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This paper presents an improved arithmetic optimization algorithm that incorporates hybrid elite pool strategies to address the limitations of the arithmetic optimization algorithm (AOA). In AOA, the linear mathematical optimization acceleration (MOA) function cannot balance global exploitation and local exploration well. Therefore, the accuracy and convergence speed of the algorithm cannot be guaranteed. To improve the performance of AOA, this paper reconstructed a nonlinear MOA function, which is expected to balance the exploitation and the exploration of AOA. Furthermore, four hybrid elite pool strategies are integrated to enhance the ability to escape local optima. The proposed algorithm inherits the fast convergence of AOA and develops the performance of escaping local optima. Numerical experiment results on benchmark functions and engineering problems show that the proposed algorithm outperforms other compared meta-heuristic algorithms in terms of convergence speed and accuracy. [ABSTRACT FROM AUTHOR]

In recent years, the Internet of Things (IoT) has led to the spread of cloud computing devices in all commercial, industrial and agricultural sectors. The use of cloud computing environment services is increasing exponentially with all technology applications based on IoT. Fog computing has led to addressing issues in cloud computing environments. Fog computing reduces load balancing, processing, bandwidth, and storage as data file replication from the cloud to the network closest to sensors in different geographic locations. There are three critical issues:—what data should be replicated?—when should the data be replicated? and—where the new replicas should be placed? These three main open questions must be tackled for data replication in the cloud environments. This strategy, the identification and mode of the data replication problem are designed as a multi-objective optimization with modern meta-heuristic optimization method. Therefore, a new hybrid method using Arithmetic Optimization Algorithm (AOA) and the salp swarm algorithm (SSA) is proposed in this paper. Firstly, a new hybrid metaheuristic method, using the Arithmetic Optimization Algorithm (AOA) and the salp swarm algorithm (SSA), is proposed to handle the problem of selection and placement data replication in fog computing. Secondly, the Floyd algorithm is used to strategy the least cost path, distance, and data transmission in different geographic locations. The performance of the designed AOASSA strategy to tackling the data replication problem is evaluated using different datasets of different sizes. To validate the AOASSA strategy, a set of experiments was carried out to validate the proposed strategy AOASSA. Experiment results show the superiority of AOASSA over its competitors in terms of performance measures, such as least cost path, distance, and bandwidth. [ABSTRACT FROM AUTHOR]

A biomedical application of a novel metaheuristic optimizer is proposed in this paper by constructing an enhanced arithmetic optimization algorithm (AOA). The latter algorithm was constructed using the logarithmic spiral (Ls) search mechanism from the whale optimization algorithm and the greedy selection scheme from the differential evolution algorithm. The proposed algorithm (Ls-AOA) was tested against unimodal and multimodal benchmark functions and demonstrated better capability comparatively using other efficient metaheuristic algorithms reported in the literature. The constructed Ls-AOA algorithm was then proposed to design a proportional-integral-derivative (PID) controller employed in a functional electrical stimulation (FES) system for the first time. The initial statistical and convergence profile assessment showed better performance of the proposed algorithm. The comparative analyses for transient and frequency responses were performed for the PID-controlled FES system using the original AOA, sine–cosine and particle swarm optimization algorithms and the traditional Ziegler-Nichols tuning scheme. Similarly, the FES system tuned with the latter methods was also assessed for disturbance rejection and noise elimination. All the comparative analyses demonstrated that the proposed Ls-AOA has the greater capability for the challenging biomedical FES system. [ABSTRACT FROM AUTHOR]

