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Nowadays, the increased amount of users’ devices produce huge volumes of data that should be efficiently managed by modern applications. Streams are adopted to deliver data that, usually, are stored into a number of partitions. Splitting the data offers a lot of advantages as applications can process them in parallel, thus, they increase the speed of processing. Progressive analytics are also adopted to deliver partial responses, during processing, thus, saving time in the execution of applications. Data exploration and analytics queries are very significant for future applications. Usually, such queries demand for an ordered set of objects as a response and require intelligent predictive schemes to deliver the responses on top of the partial results retrieved by the distributed data partitions. A finite set of query processors are adopted to produce these partial results. Processors are placed in front of each partition and report progressive analytics to a central entity. In this paper, we envision the query controller (QC) as the central entity that collects progressive analytics and return the final response to users/applications. The QC receives partial ordered sets of objects and aggregates them to derive the final outcome. We focus on a QC that applies time-optimized techniques and aggregation operators to deliver every response, i.e., ordered sets, over streams of partial ordered subsets. We perform a comprehensive performance assessment with synthetic data and report on the performance of the QC. Our experimental evaluation reveals the pros and cons of the proposed model and a comparison assessment places this paper in the respective literature. [ABSTRACT FROM AUTHOR]

The papers in this special issue represent the second one in the sequel of three special issues on spectrum sharing and aggregation for future wirelessn networks. [ABSTRACT FROM PUBLISHER]

In dynamic, open, and service-oriented computing environments, e.g., e-commerce and crowdsourcing, service consumers must choose one of the services or items to complete their tasks. Due to the scale and dynamic characteristics of these environments, service consumers may have little or no experience with the available services. To this end, reputation systems are proposed and have played a crucial role in the success of online service-oriented transactions. In this paper, we study the current reputation systems used in commercial environments. In these rating-based reputation systems, we found they are not only resilient to the changes (time lag) but also vulnerable to unfair ratings. To address the problems in parallel, we propose an adaptive reputation model (ARM). ARM can dynamically adjust its model parameters to adapt the latest changes in a service. To tackle time lag, the proposed model generalizes the fixed sliding window, used in current commercial platforms, into a dynamic sliding window mechanism. Thus, the model can completely mitigate the influence of obsolete ratings. To detect unfair ratings, our model implements a statistical strategy based on hypothesis testing after transforming the ratings in the linear window into residuals. Experiments not only validate the effectiveness of the proposed model but also show that it outperforms the existing reputation system by 45% on average based on five test cases. The results also show that the proposed model can asymptotically converge to the underlying reputation value as ratings begin to accumulate. Note to Practitioners—The reputation models adopted by current commercial platforms, such as Amazon, eBay, and Taobao, not only suffer heavily from unfair rating but also resilient to the changes in services. To address the problems simultaneously, we design and implement a hybrid model that continuously monitors received ratings and aggregates the reputation value in a self-adaptive way. Our model first fits received fair ratings using the Bayesian linear regression approach and captures the distribution of fair ratings; it then filters out unfair ratings leveraging hypothesis testing. Finally, to sensitively respond the dynamic service changes, the dynamic sliding window algorithm in our model shifts the rating collection window into a new one and discards outdated ratings, reputation value is aggregated in the new window to mitigate the influence of obsolete ratings. Extensive experiments are conducted on widely used scenarios to demonstrate the efficiency and the effectiveness of our proposed model. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy sets (T2FSs) were introduced by L. A. Zadeh in 1975 as an extension of type-1 fuzzy sets (T1FSs). In this extension, the degree to which an element belongs to a set is just a label of the linguistic variable “TRUTH,” which allows to represent reality in a more appropriate way. On the other hand, negations play an essential role within fuzzy sets theory. In fact, they are necessary in order to obtain, for example, complements of fuzzy sets, dual of a t-norm or a t-conorm, entropies, implications, as well as to study the possible contradictions appearing in a fuzzy system. However, meanwhile negations on [0, 1] (set of the membership degrees of a fuzzy set) have been deeply studied throughout the literature, the same has not happened with the negations on ${\bf M}$ = $\text{Map} \;([\text{0}, \text{1}],[\text{0}, \text{1}])$ , set of functions from [0, 1] to [0, 1] (and also set of the membership degrees of a T2FS), and so many aspects of the negations on ${\bf M}$ have not yet been investigated. In a previous paper, the axioms that an operation must satisfy to be considered a negation or a strong negation on a bounded partially ordered set were established. A family of strong negations on L and set of normal and convex functions of ${\bf M}$ were also presented. Moreover, let us note that the main characteristic of fuzzy systems is just the flexibility in order to be able to represent knowledge according to each situation, offering different models among which the expert can choose the one that best suits his/her criteria. Thus, it seems useful to find broad sets of negations in ${\bf M}$ and in L, which, as far as we know, have not been done by other researchers. According to these ideas, in this paper, the authors first present new negations and strong negations on L, and then show, for the first time, some negations on ${\bf M}$ with respect to each of the two partial orders defined in this set. [ABSTRACT FROM AUTHOR]

