Showing papers on "Operator (computer programming) published in 2021"

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Abstract: It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. Here, we thus extend this theorem to DNNs. We design a new network with small generalization error, the deep operator network (DeepONet), which consists of a DNN for encoding the discrete input function space (branch net) and another DNN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization error for 16 different diverse applications. Neural networks are known as universal approximators of continuous functions, but they can also approximate any mathematical operator (mapping a function to another function), which is an important capability for complex systems such as robotics control. A new deep neural network called DeepONet can lean various mathematical operators with small generalization error.

Complete set of dimension-eight operators in the standard model effective field theory

Abstract: We present a complete list of the dimension-eight operator basis in the standard model effective field theory using group theoretic techniques in a systematic and automated way. We adopt a new form of operators in terms of the irreducible representations of the Lorentz group and identify the Lorentz structures as states in a $SU(N)$ group. In this way, redundancy from equations of motion is absent and that from integration by part is treated using the fact that the independent Lorentz basis forms an invariant subspace of the $SU(N)$ group. We also decompose operators into the ones with definite permutation symmetries among flavor indices to deal with subtlety from repeated fields. For the first time to our knowledge, we provide the explicit form of independent flavor-specified operators in a systematic way. Our algorithm can easily be applied to higher-dimensional standard model effective field theory and other effective field theories, making these studies more approachable.

Celestial Operator Products of Gluons and Gravitons

Abstract: The operator product expansion (OPE) on the celestial sphere of conformal primary gluons and gravitons is studied. Asymptotic symmetries imply recursion relations between products of operators whos...

Top, Higgs, diboson and electroweak fit to the Standard Model effective field theory

Abstract: The search for effective field theory deformations of the Standard Model (SM) is a major goal of particle physics that can benefit from a global approach in the framework of the Standard Model Effective Field Theory (SMEFT). For the first time, we include LHC data on top production and differential distributions together with Higgs production and decay rates and Simplified Template Cross-Section (STXS) measurements in a global fit, as well as precision electroweak and diboson measurements from LEP and the LHC, in a global analysis with SMEFT operators of dimension 6 included linearly. We present the constraints on the coefficients of these operators, both individually and when marginalised, in flavour-universal and top-specific scenarios, studying the interplay of these datasets and the correlations they induce in the SMEFT. We then explore the constraints that our linear SMEFT analysis imposes on specific ultra-violet completions of the Standard Model, including those with single additional fields and low-mass stop squarks. We also present a model-independent search for deformations of the SM that contribute to between two and five SMEFT operator coefficients. In no case do we find any significant evidence for physics beyond the SM. Our underlying Fitmaker public code provides a framework for future generalisations of our analysis, including a quadratic treatment of dimension-6 operators.

CaFtR: A Fuzzy Complex Event Processing Method

Abstract: Fuzzy complex event processing-based decision-making systems have received considerable research interests recently. In particular, a well-managed operator distribution is required for improving the performance of the fuzzy complex event processing-based decision-making systems. However, the intrinsic uncertainty in dynamic input events increases the difficulties of operator distribution problem. To address these issues, a cost-aware, fault-tolerant and reliable strategy, called CaFtR is proposed for operator scheduling on fuzzy complex event processing systems based on the Technique for Order Preferences by Similarity to an Ideal Solution. The proposed CaFtR method adequately makes use of network resources to achieve continuous and highly available complex event processing regardless of dynamic operator migrations under fuzzy environment. Finally, a case study is provided to illustrate the efficiency of the proposed method, and the utility of our work is demonstrated through an application on the StreamBase system.

Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19 in Nigeria Using Atangana-Baleanu Operator

Abstract: We propose a mathematical model of the coronavirus disease 2019 (COVID-19) to investigate the transmission and control mechanism of the disease in the community of Nigeria Using stability theory of differential equations, the qualitative behavior of model is studied The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease Further, we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established We consider the data of reported infection cases from April 1, 2020, till April 30, 2020, and parameterized the model We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations The impacts of various biological parameters on transmission dynamics of COVID-19 is examined These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease In the end, the obtained results are demonstrated graphically to justify our theoretical findings

Automated one-loop computations in the standard model effective field theory

Abstract: We present the automation of one-loop computations in the standard-model effective field theory at dimension 6. Our general implementation, dubbed smeft@nlo, covers all types of operators: bosonic and two- and four-fermion ones. Included ultraviolet and rational counterterms presently allow for fully differential predictions, possibly matched to the parton shower, up to the one-loop level in the strong coupling or in four-quark operator coefficients. Exact flavor symmetries are imposed among light quark generations, and an initial focus is set on top-quark interactions in the fermionic sector. We illustrate the potential of this implementation with novel loop-induced and next-to-leading-order computations relevant for top-quark, electroweak, and Higgs-boson phenomenology at the LHC and future colliders.

