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Target threat assessment provides support for combat decision making. The multi-target threat assessment method based on a three-way decision can obtain threat classification while receiving threat ranking, thus avoiding the limitation of traditional two-way decisions. However, the heterogeneous situation information, attribute relevance, and adaptive information processing needs in complex battlefield environment bring challenges to existing methods. Therefore, this paper proposes a new multi-target three-way threat assessment method with heterogeneous information and attribute relevance. Firstly, dynamic assessment information is represented by heterogeneous information, and attribute weights are calculated by heterogeneous Criteria Importance Through Intercriteria Correlation (CRITIC). Then, the conditional probability is calculated by the heterogeneous weighted Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and the adaptive risk avoidance coefficients are constructed by calculating the uncertainty of the assessment value, and then the relative loss function matrices are constructed. Finally, the comprehensive loss function matrices are obtained by the weighted Heronian mean (HM) operator, and the comprehensive thresholds are calculated to obtain the three-way rules. The case study shows that compared with the existing methods, the proposed method can effectively handle the heterogeneous information and attribute relevance, and obtain the risk avoidance coefficients without presetting or field subjective settings, which is more suitable for the complex mission environment. [ABSTRACT FROM AUTHOR]

Environmental protection and sustainable development have become the consensus of all countries in the world. Enterprises must pay attention to the impact on the environment in their operations. Therefore, the selection of green suppliers has become a crucial issue for companies. Supplier selection is a dynamic and complex multi-attribute group decision-making process. The decision results have the tripartite characteristics of "accepted", "rejected" and "pending further investigation", and experts need to constantly negotiate in the decision-making process to achieve consensus. In view of the above characteristics, this study constructs a sequential group three-way decision making (TWDM) method to support green supplier selection. Firstly, we review the existing literature on the evaluation criteria and selection methods of green suppliers. In this process, we construct an evaluation attribution system including the following four aspects: product formation, service level, development capability, and green level. Secondly, combining with the sequential and group characteristics of decision making, we propose a multiple-attribute sequential group TWDM method based on a multi-level granularity structure. The weight of each decision maker is determined by his influence weight and interval-valued intuitionistic fuzzy entropy weight. The attribute weight is determined by entropy weight and subjective weight. By using the VIsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method improved by grey relation analysis (GRA), we calculate conditional probabilities. Since the cumulative prospect theory can reflect the risk attitude of decision makers, we apply it to calculate the decision thresholds. Finally, we apply a case of Q automobile manufacturer to verify the effectiveness, applicability and feasibility of the method. The innovation of this study is to construct social networks at each granularity level and introduce an expert information exchange model to promote group consensus. The sequential group TWDM method provides a new reference and idea for the selection of green suppliers. [ABSTRACT FROM AUTHOR]

Commonly, it is accepted that oncology treatment would yield outcomes with a certain determinism without any quantitative support or mathematical model that establishes such determinations. Nowadays, with the advent of nanomedicine, the targeting drug delivery scheme has emerged, whose central objective is the uptake of nanoparticles by tumors. Once they are injected into the bloodstream, it is unclear as to which process governs the directing of nanoparticles towards the desired target, deterministic or stochastic. In any scenario, an optimal outcome, small toxicity and minimal dispersion of drugs is expected. Commonly, it is expected that an important fraction of them can be internalized into tumor. In this manner, due to the fraction of nanoparticles that have failed to uptake, the success of the drug delivery scheme might be at risk. In this paper, a theory based on the sequence electrodynamics–diffusion–Bayes theorem is presented. The Bayesian probability that emerges at the end of the sequence might be telling us that dynamical processes based on the injection of electrically charged nanoparticles might be dictated by stochastic formalism. Thus, rather than expecting a deterministic process, the chain of events would convert the drug delivery scheme to be dependent on a sequence of conditional probabilities. [ABSTRACT FROM AUTHOR]