In group decision making, consensus models are decision aid tools and help experts modify their individual opinions to reach a closer agreement. Based on the concept of minimum-cost consensus, this paper proposes a novel framework to achieve minimum-cost consensus under aggregation operators. Analytical results indicate that the proposed framework reduces to the consensus model of Ben-Arieh when the selected aggregation operator is the ordered weighted averaging (OWA) operator with weight vector (1/2, \ldots, 0, \ldots, 1/2)^T. Furthermore, this paper closely examines the minimum-cost consensus models with a linear cost function under the common aggregation operators (e.g., the weighted averaging operator and the OWA operator). Linear-programming-based approaches are also developed to solve these models. The results of this paper significantly contribute to efforts to develop the consensus model of Ben-Arieh [ABSTRACT FROM PUBLISHER]

The focus of this paper is the linguistic weighted average (LWA), where the weights are always words modeled as interval type-2 fuzzy sets (IT2 FSs), and the attributes may also (but do not have to) be words modeled as IT2 FSs; consequently, the output of the LWA is an IT2 FS. The LWA can be viewed as a generalization of the fuzzy weighted average (FWA) where the type-1 fuzzy inputs are replaced by IT2 FSs. This paper presents the theory, algorithms, and an application of the LWA. It is shown that finding the LWA can be decomposed into finding two FWAs. Since the LWA can model more uncertainties, it should have wide applications in distributed and hierarchical decision-making. [ABSTRACT FROM AUTHOR]

Data aggregation is an essential operation for the sink to obtain summary information in a wireless sensor network (WSN). The problem of minimum latency aggregation schedule (MLAS) which seeks a fastest and conflict-free aggregation schedule has been well studied when nodes are always awake. However, in duty-cycle WSNs, nodes can only receive data in the active state. In such networks, it is of great importance to exploit the limited active time slots to reduce aggregation latency. Unfortunately, few studies have addressed this issue, and most previous aggregation methods rely on fixed structures which greatly limit the exploitation of the active time slots from neighbors. In this paper, we investigate the MLAS problem in duty-cycle WSNs without considering structures. Two distributed aggregation algorithms are proposed, in which the aggregation tree and a conflict-free schedule are generated simultaneously to make use of the active time slots from all neighbors. Compared with the previous centralized and distributed methods, the aggregation latency and the utilization ratio of available time slots are greatly improved. This paper also proposes several adaptive strategies for handling network topology changes without increasing the aggregation latency. The theoretical analysis and simulation results verify that the proposed algorithms have high performance in terms of latency and communication cost. [ABSTRACT FROM AUTHOR]

Many data-intensive applications like MapReduce are network-bound in data centers, due to transfer massive amount of flows across successive processing stages. Data flows in such an incast or shuffle transfer are highly correlated and aggregated at the receiver side. Prior work aims to aggregate correlated flows of each transfer, during the transmission phase as early as possible, so as to directly lower down the network traffic. However, many applications do not constrain the flows’ endpoints of each transfer as long as certain constraints are satisfied. Such uncertain transfers bring new opportunities and challenges to lower down the network traffic than prior deterministic transfers. In this paper, we focus on aggregating an uncertain incast transfer and minimizing the amount of caused network traffic. Prior approaches, relying on deterministic incast transfers, remain inapplicable. This paper makes the first step towards the study of aggregating uncertain incast transfer. We propose efficient approaches from two aspects, i.e., the initialization of uncertain senders and the incast tree building. We first design two initialization methods to pick the best deterministic senders for an uncertain incast transfer, so as to form the least number of disjoint sender groups. Thus, flows from each group would be aggregated as one flow on a common one-hop neighbor, irrespective of the location of a picked receiver. Accordingly, we propose the interstage-based and intrastage-based incast tree building methods to exploit the benefits of our initialization methods. We provide evidence to show that our approach can achieve the benefits of in-network aggregation for any uncertain incast transfer. Moreover, an uncertain incast transfer significantly outperforms any related deterministic one, in terms of the reduced network traffic and the saved network resources. [ABSTRACT FROM PUBLISHER]

Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational savings. To improve this tradeoff, this paper generalizes state-of-the-art distributed graph filters to filters where every node weights the signal of its neighbors with different values while keeping the aggregation operation linear. This new implementation, labeled as edge-variant graph filter, yields a significant reduction in terms of communication rounds while preserving the approximation accuracy. In addition, we characterize a subset of shift-invariant graph filters that can be described with edge-variant recursions. By using a low-dimensional parameterization, these shift-invariant filters provide new insights in approximating linear graph spectral operators through the succession and composition of local operators, i.e., fixed support matrices. A set of numerical results shows the benefits of the edge-variant graph filters over current methods and illustrates their potential to a wider range of applications than graph filtering. [ABSTRACT FROM AUTHOR]