In evidence theory, conflicting evidence and fuzzy evidence have a significant impact on the results of evidence combination. Nevertheless, the existing weight assignment methods can hardly reflect the significant influence of fuzzy evidence on the combination results. In this paper, we address this issue by proposing a new method for assigning evidence weights and the corresponding combination rule. The proposed weight assignment method strengthens the consideration of fuzzy evidence. We further incorporate the Wasserstein distance to compute the clarity degree of the evidence. This is an important reference index for the weight assignment in the proposed combination rule and effectively reduces the impact of ambiguous evidence. Using experiments, we illustrate the significant impact of fuzzy evidence on the results of combination. This justifies its integration in the weight assignment process. The proposed combination rule with the new weight assignment method is also examined on a set of numerical arithmetic and Iris datasets. Our results confirm that compared with the four existing methods, the proposed method improves decision accuracy, F1 score, computational convergence and achieves more reliable fusion results. [ABSTRACT FROM AUTHOR]

Several population-based techniques have subsequently been proposed. Despite their broad use in a variety of applications, we are still investigating the use of proposed methods to tackle real-world challenges. As a result, researchers must considerably modify and enhance their approaches based on the primary evolutionary processes in order to achieve rapid convergence, consistent equilibrium with high-quality data, and optimization. The paper proposes a fusion method (AOA–GOA) meta-heuristic optimization methods for global optimization tasks. They can be applied to different problems, including image processing, machine learning, wireless networks, power systems, engineering design, etc. The method fusion proposed is analyzed in context with GOA and AOA. To evaluate the performance, each method is tested on the same parameters like population size and number of iteration. The proposed IAOA is evaluated by varying the dimensions. The impact of varying dimensions is a standard test used in previous studies for optimizing test functions that show the effect of varying dimensions on efficiency of IAOA. From this, it is noted that it works efficiently for both high and low dimensional problems. In high dimensional problem, the proposed method gives efficient search results. [ABSTRACT FROM AUTHOR]

Many population-dependent solutions have recently been suggested. Despite their widespread adoption in many applications, we are still researching using suggested methods to solve real-world problems. As a result, researchers must significantly adjust and refine their procedures based on the main evolutionary processes to ensure faster convergence, consistent equilibrium with high-quality results, and optimization. Thus, a new hybrid method using Aquila optimizer (AO) and arithmetic optimization algorithm (AOA) is proposed in this paper. AO and AOA are both modern meta-heuristic optimization methods. They can be applied to different problems, including image processing, machine learning, wireless networks, power systems, engineering design etc. The proposed approach is examined concerning AO and AOA. To determine results, each procedure is evaluated using the same parameters, such as population size and several iterations. By changing the dimensions, the proposed approach (AO–AOA) is evaluated. The impact of varying dimensions is a standard test that has been used in previous studies to optimize test functions that demonstrate the influence of varying dimensions on the efficiency of AO–AOA. It is clear from this that it fits well with both high- and low-dimensional problems. Population-based methods achieve efficient search results in high-dimensional problems. [ABSTRACT FROM AUTHOR]

Numerical computing is a key part of the traditional computer architecture. Almost all traditional computers implement the IEEE 754-1985 binary floating point standard to represent and work with numbers. The architectural limitations of traditional computers make impossible to work with infinite and infinitesimal quantities numerically. This paper is dedicated to the Infinity Computer, a new kind of a supercomputer that allows one to perform numerical computations with finite, infinite, and infinitesimal numbers. The already available software simulator of the Infinity Computer is used in different research domains for solving important real-world problems, where precision represents a key aspect. However, the software simulator is not suitable for solving problems in control theory and dynamics, where visual programming tools like Simulink are used frequently. In this context, the paper presents an innovative solution that allows one to use the Infinity Computer arithmetic within the Simulink environment. It is shown that the proposed solution is user-friendly, general purpose, and domain independent. [ABSTRACT FROM AUTHOR]

Negation operation is important in intelligent information processing. Different existing arithmetic negation, an exponential negation is presented in this paper. The new negation can be seen as a kind of geometry negation. Some basic properties of the proposed negation are investigated, and we find that the fix point is the uniform probability distribution, which reaches the maximum entropy. The proposed exponential negation is an entropy increase operation, and all the probability distributions will converge to the uniform distribution after multiple negation iterations. The convergence speed of the proposed negation is also faster than the existed negation. The number of iterations of convergence is inversely proportional to the number of elements in the distribution. Some numerical examples are used to illustrate the efficiency of the proposed negation. [ABSTRACT FROM AUTHOR]