Adaptive crossover operator based multi-objective binary genetic algorithm for feature selection in classification

Abstract: Feature selection is a key pre-processing technique for classification which aims at removing irrelevant or redundant features from a given dataset. Generally speaking, feature selection can be considered as a multi-objective optimization problem, i.e, removing number of features and improving the classification accuracy. Genetic algorithms (GAs) have been widely used for feature selection problems. The crossover operator, as an important technique to search for new solutions in GAs, has a strong impact on the final optimization results. However, many crossover operators are problem-dependent and have different search abilities. Thus, it is a challenge to select the most efficient one to solve different feature selection problems, especially when the nature of feature selection problems is unknown in advance. In order to overcome this challenge, in this paper, a multi-objective binary genetic algorithm integrating an adaptive operator selection mechanism (MOBGA-AOS) is proposed. In MOBGA-AOS, five crossover operators with different search characteristics are used. Each of them is assigned a probability based on the performance in the evolution process. In different phases of evolution, the proper crossover operator is selected by roulette wheel selection according to the probabilities to produce new solutions for the next generation. The proposed algorithm is compared with five well-known evolutionary multi-objective algorithms on ten datasets. The experimental results reveal that MOBGA-AOS is capable of removing a large amount of features while ensuring a small classification error. Moreover, it obtains prominent advantages on large-scale datasets, which demonstrates that MOBGA-AOS is competent to solve high-dimensional feature selection problems.

Efficient quantum measurement of Pauli operators in the presence of finite sampling error

Abstract: Estimating the expectation value of an operator corresponding to an observable is a fundamental task in quantum computation. It is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed computational basis. One common solution splits the operator into a weighted sum of Pauli operators and measures each separately, at the cost of many measurements. An improved version collects mutually commuting Pauli operators together before measuring all operators within a collection simultaneously. The effectiveness of doing this depends on two factors. Firstly, we must understand the improvement offered by a given arrangement of Paulis in collections. In our work, we propose two natural metrics for quantifying this, operating under the assumption that measurements are distributed optimally among collections so as to minimise the overall finite sampling error. Motivated by the mathematical form of these metrics, we introduce SORTED INSERTION, a collecting strategy that exploits the weighting of each Pauli operator in the overall sum. Secondly, to measure all Pauli operators within a collection simultaneously, a circuit is required to rotate them to the computational basis. In our work, we present two efficient circuit constructions that suitably rotate any collection of $k$ independent commuting $n$-qubit Pauli operators using at most $kn-k(k+1)/2$ and $O(kn/\log k)$ two-qubit gates respectively. Our methods are numerically illustrated in the context of the Variational Quantum Eigensolver, where the operators in question are molecular Hamiltonians. As measured by our metrics, SORTED INSERTION outperforms four conventional greedy colouring algorithms that seek the minimum number of collections.

Learning the solution operator of parametric partial differential equations with physics-informed DeepONets.

Abstract: Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial or boundary conditions, different inputs, etc. In this work, we introduce physics-informed DeepONets, a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.

Picture fuzzy interactional partitioned Heronian mean aggregation operators: an application to MADM process

Abstract: The picture fuzzy sets (PFSs) state or model the voting information accurately without information loss. However, their existing operational laws usually generate unreasonable computing results, especially when the agreement degree (AD) or neutrality degree (ND) or opposition degree (OD) is zero. To tackle this issue, we propose the interactional operational laws (IOLs) to compute picture fuzzy numbers (PFNs), which can capture the interaction between the ADs and NDs in two PFNs, as well as the interaction between the ADs and ODs in two PFNs. Based on the proposed novel IOLs, partitioned Heronian mean (PHM) operator, and partitioned geometric Heronian mean (PGHM) operator, some picture fuzzy interactional PHM (PFIPHM), weighted PFIPHM (PFIWPHM), geometric PFIPHM (PFIPGHM), and weighted PFIPGHM (PFIWPGHM) operators are proposed in this paper. Afterwards, we investigate the properties of these operators. Using the PFIWPHM and PFIWPGHM operators, a novel multiple attribute decision-making (MADM) method with PFNs is elaborated. Finally, a study example that involves the service quality ranking of nursing facilities is provided to show the decision procedure of the proposed MADM method and we also give the comparative analysis between the proposed operators and the existing aggregation operators developed for PFNs.