The creation of sustainable artificial tropical forests is of utmost importance for addressing critical environmental issues like deforestation, habitat loss, and climate change. This research paper presents an innovative approach that considers ecological, socioeconomic, and technological factors. The proposed approach integrates multi-criteria decision-making (MCDM) methods that take into account the preferences and opinions of stakeholders. To analyze the various criteria involved, cubic picture fuzzy numbers (CPFNs) are utilized. To ensure fairness in evaluating CPFNs, the study focuses on developing operational laws and aggregation operators that promote neutrality and fairness. Specifically, the paper introduces the “cubic picture fuzzy fairly weighted average (CPFFWA) operator” and the “cubic picture fuzzy fairly ordered weighted averaging (CPFFOWA) operator.” By considering stakeholders and prioritizing their long-term sustainability and resilience, this approach proves to be highly valuable for policymakers, forest managers, and other relevant parties. This research avenue bridges the gap in current literature where limited exploration of fairly aggregation operators in tandem with picture fuzzy sets within tropical forest contexts exists. Ultimately, the research strives to contribute to the practical management of these vital ecosystems, fostering environmental conservation and sustainability through a cross-disciplinary approach amalgamating ecology, fuzzy logic, decision theory, and environmental science.

This paper is first in a series of papers studying a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. In this paper we present the paradigm and revise underlying technical tools, such as the lifting technique and some topics of the operator theory. This material facilitates a systematic and unified treatment of a wide range of sampling and reconstruction problems, recovering many hitherto considered different solutions and leading to new results. Some of these applications are discussed in the second part. [ABSTRACT FROM AUTHOR]

Partly due to lack of test problems, the impact of the Pareto set (PS) shapes on the performance of evolutionary algorithms has not yet attracted much attention. This paper introduces a general class of continuous multiobjective optimization test instances with arbitrary prescribed PS shapes, which could be used for studying the ability of multiobjective evolutionary algorithms for dealing with complicated PS shapes. It also proposes a new version of MOEA/D based on differential evolution (DE), i.e., MOEA/D-DE, and compares the proposed algorithm with NSGA-II with the same reproduction operators on the test instances introduced in this paper. The experimental results indicate that MOEA/D could significantly outperform NSGA-II on these test instances. It suggests that decomposition based multiobjective evolutionary algorithms are very promising in dealing with complicated PS shapes. [ABSTRACT FROM AUTHOR]

To be able to describe more complex fuzzy uncertainty information effectively, the concept of q-rung orthopair fuzzy sets (q -ROFSs) was first proposed by Yager. The q-ROFSs can dynamically adjust the range of indication of decision information by changing a parameter q based on the different hesitation degree from the decision-makers, where q ≥ 1, so they outperform the traditional intuitionistic fuzzy sets and Pythagorean fuzzy sets. In real decision-making problems, there is often an interaction phenomenon between attributes. For aggregating these complex fuzzy information, the Maclaurin symmetric mean (MSM) operator is more superior by considering interrelationships among attributes. In addition, the power average (PA) operator can reduce the effects of extreme evaluating data from some experts with prejudice. In this paper, we introduce the PA operator and the MSM operator based on q-rung orthopair fuzzy numbers (q-ROFNs). Then, we put forward the q-rung orthopair fuzzy power MSM (q-ROFPMSM) operator and the q-rung orthopair fuzzy power weighed MSM (q-ROFPWMSM) operator of q-ROFNs and present some of their properties. Finally, we present a novel multiple-attribute group decision-making (MAGDM) method based on the q-ROFPWA and the q-ROFPWMSM operators. The experimental results show that the novel MAGDM method outperforms the existing MAGDM methods for dealing with MAGDM problems. [ABSTRACT FROM AUTHOR]

This paper addresses the commonly used methods for solving multiple attribute group decision-making problems under an interval-valued intuitionistic fuzzy environment. It is shown that either the most popular score function and its latterly improved versions or other related methods may lead to the undesirable results. Apart from these seemly heuristic methods, we propose a generalized p-norm knowledge-based score function for the interval-valued intuitionistic fuzzy set, which is a generalization of the score function for intuitionistic fuzzy sets as well. The proposed score function is defined as the average amount of knowledge of information depicted in terms of the interval-valued intuitionistic fuzzy sets, that regards their quantitative level of information referred to a reference level, fuzziness and qualitative significance of information. It is proved that the proposed score function has good algebraic properties, such as monotonicity under multiplication or aggregation operator, which are not preserved in the case of existing score functions. We show that the proposed score function is a simple, easily interpreted approach, which provides intuitive results in ranking the IvIFSs as well as IFSs, particularly. Several illustrative examples are performed to demonstrate the superiority of the proposed method in measuring and discriminating the IvIFSs. A comparative analysis with the preceding methods in solving decision-making problems is conducted to show the effectiveness of the proposed method in real-life applications. [ABSTRACT FROM AUTHOR]

