Set Of Probabilities Research Articles

Probabilistic Answer Set Programming with Discrete and Continuous Random Variables

Abstract Probabilistic Answer Set Programming under the credal semantics extends Answer Set Programming with probabilistic facts that represent uncertain information. The probabilistic facts are discrete with Bernoulli distributions. However, several real-world scenarios require a combination of both discrete and continuous random variables. In this paper, we extend the PASP framework to support continuous random variables and propose Hybrid Probabilistic Answer Set Programming. Moreover, we discuss, implement, and assess the performance of two exact algorithms based on projected answer set enumeration and knowledge compilation and two approximate algorithms based on sampling. Empirical results, also in line with known theoretical results, show that exact inference is feasible only for small instances, but knowledge compilation has a huge positive impact on performance. Sampling allows handling larger instances but sometimes requires an increasing amount of memory.

Exploring Asymmetric Gender-Based Satisfaction of Delivery Riders in Real-Time Crowdsourcing Logistics Platforms

This study investigates gender-based differences in the satisfaction ranking of riders on real-time crowdsourcing logistics platforms, using online reviews from the Ele.me platform. Quantitative methods, including the frequency ratio-based Analytic Hierarchy Process (AHP), probabilistic linguistic term sets (PLTS), and fuzzy comprehensive evaluation (FCE), were applied to analyze satisfaction differences between men and women riders. The findings reveal an asymmetric pattern in satisfaction preferences: women riders place more emphasis on perceived value, while men riders prioritize service perceived quality. Although both groups rank platform image, product perceived quality, and rider expectations similarly, the importance of these factors varies significantly, indicating an underlying asymmetry in their expectations and values. Women riders express higher satisfaction with platform image, rider expectations, service perceived quality, and product perceived quality, with rider expectations showing the largest difference. Additionally, the multi-criteria decision-making methods used in this study offer insights for optimizing service performance in real-time crowdsourcing logistics platforms, particularly in handling uncertainty and enhancing system adaptability through fuzzy sets. These findings provide a basis for developing gender-specific strategies aimed at enhancing rider satisfaction, minimizing turnover, and improving platform adaptability—contributing to a more inclusive and sustainable logistics supply chain.

A new probabilistic linguistic decision-making process based on PL-BWM and improved three-way TODIM methods

Probabilistic linguistic term sets (PLTSs) provide a flexible tool to express linguistic preferences, which allow decision-makers to label linguistic information with different probabilities. In this paper, a method based on a PLTS is proposed to address multi-criteria decision-making problems (MCDM). We develop the theory of PLTSs and put forward a novel best–worst method (BWM), termed PL-BWM, based on PLTS. Our method fully reflects the preference information of decision-makers and accurately provides the importance level of the criteria. The combined weight of the criteria is obtained by merging PL-BWM-based subjective weights and similarity minimization-based objective weights. Upon introducing a three-way decision system to improve the TODIM method, a novel three-way TODIM method is proposed and showcased on an optimal new energy vehicle selection problem. The effectiveness and accuracy of the proposed method are verified by sensitivity analysis and comparative analysis. Our approach paves the way for new developments in solving MCDM problems and for novel applications in otherwise difficult ranking problems.

Comprehensive Analysis Using Probabilistic Linguistic Group Decision-Making and MEREC Technique With Sustainable Development Evaluation in Higher Education

University administrators should organize and coordinate various affairs, scientifically utilize resources such as budget, teaching equipment, and faculty, continuously improve teaching quality, and ensure the sustainable development of educational management. The sustainable development evaluation in higher education management is a multiple-attribute group decision-making (MAGDM) problem. Recently, the Exponential TODIM (ExpTODIM) and PROMETHEE technique was employed to put forward the MAGDM issues. The probabilistic linguistic term sets (PLTSs) are employed as a technique for characterizing uncertain information during the sustainable development evaluation in higher education management. In this paper, the probabilistic linguistic ExpTODIM-MABAC (PL-ExpTODIM-MABAC) technique is constructed to put forward the MAGDM under PLTSs. The MEREC technique is employed to obtain the weight values under PLTSs. Finally, a numerical example for sustainable development evaluation in higher education management is put forward to validate the ExpTODIM-MABAC technique.