Picture Fuzzy Maclaurin Symmetric Mean Operators and Their Applications in Solving Multiattribute Decision-Making Problems

Abstract: To evaluate objects under uncertainty, many fuzzy frameworks have been designed and investigated so far. Among them, the frame of picture fuzzy set (PFS) is of considerable significance which can describe the four possible aspects of expert’s opinion using a degree of membership (DM), degree of nonmembership (DNM), degree of abstinence (DA), and degree of refusal (DR) in a certain range. Aggregation of information is always challenging especially when the input arguments are interrelated. To deal with such cases, the goal of this study is to develop the notion of the Maclaurin symmetric mean (MSM) operator as it aggregates information under uncertain environments and considers the relationship of the input arguments, which make it unique. In this paper, we studied the theory of MSM operators in the layout of PFSs and discussed their applications in the selection of the most suitable enterprise resource management (ERP) scheme for engineering purposes. We developed picture fuzzy MSM (PFMSM) operators and investigated their validity. We developed the multiattribute decision-making (MADM) algorithm based on the PFMSM operators to examine the performance of the ERP systems using picture fuzzy information. A numerical example to evaluate the performance of ERP systems is studied, and the effects of the associated parameters are discussed. The proposed aggregated results using PFMSM operators are found to be reliable as it takes into account the interrelationship of the input information, unlike traditional aggregation operators. A comparative study of the proposed PFMSM operators is also studied.

Semilinear elliptic equations involving mixed local and nonlocal operators

Abstract: In this paper, we consider an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type. Though the methods that we develop are quite general, for concreteness we focus on the case in which the operator takes the form − Δ + ( − Δ)s, with s ∈ (0, 1). We focus here on symmetry properties of the solutions and we prove a radial symmetry result, based on the moving plane method, and a one-dimensional symmetry result, related to a classical conjecture by G.W. Gibbons.

Complete set of dimension-nine operators in the standard model effective field theory

Abstract: We present a complete and independent list of the dimension-nine operator basis in the Standard Model effective field theory by an automatic algorithm based on the amplitude-operator correspondence. A complete basis ($Y$-basis) is first constructed by enumerating the Young tableau of an auxiliary $SU(N)$ group and the gauge groups, with the equation-of-motion and integration-by-part redundancies all removed. In the presence of repeated fields, another basis ($P$-basis) with explicit flavor symmetries among them is derived from the $Y$-basis, which further induces a basis of independent monomial operators through a systematic process called desymmetrization. Our form of operators has advantages over the traditional way of presenting operators constrained by flavor relations, in the simplicity of both eliminating flavor redundancies and identifying independent flavor-specified operators. We list the 90456 (560) operators for three (one) generations of fermions, all of which violate baryon number or lepton number conservation; among them we find new violation patterns as $\mathrm{\ensuremath{\Delta}}B=2$ and $\mathrm{\ensuremath{\Delta}}L=3$, which only appear at the dimensions $d\ensuremath{\ge}9$.

A hybrid decision-making model under q-rung orthopair fuzzy Yager aggregation operators

Abstract: Aggregation operators perform a significant role in many decision-making problems. The purpose of this paper is to analyze the aggregation operators under the q-rung orthopair fuzzy environment with Yager norm operations. The q-rung orthopair fuzzy set is an extension of intuitionistic fuzzy set and Pythagorean fuzzy set in which sum of qth power of membership and non-membership degrees is bounded by 1. By applying the Yager norm operations to q-rung orthopair fuzzy set, we developed six families of aggregation operators, namely q-rung orthopair fuzzy Yager weighted arithmetic operator, q-rung orthopair fuzzy Yager ordered weighted arithmetic operator, q-rung orthopair fuzzy Yager hybrid weighted arithmetic operator, q-rung orthopair fuzzy Yager weighted geometric operator, q-rung orthopair fuzzy Yager ordered weighted geometric operator and q-rung orthopair fuzzy Yager hybrid weighted geometric operator. To prove the validity and feasibility of proposed work, we discuss two multi-attribute decision-making problems. Moreover, we investigate the influence of some values of parameter on decision-making results. Finally, we give a comparison with existing operators.