Segmentation of cardiac ventricle from magnetic resonance images is significant for cardiac disease diagnosis, progression assessment, and monitoring cardiac conditions. Manual segmentation is so time consuming, tedious, and subjective that automated segmentation methods are highly desired in practice. However, conventional segmentation methods performed poorly in cardiac ventricle, especially in the right ventricle. Compared with the left ventricle, whose shape is a simple thick-walled circle, the structure of the right ventricle is more complex due to ambiguous boundary, irregular cavity, and variable crescent shape. Hence, effective feature extractors and segmentation models are preferred. In this paper, we propose a dilated-inception net (DIN) to extract and aggregate multi-scale features for right ventricle segmentation. The DIN outperforms many state-of-the-art models on the benchmark database of right ventricle segmentation challenge. In addition, the experimental results indicate that the proposed model has potential to reach expert-level performance in right ventricular epicardium segmentation. More importantly, DIN behaves similarly to clinical expert with high correlation coefficients in four clinical cardiac indices. Therefore, the proposed DIN is promising for automated cardiac right ventricle segmentation in clinical applications. [ABSTRACT FROM AUTHOR]

In this paper, we propose the concept of a linguistic interval-valued Atanassov intuitionistic fuzzy set (LIVAIFS), whose membership and nonmembership degrees are represented by the interval-valued linguistic terms, for better dealing with imprecise and uncertain information during the decision-making process. In it, first some operational laws, score, and accuracy functions of LIVAIFS are defined with a brief study of related properties. Then, based on these operational laws, several aggregating operators are proposed to aggregate the linguistic interval-valued Atanassov intuitionistic fuzzy (LIVAIF) information. Some properties and inequalities are established to show the effectiveness and validity of proposed operators. Furthermore, a group decision making (GDM) approach, based on proposed operators, has been presented to solve the multiattribute GDM problems under LIVAIF environment. Finally, an illustrative example has been presented to demonstrate the approach. [ABSTRACT FROM AUTHOR]

Overlap and grouping functions, as two new classes of special binary aggregation functions, have been investigated by several authors for applications in image processing, decision making, classification, and fuzzy community detection problems. On the other hand, after Aczél studied the distributive law between two operations, the distributive laws among particular binary aggregation functions become an interesting and natural research area. In this paper, we continue to discuss this topic for uninorms and overlap and grouping functions. First, we give some basic properties for the distributive law of uninorms over overlap functions. Second, we study this distributive law when the uninorms belong to one of the usual classes (e.g., $\mathcal {U}_{\min }$ , $\mathcal {U}_{\max }$ , the family of idempotent uninorms, representable uninorms or uninorms continuous on $]0,1[^2$). Finally, we investigate the distributive law of uninorms over grouping functions by an analogous way. [ABSTRACT FROM AUTHOR]

Two processes are necessary to solve group decision making problems: A consensus process and a selection process. The consensus reaching process is necessary to obtain a final solution with a certain level of agreement between the experts; and the selection process is necessary to obtain such a final solution. In a previous paper, we present a selection process to deal with group decision making problems with incomplete fuzzy preference relations, which uses consistency measures to estimate the incomplete fuzzy preference relations. In this paper we present a consensus model. The main novelty of this consensus model is that of being guided by both consensus and consistency measures. Also, the consensus reaching process is guided automatically, without moderator, through both consensus and consistency criteria. To do that, a feedback mechanism is developed to generate advice on how experts should change or complete their preferences in order to reach a solution with high consensus and consistency degrees. In each consensus round, experts are given information on how to change their preferences, and to estimate missing values if their corresponding preference relation is incomplete. Additionally, a consensus and consistency based induced ordered weighted averaging operator to aggregate the experts' preferences is introduced, which can be used in consensus models as well as in selection processes. The main improvements of this consensus model is that it supports the management of incomplete information and it allows to achieve consistent solutions with a great level of agreement. [ABSTRACT FROM AUTHOR]

In this paper, an orness measure to reflect the or-like degree of the quasi-arithmetic mean operator is proposed. With the generating function representation method, some properties of a quasi-arithmetic mean, associated with its orness measure, are analyzed. Then, the paper focuses on two kinds of parameterized quasi-arithmetic means with exponential function and power function generators respectively. Some properties of them are examined and compared. As the aggregation value for any set always monotonically increases with the orness level, the orness level can be used as a control parameter to represent the decision maker's preference. A generic method to get the quasi-arithmetic mean operator which makes the aggregation result consistent with its orness level is also examined. Finally, the properties of the quasi-arithmetic mean and that of the exponential and power function generators are extended to the weighted quasi-arithmetic mean by considering the importance of the aggregated elements. [ABSTRACT FROM AUTHOR]

This paper presents an aggregation method to build a coherency-based dynamic equivalent of detailed generating units models and their control systems. The proposed method is based on the preservation of the coefficients matrices structure in the time domain representation. According to the principle of structure preservation, the parameters of the equivalent generator and its control systems are calculated directly. This procedure requires much less computation effort and is suitable for online studies compared to other methods, which use mainly the iterative process in frequency domain to derive equivalent parameters. For validation purposes, this aggregation method is applied to group an area of eight generators inside a test system of 16 generators and 68 buses. Results show that the reduced system retains the dynamic performance of the original system with good accuracy, and all inter-area modes of the original system are preserved in the reduced system. [ABSTRACT FROM AUTHOR]