As an important branch of modern decision-making theory, multi-attribute decision-making (MADM) plays an important role in various fields. Classic MADM methods can provide a ranking of alternatives, and decision-makers need to evaluate the level subjectively based on the ranking results. Because of the limitation of knowledge, this is likely to lead to potential individual losses. Three-way decision (3WD) theory has good classification ability. Therefore, this paper proposes a dynamic hybrid multi-attribute 3WD (MA3WD) model. First, a new scheme for constructing loss functions is proposed from the perspective of gray relational analysis (GRA), which is an accurate and objective way to describe the relationship between loss functions and attribute values. Then, conditional probabilities are determined by employing the gray relational analysis technique for order preference by similarity to the ideal solution (GRA-TOPSIS). With these discussions, a GRA-based hybrid MA3WD model for a single period is proposed by considering multi-source information. Furthermore, by extending the single-period scenario to a multi-period one, we construct a dynamic hybrid MA3WD model, which can obtain the final three-way decision rules as well as the results of each period and each attribute. Finally, the proposed method is applied to the case of performance evaluation of elderly-care services to demonstrate the effectiveness of the method, and comparative analyses are given to verify the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

As one of the most widely used applications in domain adaption (DA), Cross-domain sentiment analysis (CDSA) aims to tackle the barrier of lacking in sentiment labeled data. Applying an adversarial network to DA to reduce the distribution discrepancy between source and target domains is a significant advance in CDSA. This adversarial DA paradigm utilizes a single global domain discriminator or a series of local domain discriminators to reduce marginal or conditional probability distribution discrepancies. In general, each discrepancy has a different effect on domain adaption. However, the existing CDSA algorithms ignore this point. Therefore, in this paper, we propose an effective, novel and unsupervised adversarial DA paradigm, Global-Local Dynamic Adversarial Learning (GLDAL). This paradigm is able to quantitively evaluate the weights of global distribution and every local distribution. We also study how to apply GLDAL to CDSA. As GLDAL can effectively reduce the distribution discrepancy between domains, it performs well in a series of CDSA experiments and achieves improvements in classification accuracy compared to similar methods. The effectiveness of each component is demonstrated through ablation experiments on different parts and a quantitative analysis of the dynamic factor. Overall, this approach achieves the desired DA effect with domain shifts. [ABSTRACT FROM AUTHOR]

The research on risk control during the construction stage of catenary is relatively limited. Based on a comprehensive analysis of the risk factors during catenary construction, this study determined the causal relationships between the risk factors and established a risk assessment model for catenary construction that analyzed the risks from a causal logic perspective. During the evaluation process, we identified six exogenous variables and twenty-one endogenous variables for risk factors in the construction of catenary based on a literature review in the field of catenary construction and expert opinions, described the cause-and-effect relationships between variables using structural equations and causal diagrams, and established a multi-level catenary construction risks structural causal model. Based on expert fuzzy evaluation and expert experience, the occurrence probability of exogenous variables and the conditional probability of endogenous variables were determined, respectively. Then, the risk assessment model of catenary construction stage based on fuzzy Bayesian Network was constructed to analyze the risk of catenary construction process. The results showed that the personal quality of the construction personnel and the sense of responsibility of the supervision unit had a great impact on the risk level of catenary construction. The findings can help construction personnel fully consider various weak points in catenary construction, thereby ensuring efficient and high-quality catenary construction. [ABSTRACT FROM AUTHOR]

In fuzzy artificial intelligent decision support systems, three-way intelligent-decision making (TWIDM) has played a very important role in ranking objects under the double hierarchy linguistic variable (DHLV). The 8 × 8 S-boxes are very important for image encryption in secure communication. Therefore, the aim of the present study is to develop a new approach to artificial intelligent three-way decision making via DHLV and apply it to S-box image encryption. Artificial intelligent based three-way decision-making problems with double hierarchy hesitant linguistic terms are developed. The first and second hierarchy hesitant linguistic term sets make up the double hierarchy hesitant linguistic term set, which allows for more flexible expressions of doubt and fuzziness. First, we define the Einstein operational laws, score function, and Einstein aggregation operators; i.e., double hierarchy hesitant linguistic Einstein weighted averaging and weighted geometric operators. First, the unknown weight vector for decision experts is determined by using aggregation operators and entropy measures for DHLV. Then, we find the weight vector for our criteria by using the distance measure. In TWIDM, conditional probability is determined by using the extended TOPSIS method for evaluating the S-boxes for image encryption. The expected losses are then computed by aggregating the loss functions with the help of Einstein-weighted averaging aggregation operators. Finally, we apply the minimum-loss decision rules for the selection of S-box to image encryption. The proposed decision technique has been compared with existing three-way decisions and the result of proposed three-way decision making for analyzing and ranking the S-box is very good and reliable for decision making. [ABSTRACT FROM AUTHOR]

Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 10 6 for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy. [ABSTRACT FROM AUTHOR]

It has been more than a decade since sequential indicator simulation was proposed to model geological features. Due to its simplicity and easiness of implementation, the algorithm attracts the practitioner's attention and is rapidly becoming available through commercial software programs for modeling mineral deposits, oil reservoirs, and groundwater resources. However, when the algorithm only uses hard conditioning data, its inadequacy to model the long-range geological features has always been a research debate in geostatistical contexts. To circumvent this difficulty, one or several pieces of soft information can be introduced into the simulation process to assist in reproducing such large-scale settings. An alternative format of Bayesian sequential indicator simulation is developed in this work that integrates a log-linear pooling approach by using the aggregation of probabilities that are reported by two sources of information, hard and soft data. The novelty of this revisited Bayesian technique is that it allows the incorporation of several influences of hard and soft data in the simulation process by assigning the weights to their probabilities. In this procedure, the conditional probability of soft data can be directly estimated from hard conditioning data and then be employed with its corresponding weight of influence to update the weighted conditional portability that is simulated from the same hard conditioning and previously simulated data in a sequential manner. To test the algorithm, a 2D synthetic case study is presented. The findings showed that the resulting maps obtained from the proposed revisited Bayesian sequential indicator simulation approach outperform other techniques in terms of reproduction of long-range geological features while keeping its consistency with other expected local and global statistical measures. [ABSTRACT FROM AUTHOR]

The Asymmetric Simple Inclusion Process (ASIP) is an n-site tandem stochastic network with a Poisson arrival influx into the first site. Each site has an unlimited buffer with a gate in front of it. Each gate opens, independently of all other gates, following a site-dependent Exponential inter-opening time. When a site's gate opens, all particles occupying the site move simultaneously to the next site. In this paper, a Generalized ASIP network is analyzed where the influx is to all sites, while gate openings are determined by a general renewal process. A compact matrix approach—instead of the conventional (and tedious) successive substitution method—is constructed for the derivation of the multidimensional probability-generating function (PGF) of the site occupancies. It is shown that the set of ( 2 n n ) linear equations required to obtain the PGF of an n-site network can be first cut by half into a set of 2 n − 1 n equations, and then further reduced to a set of 2 n − n + 1 equations. The latter set can be additionally split into several smaller triangular subsets. It is also shown how the PGF of an n + 1 -site network can be derived from the corresponding PGF of an n-site system. Explicit results for networks with n = 3 and n = 4 sites are obtained. The matrix approach is utilized to explicitly calculate the probability that site k   k = 1 , 2 , ... , n is occupied. We show that, in the case where arrivals occur to the first site only, these probabilities are functions of both the site's index and the arrival flux and not solely of the site's index. Consequently, refined formulas for the latter probabilities and for the mean conditional site occupancies are derived. We further show that in the case where the arrival process to the first site is Poisson with rate λ , the following interesting property holds: P s i t e   k   i s   o c c u p i e d   |   λ = 1 = P s i t e   k + 1   i s   o c c u p i e d   |   λ → ∞ . The case where the inter-gate opening intervals are Gamma distributed is investigated and explicit formulas are obtained. Mean site occupancy and mean total load of the first k sites are calculated. Numerical results are presented. [ABSTRACT FROM AUTHOR]

In the era of internet connection and IOT, data-driven decision-making has become a new trend of decision-making and shows the characteristics of multi-granularity. Because three-way decision-making considers the uncertainty of decision-making for complex problems and the cost sensitivity of classification, it is becoming an important branch of modern decision-making. In practice, decision-making problems usually have the characteristics of hybrid multi-attributes, which can be expressed in the forms of real numbers, interval numbers, fuzzy numbers, intuitionistic fuzzy numbers and interval-valued intuitionistic fuzzy numbers (IVIFNs). Since other forms can be regarded as special forms of IVIFNs, transforming all forms into IVIFNs can minimize information distortion and effectively set expert weights and attribute weights. We propose a hybrid multi-attribute three-way group decision-making method and give detailed steps. Firstly, we transform all attribute values of each expert into IVIFNs. Secondly, we determine expert weights based on interval-valued intuitionistic fuzzy entropy and cross-entropy and use interval-valued intuitionistic fuzzy weighted average operator to obtain a group comprehensive evaluation matrix. Thirdly, we determine the weights of each attribute based on interval-valued intuitionistic fuzzy entropy and use the VIKOR method improved by grey correlation analysis to determine the conditional probability. Fourthly, based on the risk loss matrix expressed by IVIFNs, we use the optimization method to determine the decision threshold and give the classification rules of the three-way decisions. Finally, an example verifies the feasibility of the hybrid multi-attribute three-way group decision-making method, which provides a systematic and standard solution for this kind of decision-making problem. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behaviour of the tail probability of the number of customers in the steady-state M / G / 1 retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. Detailed tail asymptotic properties are obtained for the conditional probability of the number of customers in the (priority) queue and orbit, respectively, in terms of the recently proposed exhaustive stochastic decomposition approach. Numerical examples are presented to show the impacts of system parameters on the tail asymptotic probabilities. [ABSTRACT FROM AUTHOR]