Data-driven reduced-order models via regularised Operator Inference for a single-injector combustion process

Abstract: This paper derives predictive reduced-order models for rocket engine combustion dynamics via Operator Inference, a scientific machine learning approach that blends data-driven learning with physics...

T-spherical fuzzy power aggregation operators and their applications in multi-attribute decision making

Abstract: The paper aims to present the concept of power aggregation operators for the T-spherical fuzzy sets (T-SFSs). T-SFS is a powerful concept, with four membership functions denoting membership, abstinence, non-membership and refusal degree, to deal with the uncertain information as compared to other existing fuzzy sets. On the other hand, the relationship between the different pairs of the attributes are well recorded in terms of power operators. Thus, keeping these advantages of T-SFSs and power operator, the objective of this work is to define several weighted averaging and geometric power aggregation operators. The stated operators named as T-spherical fuzzy weighted, ordered weighted, hybrid averaging and geometric operators for the collection of the T-SFSs. The various properties and the special cases of them are also derived. Further, the consequences of proposed new power aggregation operators are studied in view of some constraints. Finally, a multiple attribute decision making algorithm, based on the proposed operators, is established to solve the problems with uncertain information and illustrate with numerical examples. A comparative study, superiority analysis and discussion of the proposed approach are furnished to confirm the approach.

Group decision-making framework under linguistic q-rung orthopair fuzzy Einstein models

Abstract: The q-rung orthopair fuzzy sets dynamically change the range of indication of decision knowledge by adjusting a parameter q from decision makers, where $$q \ge 1$$ , and outperform the conventional intuitionistic fuzzy sets and Pythagorean fuzzy sets. Linguistic q-rung orthopair fuzzy sets (Lq-ROFSs), a qualitative type of q-rung orthopair fuzzy sets, are characterized by a degree of linguistic membership and a degree of linguistic non-membership to reflect the qualitative preferred and non-preferred judgments of decision makers. Einstein operator is a powerful alternative to the algebraic operators and has flexible nature with its operational laws and fuzzy graphs perform well when expressing correlations between attributes via edges between vertices in fuzzy information systems, which makes it possible for addressing correlational multi-attribute decision-making (MADM) problems. Inspired by the idea of Lq-ROFS and taking the advantage of the flexible nature of Einstein operator, in this paper, we aim to introduce a new class of fuzzy graphs, namely, linguistic q-rung orthopair fuzzy graphs (Lq-ROFGs) and further explore efficient approaches to complicated MAGDM situations. Following the above motivation, we propose the new concepts, including product-connectivity energy, generalized product-connectivity energy, Laplacian energy and signless Laplacian energy and discuss several of its desirable properties in the background of Lq-ROFGs based on Einstein operator. Moreover, product-connectivity energy, generalized product-connectivity energy, Laplacian energy and signless Laplacian energy of linguistic q-rung orthopair fuzzy digraphs (Lq-ROFDGs) are presented. In addition, we present a graph-based MAGDM approach with linguistic q-rung orthopair fuzzy information based on Einstein operator. Finally, an illustrative example related to the selection of mobile payment platform is given to show the validity of the proposed decision-making method. For the sake of the novelty of the proposed approach, comparison analysis is conducted and superiorities in contrast with other methodologies are illustrated.

Complexity growth of operators in the SYK model and in JT gravity

Abstract: The concepts of operator size and computational complexity play important roles in the study of quantum chaos and holographic duality because they help characterize the structure of time-evolving Heisenberg operators. It is particularly important to understand how these microscopically defined measures of complexity are related to notions of complexity defined in terms of a dual holographic geometry, such as complexity-volume (CV) duality. Here we study partially entangled thermal states in the Sachdev-Ye-Kitaev (SYK) model and their dual description in terms of operators inserted in the interior of a black hole in Jackiw-Teitelboim (JT) gravity. We compare a microscopic definition of complexity in the SYK model known as K-complexity to calculations using CV duality in JT gravity and find that both quantities show an exponential-to-linear growth behavior. We also calculate the growth of operator size under time evolution and find connections between size and complexity. While the notion of operator size saturates at the scrambling time, our study suggests that complexity, which is well defined in both quantum systems and gravity theories, can serve as a useful measure of operator evolution at both early and late times.