Fuzzy pattern trees have recently been introduced as a novel type of fuzzy system, specifically with regard to the modeling of classification functions in machine learning. Moreover, different algorithms for learning pattern trees from data have been proposed in the literature. While showing strong performance in terms of predictive accuracy, these algorithms exhibit a rather high computational complexity, and their runtime may become prohibitive for large datasets. In this paper, we therefore propose extensions of an existing state-of-the-art algorithm for fuzzy pattern tree induction, which are aimed at making this algorithm faster without compromising its predictive accuracy. These extensions include the use of adaptive sampling schemes, as well as heuristics for guiding the growth of pattern trees. The effectiveness of our modified algorithm is confirmed by means of several experimental studies. [ABSTRACT FROM AUTHOR]

In object-oriented conceptual modeling, the generalization/specialization hierarchy and the whole/part relationship are prevalent classification schemes for object types. This paper presents an object-oriented conceptual model where, in the end, object types are classified according to two relationships only: existence dependency and generalization/specialization. Existence dependency captures some of the interesting semantics that are usually associated with the concept of aggregation (also called composition or Part Of relation), but in contrast with the latter concept, the semantics of existence dependency are very precise and its use clear cut. The key advantage of classifying object types according to existence dependency are the simplicity of the concept, its absolute unambiguity, and the fact that it enables to check conceptual schemes for semantic integrity and consistency. We will first define the notion of existence dependency and claim that it is always possible to classify objects according to this relationship, thus removing the necessity for the Part Of relation and other kinds of associations between object types. The second claim of this paper is that existence dependency is the key to semantic integrity checking to a level unknown to current object-oriented analysis methods. In other words: Existence dependency allows us to track and solve inconsistencies in an object-oriented conceptual schema. [ABSTRACT FROM AUTHOR]

This paper explores scenarios in which independent wind power producers form willing coalitions to exploit the reduction in aggregate power output variability obtainable through geographic diversity. In the setting of a two settlement electricity market, we examine the advantage gained through optimal coalitional contract offering strategies for quantity risk reduction. We show that a group of independent wind power producers can always improve their expected profit by cooperatively offering their aggregated power. Using coalitional game theory we identify sharing mechanisms to fairly allocate the profits to coalition members. We show that the resulting coalitional game is balanced, guaranteeing that the core of the game is necessarily nonempty. In addition, we propose a profit sharing mechanism that minimizes the worst-case dissatisfaction to recover an imputation in the core. Finally, we illustrate our theoretical results with empirical studies using data from five representative wind farms in upstate New York. [ABSTRACT FROM PUBLISHER]

The article presents an introduction to a special issue of "IEEE Transactions on Fuzzy Systems" on aggregation operators.

It is known that bisymmetry generalizes the simultaneous commutativity and associativity in the framework of the unit interval. In this work, we will completely characterize two classes of bisymmetric aggregation operators: one with a neutral element and the other with the vertical and horizontal sections of the idempotent elements being smooth on a finite chain, but not necessarily smooth and commutative. Thus, the previous results, based on the smoothness that is known as a very restrictive condition, are improved. For example, there is only one smooth Archimedean t-norm on a finite chain. In this paper, the discrete bisymmetric aggregation operators are explored without the limit of the smoothness. As a by-product, it is deduced that for smooth aggregation operators on a finite chain, the bisymmetry is equivalent to the commutativity and associativity, which improves the conclusion obtained by Mas et al. that associativity and bisymmetry are equivalent for commutative smooth aggregation operators on a finite chain. [ABSTRACT FROM PUBLISHER]

Fuzzy measures are monotonic set functions on a reference set; they generalize probabilities replacing the additivity condition by monotonicity. The typical application of these measures is with fuzzy integrals. Fuzzy integrals integrate a function with respect to a fuzzy measure, and they can be used to aggregate information from a set of sources (opinions from experts or criteria in a multicriteria decision-making problem). In this context, background knowledge on the sources is represented by means of the fuzzy measures. For example, interactions between criteria are represented by means of nonadditive measures. In this paper, we introduce fuzzy measures on multisets. We propose a general definition, and we then introduce a family of fuzzy measures for multisets which we show to be equivalent to distorted probabilities when the multisets are restricted to proper sets. [ABSTRACT FROM PUBLISHER]

Data aggregation is a fundamental task in multihop wireless sensor networks. Minimum-latency aggregation scheduling (MLAS) seeks to minimize the number of scheduled time slots to perform an aggregation. In this paper, we present the first work on a solvable mathematical formulation of the MLAS problem. The optimal solution of small example networks suggests that an optimal scheduling can be neither shortest path nor dominating set based. Instead of yet another theoretical analysis with provable bounds, our work focuses on reducing the average latency of general random topologies. Inspired by backward induction theory, we propose to schedule the aggregation in a reverse order, and the tree construction of Greedy Growing Tree (GGT) is directly guided by the scheduling algorithm in a step-by-step way. By following priority rules when we schedule candidate \langle sender, receiver \rangle pairs, the opportunity of parallel transmission is maximized. As a result, the aggregation latency can be minimized. Our extensive evaluation results demonstrate the superiority of the GGT algorithm: For sparse networks, the resultant latency is comparable with the best practice, whereas for high-degree networks, the latency is only half of that using state-of-art competitors. [ABSTRACT FROM PUBLISHER]