In this paper, we define some Einstein operations on TrCHFS and develop three arithmetic averaging operators, that is TrCHFEWA operator, TrCHFEOWA operator, and TrCHFEHWA operator, for aggregating trapezoidal cubic fuzzy information. The TrCHFEHWA operator generalizes both the TrCHFEWA and TrCHFEOWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the exiting aggregation operators. We apply on the TrCHFEHWA operator to multiple attribute decision making with trapezoidal cubic hesitant fuzzy information. Further, a numerical example is provided to illustrate the flexibility and accuracy of the proposed operators. Last, the proposed methods are compared with the existing methods to examine the best developing skill initiatives. [ABSTRACT FROM AUTHOR]

The paper addresses the problem of constructing lower and upper estimators for univariate functions. This problem is of crucial importance in global optimization, where such bounds are used to reduce the search area. We propose to use piecewise linear estimators for bounding univariate functions and show how such estimators can be derived from the function's algebraic expression. The basic properties of such estimators are formulated and proved. We implemented the algorithms for the automated construction of lower and upper piecewise linear estimators and experimentally compared the proposed approach with the first-order interval bounds, Pijavskij method, and slope arithmetic. Numerical examples demonstrate that the piecewise linear estimators are more accurate with respect to the mentioned approaches. We also show that global optimization algorithms can significantly benefit from using piecewise linear estimators. Another advantage of the proposed approach is that the objective function does not have to be differentiable. This feature can favorably distinguish this method from other methods where the first and second derivatives are used. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some aspects of Spencer–Brown's Calculus of Indications. Drawing from earlier work by Kauffman and Varela, we present a new categorical framework that allows to characterize the construction of infinite arithmetic expressions as sequences taking values in grossone. [ABSTRACT FROM AUTHOR]

In this paper, by using the CESTAC method and the CADNA library a procedure is proposed to solve a fuzzy initial value problem based on RBF-meshless methods under generalized H-differentiability. So a reliable approach is presented to determine optimal shape parameter and number of points for RBF-meshless methods. The results reveal that the proposed method is very effective and simple. Also, the numerical accuracy of the method is shown in the tables and figures, and algorithms are given based on the stochastic arithmetic. The examples illustrate the efficiency and importance of using the stochastic arithmetic in place of the floating-point arithmetic. [ABSTRACT FROM AUTHOR]

q-Rung orthopair fuzzy sets, originally proposed by Yager, can dynamically adjust the range of indication of decision information by changing a parameter q based on the different hesitation degree, and point operator is a useful aggregation technology that can control the uncertainty of valuating data from some experts and thus get intensive information in the process of decision making. However, the existing point operators are not available for decision-making problems under q-Rung orthopair fuzzy environment. Thus, in this paper, we firstly propose some new point operators to make it conform to q-rung orthopair fuzzy numbers (q-ROFNs). Then, associated with classic arithmetic and geometric operators, we propose a new class of point weighted aggregation operators to aggregate q-rung orthopair fuzzy information. These proposed operators can redistribute the membership and non-membership in q-ROFNs according to different principle. Furthermore, based on these operators, a novel approach to multi-attribute decision making (MADM) in q-rung orthopair fuzzy context is introduced. Finally, we give a practical example to illustrate the applicability of the new approach. The experimental results show that the novel MADM method outperforms the existing MADM methods for dealing with MADM problems. [ABSTRACT FROM AUTHOR]