Probing new physics in dimension-8 neutral gauge couplings at e+e− colliders

Abstract: Neutral triple gauge couplings (nTGCs) are absent in the standard model effective theory up to dimension-6 operators, but could arise from dimension-8 effective operators. In this work, we study the pure gauge operators of dimension-8 that contribute to nTGCs and are independent of the dimension-8 operator involving the Higgs doublet. We show that the pure gauge operators generate both ZγZ* and Zγγ* vertices with rapid energy dependence ∝ E5, which can be probed sensitively via the reaction e+e− → Zγ. We demonstrate that measuring the nTGCs via the reaction e+e− → Zγ followed by $$Z\rightarrow q\bar{q}$$ decays can probe the new physics scales of dimension-8 pure gauge operators up to the range (1-5) TeV at the CEPC, FCC-ee and ILC colliders with $$\sqrt{s}=(0.25-1)$$ TeV, and up to the range (10–16) TeV at CLIC with $$\sqrt{s}=(3-5)$$ TeV, assuming in each case an integrated luminosity of 5 ab−1. We compare these sensitivities with the corresponding probes of the dimension-8 nTGC operators involving Higgs doublets and the dimension-8 fermionic contact operators that contribute to the e+e−Zγ vertex.

New exponential operation laws and operators for interval-valued q-rung orthopair fuzzy sets in group decision making process

Abstract: The paper aims to introduce the novel concept of q-connection number (q-CN) for interval-valued q-rung orthopair fuzzy set (IVq-ROFSs) and thus to develop a method for solving the multiple-attribute group decision making (MAGDM) problem. The IVq-ROFS is a tool to represent the uncertain information with an integer parameter $$q\ge 1$$ , while the connection number (CN) processes the uncertainties and certainties into a single system with three degrees, namely “identity”, “contrary” and “discrepancy”. Driven by these required properties, this paper introduces a q-CN for IVq-ROFSs to represent the information in a more concise way. To this end, we divide the paper into three aspects. First, we define q-CN and a scoring function to evaluate the numbers. Second, we give some new q-exponential operation laws (q-EOLs) and operators over q-CNs in which bases are real numbers and exponents are q-CNs. Moreover, we define an operator based on these laws and derive their properties. Third, a novel MAGDM method for solving decision problems with IVq-ROFS information is illustrated with several examples. The advantages and superiority analysis of the proposed framework are also given to assert the results.

Linear Dynamical Systems on Hilbert Spaces: Typical Properties and Explicit Examples

Abstract: We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples In particular, we prove the following results (i) A typical hypercyclic operator is not topologically mixing, has no eigenvalues and admits no non-trivial invariant measure, but is densely distributionally chaotic (ii) A typical {upper-triangular} operator with coefficients of modulus $1$ on the diagonal is ergodic in the Gaussian sense, whereas a typical operator of the form ``diagonal with coefficients of modulus $1$ on the diagonal plus backward unilateral weighted shift" is ergodic but has only countably many unimodular eigenvalues; in particular, it is ergodic but {not} ergodic in the Gaussian sense (iii) There exist Hilbert space operators which are chaotic and $\mathcal U$-frequently hypercyclic but not frequently hypercyclic, Hilbert space operators which are {chaotic and} frequently hypercyclic but not ergodic, and Hilbert space operators which are chaotic and topologically mixing but not $\mathcal U$-frequently hypercyclic We complement our results by investigating the descriptive complexity of some natural classes of operators defined by dynamical properties

Learn To Match: Automatic Matching Network Design for Visual Tracking

Abstract: Siamese tracking has achieved groundbreaking performance in recent years, where the essence is the efficient matching operator cross-correlation and its variants. Besides the remarkable success, it is important to note that the heuristic matching network design relies heavily on expert experience. Moreover, we experimentally find that one sole matching operator is difficult to guarantee stable tracking in all challenging environments. Thus, in this work, we introduce six novel matching operators from the perspective of feature fusion instead of explicit similarity learning, namely Concatenation, Pointwise-Addition, Pairwise-Relation, FiLM, Simple-Transformer and Transductive-Guidance, to explore more feasibility on matching operator selection. The analyses reveal these operators' selective adaptability on different environment degradation types, which inspires us to combine them to explore complementary features. To this end, we propose binary channel manipulation (BCM) to search for the optimal combination of these operators. BCM determines to retrain or discard one operator by learning its contribution to other tracking steps. By inserting the learned matching networks to a strong baseline tracker Ocean, our model achieves favorable gains by $67.2 \rightarrow 71.4$, $52.6 \rightarrow 58.3$, $70.3 \rightarrow 76.0$ success on OTB100, LaSOT, and TrackingNet, respectively. Notably, Our tracker, dubbed AutoMatch, uses less than half of training data/time than the baseline tracker, and runs at 50 FPS using PyTorch. Code and model will be released at this https URL.