In this paper, the complex network of the urban functions in Shenzhen of China under the lockdown of the corona virus disease 2019 (COVID-19) is studied. The location quotient is used to obtain the dominant urban functions of the districts in Shenzhen before and under the lockdown of COVID-19. By using the conditional probability, the interdependencies between the urban functions are proposed to obtain the complex networks of urban functions and their clusters. The relationships between the urban functions, and the overall and cluster characteristics of the urban functions before and under the lockdown of COVID-19 are analyzed based on the complex networks. The mean degree and mean weighted degree of the primary categories of the urban functions are obtained to discuss the classification characteristics of the urban functions before and under the lockdown of COVID-19. Then, the differences and changes of the urban functions before and under the lockdown of COVID-19 are compared, and the corresponding policy implications under the lockdown of COVID-19 are presented. The results show that under the lockdown of COVID-19, the correlation of the urban functions is stronger than that before the lockdown; the common urban functions are more useful and essential, and finance, fine food and medical treatment are important; public service and government departments have the most positive relationship with other urban functions, and finance service has the highest spatial agglomeration distribution trend; and the cluster characteristics of urban functions are more related to people's livelihood, and the urban functions show incomplete and cannot be operated for long term. [ABSTRACT FROM AUTHOR]

Bayesian Reasoning is both a fundamental idea of probability and a key model in applied sciences for evaluating situations of uncertainty. Bayesian Reasoning may be defined as the dealing with, and understanding of, Bayesian situations. This includes various aspects such as calculating a conditional probability (performance), assessing the effects of changes to the parameters of a formula on the result (covariation) and adequately interpreting and explaining the results of a formula (communication). Bayesian Reasoning is crucial in several non-mathematical disciplines such as medicine and law. However, even experts from these domains struggle to reason in a Bayesian manner. Therefore, it is desirable to develop a training course for this specific audience regarding the different aspects of Bayesian Reasoning. In this paper, we present an evidence-based development of such training courses by considering relevant prior research on successful strategies for Bayesian Reasoning (e.g., natural frequencies and adequate visualizations) and on the 4C/ID model as a promising instructional approach. The results of a formative evaluation are described, which show that students from the target audience (i.e., medicine or law) increased their Bayesian Reasoning skills and found taking part in the training courses to be relevant and fruitful for their professional expertise. [ABSTRACT FROM AUTHOR]

