their results might be misleading. Therefore, an aggregation function is introduced that guarantees a balanced and fair aggregation. The appraisal scores are defuzzified, and the alternative with the highest appraisal score is the best. Two practical examples in MCDM are solved and a comparative study is presented to demonstrate and validate the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we explore the concept of local contrast of a fuzzy relation, which can be perceived as a measure for distinguishing the degrees of membership of elements within a defined region of an image. We introduce four distinct methods for constructing fuzzy local contrast: one uses a similarity measure, the second relies on the aggregation of similarity, the third is based on the aggregation of restricted equivalence, and the fourth utilizes the notion of equivalence. We further divide the constructions using similarity measures into two categories based on the two known definitions of similarity: distance-based similarity and aggregation function-based similarity. These construction methods also incorporate fuzzy implications and negations. Aggregation functions, which can be manipulated to enhance the effectiveness of the constructed fuzzy local contrast, play a significant role in most of our proposed constructions. For each construction method, several examples of fuzzy local contrasts are provided. The usefulness of the new fuzzy local contrasts is examined by applying them in image processing for salient region detection. • Aggregation functions used in a few construction methods of a fuzzy local contrast. • Numerous examples of fuzzy local contrasts provided. • Effectivness of aggregation functions examined in fuzzy local contrast in image processing for salient region detection. [ABSTRACT FROM AUTHOR]

The enumeration of logical connectives and aggregation functions defined on a finite chain has been a hot topic in the literature for the last decades. Multiple advantages can be derived from knowing a general formula about their cardinality, for instance, the ability to anticipate the computational cost required for generating operators with different properties. This is of paramount importance in image processing and decision making scenarios, where the identification of the most optimal operator is essential. Furthermore, it facilitates the examination of how constraining a certain property is in relation to its parent class. As a consequence, this paper aims to compile the main existing formulas and the methodologies with which they have been derived. Additionally, we introduce some novel formulas for the number of smooth discrete aggregation functions with neutral element or absorbing element, idempotent conjunctions, and commutative and idempotent conjunctions. [ABSTRACT FROM AUTHOR]

This paper proposes a novel method for the construction of a fuzzy metrics and demonstrates application in image segmentation. Some new properties of t-norms, t-conorms, aggregation functions, and fuzzy metrics are proved, which provides the procedures for constructing a new fuzzy metric. We prove that by applying some types of t-norms, tconorms and aggregation functions on the sequence of fuzzy metrics, a new fuzzy metric could be obtained. The application of the fuzzy metric constructed in this way is illustrated in image segmentation by using the FCM algorithm. For the purpose of constructing a new fuzzy metric, an extended aggregation function called generalized quasi-arithmetic mean is considered. [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]