Two Weight Commutators on Spaces of Homogeneous Type and Applications

Abstract: In this paper, we establish the two weight commutator theorem of Calderon–Zygmund operators in the sense of Coifman–Weiss on spaces of homogeneous type, by studying the weighted Hardy and BMO space for $$A_2$$ weights and by proving the sparse operator domination of commutators. The main tool here is the Haar basis, the adjacent dyadic systems on spaces of homogeneous type, and the construction of a suitable version of a sparse operator on spaces of homogeneous type. As applications, we provide a two weight commutator theorem (including the high order commutators) for the following Calderon–Zygmund operators: Cauchy integral operator on $${\mathbb {R}}$$ , Cauchy–Szego projection operator on Heisenberg groups, Szego projection operators on a family of unbounded weakly pseudoconvex domains, the Riesz transform associated with the sub-Laplacian on stratified Lie groups, as well as the Bessel Riesz transforms (in one and several dimensions).

Complex Pythagorean Dombi fuzzy operators using aggregation operators and their decision-making

Abstract: A complex Pythagorean fuzzy set, an extension of Pythagorean fuzzy set, is a powerful tool to handle two dimension phenomenon. Dombi operators with operational parameters have outstanding flexibility. This article presents certain aggregation operators under complex Pythagorean fuzzy environment, including complex Pythagorean Dombi fuzzy weighted arithmetic averaging (CPDFWAA) operator, complex Pythagorean Dombi fuzzy weighted geometric averaging (CPDFWGA) operator, complex Pythagorean Dombi fuzzy ordered weighted arithmetic averaging (CPDFOWAA) operator and complex Pythagorean Dombi fuzzy ordered weighted geometric averaging (CPDFOWGA) operator. Moreover, this paper explores some fundamental properties of these operators with appropriate elaboration. A decision‐making numerical example related to the selection of bank to purchase loan is given to demonstrate the significance of our proposed approach. Finally, a comparative analysis with existing operators is given to demonstrate the peculiarity of our proposed operators.

EDA S Method for Multi-Criteria Group Decision Making Based on Intuitionistic Fuzzy Rough Aggregation Operators

Abstract: The primitive notions of rough sets and intuitionistic fuzzy set (IFS) are general mathematical tools having the ability to handle the uncertain and imprecise knowledge easily. EDA $\mathcal {S}$ (Evaluation based on distance from average solution) method has a significant role in decision making problems, especially when more conflicting criteria exist in multicriteria group decision making (MCGDM) problems. The aim of this manuscript is to present intuitionistic fuzzy rough- EDA $\mathcal {S}$ (IFR- EDA $\mathcal {S}$ ) method based on IF rough averaging and geometric aggregation operators. In addition, we put forward the concept of IF rough weighted averaging (IFRWA), IF rough ordered weighted averaging (IFROWA) and IF rough hybrid averaging (IFRHA) aggregation operators. Furthermore, the concepts of IF rough weighted geometric (IFRWG), IF rough ordered weighted geometric (IFROWG) and IF rough hybrid geometric (IFRHG) aggregation operators are investigated. The basic desirable characteristics of the investigated operator are given in detail. A new score and accuracy functions are defined for the proposed operators. Next, IFR-EDA $\mathcal {S}$ model for MCGDM and their stepwise algorithm are demonstrated by utilizing the proposed approach. Finally, a numerical example for the developed model is presented and a comparative study of the investigated models with some existing methods are expressed broadly which show that the investigated models are more effective and useful than the existing approaches.

Operator bases in effective field theories with sterile neutrinos: d ≤ 9

Abstract: We obtain the complete and independent bases of effective operators at mass dimension 5, 6, 7, 8, 9 in both standard model effective field theory with light sterile right-handed neutrinos ($ u$SMEFT) and low energy effective field theory with light sterile neutrinos ($ u$LEFT). These theories provide systematical parametrizations on all possible Lorentz-invariant physical effects involving in the Majorana/Dirac neutrinos, with/without the lepton number violations. In the $ u$SMEFT, we find that there are 2 (18), 29 (1614), 80 (4206), 323 (20400), 1358 (243944) independent operators with sterile neutrinos included at the dimension 5, 6, 7, 8, 9 for one (three) generation of fermions, while 24, 5223, 3966, 25425, 789426 independent operators in the $ u$LEFT.