As a typical model of three-way decisions (3WD), decision-theoretic rough sets (DTRS), have gained attention from scholars in decision-making problems. The q-rung orthopair fuzzy 2-tuple linguistic variable (QROF2-TLV) is a mixture of two different notions, q-rung orthopair fuzzy sets (QROFS) and 2-tuple linguistic variables (2-TLV), and is an extensive and proficient technique for coping with awkward and complicated information in realistic decision-making. In this paper, we first propose a DTRS model for 3WD based on QROF2-TLV that gives a new method for evaluating loss functions (LF) of DTRS. We further present the q-rung orthopair fuzzy 2-tuple linguistic generalized Maclaurin symmetric mean (QROF2-TLGMSM) and weighted QROF2-TLGMSM operators and then provide the LFs of DTRS based on QROF2-TLV with the values aggregated by the QROF2-TLGMSM operator. Thus, we propose the q-rung orthopair fuzzy 2-tuple linguistic variable DTRS (QROF2-TLV-DTRS) model. Subsequently, a technique for concluding another DTRS model, which can give the related semantic translation of the decision consequences of every other option, is presented. The model is applied to expound the proposed technique in detail, and the impacts of various conditional probabilities on decision outcomes are discussed. A comparative analysis of the proposed approach is also conducted to examine the proficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Multivariate Statistical Process Control (MSPC) seeks to monitor several quality characteristics simultaneously. However, it has limitations derived from its inability to identify the source of special variation in the process. In this research, a proposed model that does not have this limitation is presented. In this paper, data from two scenarios were used: (A) data created by simulation and (B) random variable data obtained from the analysed product, which in this case corresponds to cheese production slicing process in the dairy industry. The model includes a dimensional reduction procedure based on the centrality and data dispersion. The goal is to recognise a multivariate pattern from the conjunction of univariate variables with variation patterns so that the model indicates the univariate patterns from the multivariate pattern. The model consists of two stages. The first stage is concerned with the identification process and uses Moving Windows (MWs) for data segmentation and pattern analysis. The second stage uses Bayesian Inference techniques such as conditional probabilities and Bayesian Networks. By using these techniques, the univariate variable that contributed to the pattern found in the multivariate variable is obtained. Furthermore, the model evaluates the probability of the patterns of the individual variables generating a specific pattern in the multivariate variable. This probability is interpreted as a signal of the performance of the process that allows to identify in the process a multivariate out-of-control state and the univariate variable that causes the failure. The efficiency results of the proposed model compared favourably with respect to the results obtained using the Hotelling's T 2 chart, which validates our model. [ABSTRACT FROM AUTHOR]

For the first time, the concept of conditional probability on intuitionistic fuzzy sets was introduced by K. Lendelová. She defined the conditional intuitionistic fuzzy probability using a separating intuitionistic fuzzy probability. Later in 2009, V. Valenčáková generalized this result and defined the conditional probability for the MV-algebra of inuitionistic fuzzy sets using the state and probability on this MV-algebra. She also proved the properties of conditional intuitionistic fuzzy probability on this MV-algebra. B. Riečan formulated the notion of conditional probability for intuitionistic fuzzy sets using an intuitionistic fuzzy state. We use this definition in our paper. Since the convergence theorems play an important role in classical theory of probability and statistics, we study the martingale convergence theorem for the conditional intuitionistic fuzzy probability. The aim of this contribution is to formulate a version of the martingale convergence theorem for a conditional intuitionistic fuzzy probability induced by an intuitionistic fuzzy state m. We work in the family of intuitionistic fuzzy sets introduced by K. T. Atanassov as an extension of fuzzy sets introduced by L. Zadeh. We proved the properties of the conditional intuitionistic fuzzy probability. [ABSTRACT FROM AUTHOR]

Sample size calculation in biomedical practice is typically based on the problematic Wald method for a binomial proportion, with potentially dangerous consequences. This work highlights the need of incorporating the concept of conditional probability in sample size determination to avoid reduced sample sizes that lead to inadequate confidence intervals. Therefore, new definitions are proposed for coverage probability and expected length of confidence intervals for conditional probabilities, like sensitivity and specificity. The new definitions were used to assess seven confidence interval estimation methods. In order to determine the sample size, two procedures—an optimal one, based on the new definitions, and an approximation—were developed for each estimation method. Our findings confirm the similarity of the approximated sample sizes to the optimal ones. R code is provided to disseminate these methodological advances and translate them into biomedical practice. [ABSTRACT FROM AUTHOR]

The unit return is determined as the return in the quotation currency (QCR) per the unit of base exchange medium (BEM). The main purpose is to examine the applicability of a trading system with a constant modulus of unit return (CMUR). The CMUR system supports speculative operations related to the exchange rate, given as the BEM quotation per the QCR. Premises for investment decisions are based on knowledge about the quotation dynamics described by its binary representation. This knowledge is described by a prediction table containing the conditional probability distributions of exchange rate increments. Any prediction table depends on observation range. Financial effectiveness of any CMUR system is assessed in the usual way by interest rate and risk index based on Shannon entropy. The main aim of our paper is to present algorithms which may be used for selecting effective CMUR systems. Required unit return modulus and observation range are control parameters applied for management of CMUR systems. Optimal values of these parameters are obtained by implementation of the proposed algorithm. All formal considerations are illustrated by an extensive case study linked to gold trading. [ABSTRACT FROM AUTHOR]