This paper describes an artificial neuron structure and an efficient learning procedure in the complex domain. This artificial neuron aims at incorporating an improved aggregation operation on the complex-valued signals. The aggregation operation is based on the idea underlying the weighted root-power mean of input signals. This aggregation operation allows modeling the degree of compensation in a natural manner and includes various aggregation operations as its special cases. The complex resilient propagation algorithm (\BBC-RPROP) with error-dependent weight backtracking step accelerates the training speed significantly and provides better approximation accuracy. Finally, performance evaluation of the proposed complex root-power mean neuron with the \BBC-RPROP learning algorithm on various typical examples is given to understand the motivation. [ABSTRACT FROM AUTHOR]

In this paper, we study the major problems in applying Slepian-Wolf coding for data aggregation in cluster-based wireless sensor networks (WSNs). We first consider the clustered Slepian-Wolf coding (CSWC) problem, which aims at selecting a set of disjoint potential clusters to cover the whole network such that the global compression gain of Slepian-Wolf coding is maximized, and propose a distributed optimal-compression clustering (DOC) protocol to solve the problem. Under a cluster hierarchy constructed by the DOC protocol, we then consider the optimal intracluster rate-allocation problem. We prove that there exists an optimization algorithm that can find an optimal rate allocation within each cluster to minimize the intracluster communication cost and present an intracluster coding protocol to locally perform Slepian-Wolf coding within a single cluster. Furthermore, we propose a low-complexity joint-coding scheme that combines CSWC with intercluster explicit entropy coding to further reduce data redundancy caused by the possible spatial correlation between different clusters. [ABSTRACT FROM AUTHOR]

Three ways to approximate a proximity relation R (i.e., a reflexive and symmetric fuzzy relation) by a T-transitive one where T is a continuous Archimedean t-norm are given. The first one aggregates the transitive closure R― of R with a (maximal) T-transitive relation B contained in R. The second one computes the closest homotecy of R― or B to better fit their entries with the ones of R. The third method uses nonlinear programming techniques to obtain the best approximation with respect to the Euclidean distance for T the Lukasiewicz or the product t-norm. The previous methods do not apply for the minimum t-norm. An algorithm to approximate a given proximity relation by a Mintransitive relation (a similarity) is given in the last section of the paper. [ABSTRACT FROM AUTHOR]

This paper addresses a real-world engineering design requiring the application of effective and global optimization techniques. The problem it deals with is the design of nonlinear tracking filters under up to several hundreds of performance specifications. The suitability of different evolutionary computation techniques for solving multiobjective problems is explored, contrasting the performance achieved with recent multiobjective evolutionary algorithm (MOEAs) proposals and different aggregation schemes. In particular, a new scheme is proposed to build a fitness function based on an operator that selects worst cases of multiple specifications in different situations. They have been evaluated in the design of an air traffic control (ATC) tracking filter that should accomplish a specific normative with 264 specifications. Results show their performance in terms of effectiveness and computational load, comparing their capability to scale the problem with respect to problem size. [ABSTRACT FROM AUTHOR]

Aggregation plays a central role as a means of combining all opinions that are expressed by group members in a group decision support system (GDSS). In this paper, we propose a new r-ASA (Aggregation based on Situation Assessment) algorithm to reflect a decision situation in the aggregation process. Al- though some research findings showed the importance of cultural factors in GDSS, most of them did not present how to implement cultural factors in GDSS. To handle this problem, we present a proposal for reflecting status differentials in GDSS. It may be used to reflect cultural differences in GDSS design. It is a further step toward the integration of cultural factors into existing GDSS design. [ABSTRACT FROM AUTHOR]

This paper aims at expressing MIN and MAX operations when triangular fuzzy intervals are taken as inputs, that is when Zadeh's extension principle is considered. First presented approach consists in representing fuzzy intervals by means of their profiles. In this context, a computation algorithm can be easily derived for implementing the MIN and MAX operations. Another methodology based on interval relations is then proposed for determining a general analytical expression of the MIN and MAX operations. The potential use of these expressions in the framework of uncertain aggregation operators is illustrated with the two-additive Choquet integral. [ABSTRACT FROM AUTHOR]

Aggregation operators have been used and studied for a long time. More than ten different types of means (including the arithmetic, geometric, and harmonic ones) were already studied 2000 years ago. Nevertheless, this topic has gained relevance in recent years. This is partly due to the increasing need of methods and operators for fusing information within computer programs. In this paper, we will present a personal view of the field, focusing on the application issues and on averaging aggregation operators. We will point out some research topics and open lines for future research. [ABSTRACT FROM AUTHOR]