Similarity Measures of Probabilistic Interval Preference Ordering Sets and Their Applications in Decision-Making

The concept of probabilistic interval preference ordering sets (PIPOSs) provides a scientific and intuitive framework for solving real-life multi-criteria group decision-making problems. In some areas such as investment decision-making and supplier selection, PIPOSs have a wider application space, and the development of similarity and distance measures based on PIPOSs holds great significance. Similarity measure is a basic and prominent tool for dealing with imperfect and ambiguous information in fuzzy sets, but it can also be used to deal with uncertain information in preference ordering. These metrics play an important role in the actual decision-making process, as they effectively quantify the degree of similarity between two PIPOSs, and further allow for the prioritization of different scenarios. In this article, we sort out the definitions and arithmetic rules of PIPOSs, and creatively propose several new similarity measures based on PIPOSs. Then, we propose a group decision-making method based on similarity measures and conduct a comparative study with three existing similarity measures to illustrate its advantages over existing metrics. Finally, we confirm its validity through numerical illustrations in the case study, and also conduct a comparative assessment to verify the scientific validity and effectiveness of the newly introduced measure against the existing metrics.

Expectation analysis for bounding solutions of the 0–1 knapsack problem

In this paper, an entirely novel discrete probabilistic model is presented to generate 0–1 Knapsack Problem instances. We analyze the expected behavior of the greedy algorithm, the eligible-first algorithm and the linear relaxation algorithm for these instances; all used to bound the solution of the 0–1 Knapsack Problem (0–1 KP) and/or its approximation. The probabilistic setting is given and the main random variables are identified. The expected performance for each of the aforementioned algorithms is analytically established in closed forms in an unprecedented way.

Stakeholder requirement-oriented prioritization method of quality characteristics based on probabilistic linguistic term set

Stakeholder requirement-oriented prioritization method of quality characteristics based on probabilistic linguistic term set

Last-train timetable synchronization for service compatibility maximization in urban rail transit networks with arrival uncertainties

The last train services of urban rail transit offer all passengers the final chance to reach their destinations. In the context of multimodal transport, considering the random delayed arrivals of late-night vehicles of other transport modes at urban hub stations and their adverse effects on multimodal passengers transferring to urban rail transit, a probabilistic scenario set is established to determine the arrival uncertainties of multimodal passengers. In each scenario, the timetable synchronization problem is formulated as a mixed-integer nonlinear programming model that requires a performance trade-off between destination reachability and the remaining path distance of both non-multimodal and multimodal passengers, integrally termed last train service compatibility. Through linearization techniques, the model is transformed into an equivalent mixed-integer linear programming form, which can be efficiently solved using the Gurobi solver to obtain the optimal last train timetable for each scenario and form an alternative scheme set. An improved probabilistic scenario set-based regret value theory is then developed, in which a novel regret value calculation method is proposed. The scheme with the minimum total weighted opportunity loss in all scenarios is selected as the optimal robust. Real case experiments based on the Chengdu–Chongqing high-speed railway line and Chengdu metro network are conducted to test the performance of our model. The results show that compared with the original timetable, the optimized timetable reduces the number of unreachable passengers by 34.29% and the sum of the average remaining path distance of non-multimodal and multimodal passengers by 57.43% with the help of path planning for all passengers. The proposed approach is proven not only to balance the demands of both reachable and unreachable passengers, but also to significantly improve the robustness of the last train timetable to arrival uncertainties of multimodal passengers and reduce their service inequity.

AI-powered decision making for road safety optimization under probabilistic linguistic Sugeno-Weber aggregation information

Traffic accidents, a global concern, pose threats to lives and carry substantial economic and societal burdens. This paper explores the innovative integration of artificial intelligence (AI) into the ambiance of Multi Criteria Decision Making (MCDM) to address the challenge. We investigate AI's potential to enhance road safety globally, utilizing data analysis, predictive modeling, and intelligent traffic management systems. Our goal is to revolutionize accident prevention by optimizing decision-making processes and promoting safer and more efficient road environments. In the realm of information aggregation and fusion, growing interest among researchers has centered on probabilistic linguistic expression sets, which adeptly aggregate uncertain data. This article's primary aim is to explore methodologies for aggregating information within a probabilistic linguistic environment. To achieve this goal, we have introduced procedural laws based on the Sugeno-Weber (SW) framework for handling probabilistic linguistic term elements (PLTEs), rooted in both the product and sum of SW operations. Consequently, we have crafted a range of probabilistic linguistic aggregation techniques, encompassing the probabilistic linguistic SW Average (PLSWA) and Geometric (PLSWG), followed by weighted as well as ordered aggregation operators like PLSWWA and PLSWWG, PLSWOWA and PLSWOWG. By harnessing SW τ-norm and τ-conorm, we have developed versatile aggregation tools that facilitate information reinforcement. Through the utilization of proposed operators, we have presented strategies for effectively integrating probabilistic linguistic term sets (PLTs) in the context of MCDM. We have compared our suggested procedures with the TOPSIS approach and elucidated the diverse features inherent to these operators.