The transformations between multiplicatively and additively reciprocal fuzzy pairwise comparison matrices are dealt with, and formulas for obtaining multiplicative fuzzy priorities from additively reciprocal fuzzy pairwise comparison matrices are proposed in this paper. The formulas are based on the concept of constrained fuzzy arithmetic and preserve the additive reciprocity of pairwise comparisons. Further, the consistency issue is approached in the paper; the consistency check is employed directly in the formulas for obtaining multiplicative fuzzy priorities of objects both from multiplicatively and additively reciprocal fuzzy pairwise comparison matrices. Two definitions of consistency based on transitivity are employed in this paper-the traditional additive/multiplicative transitivity and the weak consistency. However, also several other transitivity conditions are discussed in this context. Finally, the proposed formulas for obtaining multiplicative fuzzy priorities from an additively reciprocal fuzzy pairwise comparison matrix and the formulas with employed consistency check are applied in an illustrative example. Triangular fuzzy numbers are used for the fuzzy extension in this paper. However, all the formulas can be modified easily to be applied on intervals, trapezoidal fuzzy numbers or any other fuzzy numbers given by $$\alpha $$ -cuts. [ABSTRACT FROM AUTHOR]

In this paper we study the theory Q. We prove a basic result that says that, in a sense explained in the paper, Q can be split into two parts. We prove some consequences of this result. (i) Q is not a poly-pair theory. This means that, in a strong sense, pairing cannot be defined in Q. (ii) Q does not have the Pudlák Property. This means that there two interpretations of $$\mathsf{S}^1_2$$ in Q which do not have a definably isomorphic cut. (iii) Q is not sententially equivalent with $$\mathsf{PA}^-$$ . This tells us that we cannot do much better than mutual faithful interpretability as a measure of sameness of Q and $$\mathsf{PA}^-$$ . We briefly consider the idea of characterizing Q as the minimal-in-some-sense theory of some kind modulo some equivalence relation. We show that at least one possible road towards this aim is closed. [ABSTRACT FROM AUTHOR]

By simply describing a classic weakly hard real-time system's performance with the number of tasks meeting or missing deadlines, the system's real-time characteristics cannot be expressed accurately and its reliability cannot be established. The path real-time logic (RTL) is used to determine the reliability of real-time systems; though desirable, it cannot be used as a tool to configure an optimized real-time system. This paper introduces the notion of optimizing path RTL, where integer constants of arithmetic inequality in path RTL are replaced by integer constants or integer variables. With further modifications, optimizing path RTL can not only determine the reliability of a real-time system, but also be used to optimize the system. Furthermore, a unified framework for hard, soft and weakly hard real-time system is established based on optimizing path RTL. The process of transforming a weakly hard real-time system into this unified framework is demonstrated. Moreover, this work proposes and proves a theorem that if the directed ring of a constraint graph contains all elements of behaviour specification (SP) and only SP, then its value must not be greater than zero. This theorem can be used to quickly determine the reliability and safety of a real-time system. A case study is presented to show the validity and reliability of optimizing path RTL and the unified real-time system. [ABSTRACT FROM AUTHOR]

Fuzzy sets are a good model of the flexible definitions used in human language, but do not always give results in accordance with human reasoning. One reason is that operations on fuzzy sets do not obey all identities from crisp set algebra, such as the law of the excluded middle. Additionally, when used to represent fuzzy numbers they lead to a generalised interval arithmetic rather than a fuzzy version of standard arithmetic. In this paper, we outline the $$X\hbox {-}\mu $$ approach, a new method of representing, visualizing and calculating functions of fuzzy values. This fuzzy representation retains standard Boolean operations and leads to standard arithmetic when applied to numerical quantities. It includes the idea of strict fuzzy values, which do not incorporate set or interval-based uncertainty. Using simple examples, we illustrate the $$X\hbox {-}\mu $$ approach and outline the notion of a strict fuzzy value. [ABSTRACT FROM AUTHOR]

In this paper we define the Boolean lifting property (BLP) for residuated lattices to be the property that all Boolean elements can be lifted modulo every filter, and study residuated lattices with BLP. Boolean algebras, chains, local and hyperarchimedean residuated lattices have BLP. BLP behaves interestingly in direct products and involutive residuated lattices, and it is closely related to arithmetic properties involving Boolean elements, nilpotent elements and elements of the radical. When BLP is present, strong representation theorems for semilocal and maximal residuated lattices hold. [ABSTRACT FROM AUTHOR]