This paper deals with a class of conjunction-like binary operations defined on a finite totally ordered set. The concept of additive generator of a discrete conjunctive aggregation operation is introduced and we obtain a description of those operations having an additive generator by means of nonstrict Archimedean t-norms. The main goal is to give a procedure for deciding whether a conjunctive aggregation operation is additively generated or not. The problem of the existence of additive generators for discrete t-norms is also discussed. [ABSTRACT FROM AUTHOR]

Group decision making is a common and important activity in everyday life. In many cases, due to inherent uncertainty, experts cannot express their score or preference using exact numbers. The use of linguistic labels makes expert judgment more reliable and informative for decision-making. One of the problems of group decision making in fuzzy domains is aggregating experts' opinions, expressed using linguistic labels, into a group opinion. This aggregation allows the group to select the most "preferred" alternative from a finite set of candidates. The aggregation of individual judgments into a group opinion requires a measured level of consensus. In this paper, by introducing a new linguistic-labels aggregation operation, we present a procedure for handling an autocratic group decision-making process under linguistic assessments. The methodology presented results in two consequent outcomes: a group-based recommendation, and a score for each expert, reflecting the expert's contribution towards the group recommendation. By changing the weights of the experts based on their contributions, we increase the consensus and reinforce the common decision, without forcing the experts to modify their opinions. This methodology allows an autocratic decision maker to use a diversified group of consultants for a succession of decisions reaching a high level of consensus. [ABSTRACT FROM AUTHOR]

This paper deals with discrete copulas considered as a class of binary aggregation operators on a finite chain. A representation theorem by means of permutation matrices is given. From this characterization, we study the structure of associative discrete copulas and a theorem of decomposition of any discrete copula in terms of associative discrete copulas is obtained. Finally, some aspects concerning their extension to copulas are dealt with. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that aggregation operators cannot be associative and strictly compensatory at the same time. As a way out, the rotation construction and the rotation-annihilation construction are applied to construct wide classes of associative aggregation operators that are compensatory on a subdomain only. From this point of view, the resulting operators are similar to uninorms, a class of aggregation operators that is being reported on extensively in the literature. The constructions are demonstrated by means of ample examples. [ABSTRACT FROM AUTHOR]

We propose the concept of ordered weighted averaging (OWA) generation function with some properties, illustrative examples, and usages. A number of new properties of OWA operators and relations between some well-known OWA operators are proposed and proved using OWA Generation Functions. We discuss some orness/andness adjustment methods for a predetermined OWA operator. A practical application about investment prediction problem is given with detailed illustration and analysis, which can show the advantages of the adjustment methods proposed in this paper. In particular, the concept consistent adjustment matrix is proposed and the interests and advantages of it can be shown by its special properties. [ABSTRACT FROM PUBLISHER]

$p,q,r-$ spherical fuzzy ( $p,q,r-$ SF) sets are a significant advancement in fuzzy set (FS) theory, providing an effective way to describe hesitation inside a set. This development goes beyond membership degrees (MDs) by incorporating three parameters (p, q and r) that shape and define the spread of FS. The presence of these parameters makes $p,q,r-$ SF sets ideal for dealing with complicated decision-making (DM) scenarios in a wide range of applications. In this paper, we proposed a new reliable method for smart DM in logo design projects that uses $p,q,r-$ SF Einstein aggregation operators (AOs). First, we present the $p,q,r-$ SF Einstein operators, which are accomplished of capturing the relationship and interrelationship of numerous criteria while making decisions on logo design, including originality, relevance, beauty, and usability. Next, we use the proposed framework, a multi-criteria decision analysis tool, to rank the choices. We demonstrate the practical application and efficiency of our method in a scenario in which a team of three designers is entrusted with developing five different logo styles for diverse enterprises. Moreover, we compare proposed procedure with some existing methods, demonstrating its advantages in terms of precision and reliability.

This paper presents novel operational laws for $p,q,r-$ spherical fuzzy sets ( $p,q,r-$ SFSs) by harnessing the Dombi t-norm (DTN) and t-conorm (DTCN). These laws serve as the foundation for a set of aggregation operators (AOs) designed to consolidate $p,q,r-$ spherical fuzzy ( $p,q,r-$ SF) information. Additionally, a multi-criteria decision-making (MCDM) method is outlined for addressing practical decision-making (DM) challenges. To demonstrate the application of the proposed approach, a numerical example is offered. Furthermore, we conducted a comparative study to validate the efficacy of the suggested approach. Finally, we discuss both the advantages and limitations of this innovative approach.