A hybrid BWM–CRITIC–VIKOR approach for assessing oil and gas risk scenarios in probabilistic linguistic term set

The oil and gas industry plays a crucial role in supporting energy supply and economic development. Mitigating risks in oil and gas projects is essential for reducing decision-making uncertainties, optimizing resource allocation, and fostering the competitiveness and sustainable growth of enterprises. Therefore, evaluating decision-making risks in the oil and gas sector is of significant practical importance. This paper proposes a comprehensive approach based on the BWM–CRITIC–VIKOR multi-criteria decision-making (MCDM) evaluation model. An evaluation index system encompassing six critical dimensions—technology, economics, environment, security, societal impact, and political factors—is established. To enhance assessment precision, the AHP interval estimation method is employed to identify and eliminate indicators with low contributions. Subsequently, the probabilistic linguistic term set (PLTS) is introduced into the best–worst method (BWM) and CRITIC methods to calculate the weights for each index. This approach helps to circumvent the subjectivity inherent in single subjective weighting methods. To evaluate and rank alternatives, the PLTS is used as an evaluation linguistic tool within the VIKOR framework. Finally, this methodology is applied to decision-making in the oil and gas industry, and its effectiveness and superiority are compared with the AHP–TOPSIS method and the BWM–CRITIC method.

A volume‐averaging and stochastic turbulence modeling framework for homogeneous roughness‐induced drag in turbulent flows

AbstractThe goal of this work is the formulation of a model for the parameterization of homogeneous roughness‐induced drag in turbulent flow simulations. We characterize rough surfaces using their surface‐area moments of roughness‐peaks. Additionally, we consider a probabilistic self‐similar power law distribution for the roughness heights, in such a way that an assumed set of discrete roughness elements can behave as a probabilistic fractal set. Upon these assumptions, the surface characterization is complete and yields wall‐normal profiles of porosity, average roughness element diameter, and equivalent pore diameter of the roughness affected porous flow. The profiles are supplied to a (pore‐based) Reynolds number and porosity‐based drag parameterization for staggered cylinder arrays available in the literature, as well as a one‐dimensional map‐based turbulence model, the one‐dimensional turbulence (ODT) model. The purpose of the latter is a way to provide the missing effects of the equivalent dispersion tensor in the porous flow close to the rough surface, as well as that of the nonlinear turbulent transport away from the wall. Simulations are then carried out in order to evaluate the effects of two different rough surfaces on a turbulent channel flow, comparing results with existing direct numerical simulation (DNS) data. Overall, reasonable agreement is obtained, which suggests that, by using the proposed model, it is possible to model the effects of rough surfaces on wall‐bounded turbulent flows, without the explicit need of the full topological representation of the surface on the numerical domain. To that extent, one clear flow control application for the suggested approach would be that of drag‐based surface optimization.

A three-way decision method based on COPRAS in the weak probabilistic linguistic term set information systems

A three-way decision method based on COPRAS in the weak probabilistic linguistic term set information systems

An integrated probabilistic bipolar fermatean hesitant fuzzy transportation configuration for sustainable management of floral waste with risk assessment

This paper proposes the probabilistic bipolar fermatean hesitant fuzzy set (PBFHFS) and its triangular version as generalizations of bipolar fuzzy set (BFS) for delineating randomness and imprecision in a single framework. To enhance pragmatic applicability, the devised set has been examined based on its fundamental operations, basic properties, and defuzzification mechanism. Offerings made to temples are considered sacred, so they cannot be disposed of in landfills. Waste from temples is usually disposed of in nearby lakes, ponds, and rivers. Thus, management of the temple floral waste (TFW) is essential to enhance the sustainability of the environment. In this regard, a green 4-dimensional transportation system under PBFHF settings is developed for the effective and sustainable managements of floral waste that is dumped from places of worship. For the most cost-effective and environmentally friendly results, this transportation system optimises a number of metrics, transportation expenditure (TE), carbon emission (CE), transportation time (TT), and labour cost (LC). Three sub-models are further developed from the proposed model under PBFHF conditions by incorporating the theory of carbon policy and risk assessments. The suggested transportation system is addressed by employing a fuzzy methodology, fuzzy programming (FP) as well as two non-fuzzy approaches, weighted sum technique (WST) and goal programming technique (GP). At last, there is a numerical computation along with comparison analysis, management insights, a conclusion with limitations, and a scope for further study.