Atanassov's intuitionistic fuzzy set (A-IFS) is a generalized form of Zadeh's fuzzy set, and the basic elements of an A-IFS are intuitionistic fuzzy numbers (IFNs). Recently, lots of aggregation techniques have been proposed for fusing IFNs. However, they only deal with a limited number of IFNs that take the form of discrete information. In this paper, we will first apply the definite integral to give the notion of definite integration for IFNs and investigate a lot of novel integral operators and, then, utilize these integral operators to get some new aggregation operators that can aggregate the IFNs spreading all over an area, which means that each point in a 2-D plane is an IFN that we want to aggregate. The new techniques can help us to deal with more complicated intuitionistic fuzzy information. [ABSTRACT FROM PUBLISHER]

A critical issue when selecting an ordered weighted aggregation (OWA) operator is the determination of the associated weights. For this reason, numerous weight generating methods have appeared in the literature. In this paper, a generalization of the binomial OWA operator on the basis of the Stancu polynomial is proposed and analyzed. We propose a weight function in the parametric form using the Stancu polynomial by which the weights of OWA operators can be generated easily. The proposed Stancu OWA operator provides infinitely many sets of weight vectors for a given level of the orness value. An important property of this kind of OWA operator is its orness, which remains constant, irrespective of the number of objectives aggregated and always equal to one of its parameters. This approach provides a significant advantage for generating the OWA operators’ weights over existing methods. One can choose a set of weight vectors based on his/her own preference. This class of OWA operators can utilize a prejudiced preference to determine the corresponding weight vector. The maximum entropy (Shannon) OWA operator's weights for a given level of orness is calculated by the purposed weight function and compared with the existing maximum entropy OWA operator. [ABSTRACT FROM AUTHOR]

With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural networks) calls for advanced techniques in exploring and interpreting model behaviors. Second, the rapid growth in computing has produced enormous datasets that require techniques that can handle millions or more samples. Although some solutions to these interpretability challenges have been proposed, they typically do not scale beyond thousands of samples, nor do they provide the high-level intuition scientists are looking for. Here, we present the first scalable solution to explore and analyze high-dimensional functions often encountered in the scientific data analysis pipeline. By combining a new streaming neighborhood graph construction, the corresponding topology computation, and a novel data aggregation scheme, namely topology aware datacubes, we enable interactive exploration of both the topological and the geometric aspect of high-dimensional data. Following two use cases from high-energy-density (HED) physics and computational biology, we demonstrate how these capabilities have led to crucial new insights in both applications. [ABSTRACT FROM AUTHOR]

This paper mainly investigates a particular type of multicriteria aggregation imperative called prioritized aggregations in order to handle a class of multicriteria decision making problems, in which there are prioritizations among criteria. In such problems, the satisfaction degrees of higher prioritized criteria cannot be compensated by the lower prioritized criteria. To describe the prioritizations among criteria quantitatively, Yager has introduced a prioritized measure from the viewpoint of fuzzy measure, which is validated as an effective method, except for some little imperfectness. On the basis of detailed analysis with respect to Yager's prioritized measure, we elaborate the properties of prioritized measures and then propose a generalized form of prioritized measure. Moreover, by using the generalized prioritized measure to convey the prioritized imperative, we develop a generalized prioritized measure-guided aggregation operator that is based on the Choquet integral. Additionally, the prioritized weight aggregation operator, introduced by Yager, is verified to be a special case of the generalized prioritized measure-guided aggregation operator. At length, we develop a concrete prioritized measure and the corresponding prioritized measure-guided aggregation operator under the framework of the generalized prioritized measure-guided aggregation operator and illustrate their feasibility and effectiveness through several numerical examples. [ABSTRACT FROM AUTHOR]

The ordered weighted averaging (OWA) operators are an extensively used class of aggregation operators. The weight vector that is associated with an OWA can determine the attitudinal characters of the aggregation. One of these characterizing measures is called the orness measure. The aim of this paper is to introduce orness measures in an axiomatic framework and to propose an alternate definition of orness that is based on these axioms. The proposed orness measure satisfies a more generalized set of axioms than Yager’s orness measure. We further calculate the maximum Shannon’s entropy of the OWA operator corresponding to a fixed value of orness of our proposed measure as well as of Yager’s orness. For a given level of orness, the maximum entropy corresponding to the proposed orness measure, is more than that of Yager’s. This suggests that the proposed measure is a more plausible one. [ABSTRACT FROM AUTHOR]

An intuitionistic multiplicative preference relation was recently introduced by Xia et al. to characterize the preference information that is given by a decision maker over a set of objects. All the elements of the intuitionistic multiplicative preference relation are the 2-tuples, which can simultaneously depict the degree that one object is prior to another, and the degree that the object is not prior to another. Each part of the 2-tuples takes its value from the closed interval [1/9, 9], and thus can describe the decision maker's preferences over objects more comprehensively than the traditional multiplicative preference relation. How to derive the priority weights of the objects from an intuitionistic multiplicative preference relation is an important research topic for decision making with intuitionistic multiplicative preference information. In this paper, we shall focus on solving this issue. We first define the concepts of expected intuitionistic multiplicative preference relation, left and right error matrices, etc. Then based on the geometric aggregation operator and the error propagation formula, we derive the priority weight intervals from an intuitionistic multiplicative preference relation. After that, some approaches to decision making based on intuitionistic multiplicative preference relations are developed, and furthermore, two practical examples are given to illustrate our approaches. [ABSTRACT FROM AUTHOR]