Multi-position two-phase person-position matching decision-making with intermediary participation

With the rapid development in society, intermediaries play an increasingly important role in person-position matching decision-making. To obtain reasonable enterprise-intermediary matching and enterprise-candidate matching schemes under multiple positions, preferences of enterprises, headhunting companies and candidates should be fully considered from a two-phase perspective. Thus, a two-sided matching decision-making method under the probabilistic linguistic environment is proposed to solve the multi-position two-phase person-position matching problem. First, related theories of probabilistic linguistic term sets and two-sided matching are given. On this basis, the problem of multi-position two-phase person-position matching under the probabilistic linguistic environment is described. The decision-making process is divided into the following two phases: In the first phase, satisfactions of enterprises and headhunting companies are calculated considering subject expectations based on prospect theory. Then, considering the maximization of satisfactions of two-sided subjects, the many-to-many two-sided matching model between enterprises and headhunting companies is established and solved to obtain the optimal many-to-many matching scheme. In the second phase, according to evaluation matrices and expectation matrices, satisfactions of enterprises and candidates under multiple positions are calculated considering intermediary evaluations. Then, considering the maximization of satisfactions of enterprises and candidates, one-to-many matching models and one-to-one stable matching models under multiple positions are developed and solved to obtain the optimal person-position matching schemes under multiple positions. Finally, an example of the person-position matching with intermediary participation is used to illustrate the feasibility and effectiveness of the proposed method.

A novel distance measure for probabilistic linguistic term sets with application to emergency decision-making

A novel distance measure for probabilistic linguistic term sets with application to emergency decision-making

Selection of third-party logistics in supply chain finance under probabilistic complex hesitant fuzzy sets and distance measures

Financial institutions attach great importance to the multiple attribute decision-making (MADM) problems of selecting an effective third-party logistics (3PL) service provider in supply chain finance. A suitable 3PL service provider can not only assist financial institutions in carrying out supply chain finance activity but can also replace financial institutions in supervising the operation of a target financing supply chain, therefore minimizing financial institutions' operating risks. However, there is no sufficient study on the selection of a 3PL service provider. Hence, the objective of this paper is to establish an innovative concept of the “probabilistic complex hesitant fuzzy set” (PCHFS), which is a hybrid structure of the complex hesitant fuzzy set and the probabilistic fuzzy set to manage complex information in real-decision theory. This paper examines the periodicity of probabilistic fuzzy information and extends the range from [0,1] to the unit disc in the complex plane to provide more ability to describe the full meaning of the information in a mathematical model. Based on the internal structure of the set and to find the degree of discrimination between the pairs of PCHFSs, the generalized distance measures and modified generalized distance measures are defined. Several properties and their relationships between them are derived in detail. Also, several cases of the proposed measures are exposed, which reduces them to the existing studies. Furthermore, based on these proposed measures, a multiple-attribute decision-making (MADM) approach is established in an uncertain environment, and several numerical examples are given to examine the feasibility and validity of the explored measures. Finally, the modified and parameterized distance measures based on PCHFSs are verified by comparing them with some existing measures.

Hotel recommendation mechanism based on online reviews considering multi-attribute cooperative and interactive characteristics

Online reviews of hotels provide important information to consumers. The process of extracting useful information from diverse online reviews is crucial for making the best final decisions. To explore the hidden intrinsic information behind online reviews, this paper optimizes information extraction by integrating multiple sources, and gives the recommendation alternative. First, to meet quantitative requirements, the probabilistic linguistic term set is introduced to demonstrate the massive number of comments crawled. Second, considering preference and fluctuation, the relative importance of multiple attributes is determined. Because multiple attributes typically have cooperative or mutually exclusive relationships, a novel model is presented by introducing such relationship to modify relative importance. Third, inspired by the 2-additive Choquet integral operator and the Mahalanobis-Taguchi System, a bi-objective optimization model is proposed to illustrate the interactive effect of comments and develop an attribute correlation network. The specific relationships between attributes are reflected, including the positive and negative interactions. The relative importance, interactive imporantce and subgroup utility can be obtained. Fourth, to guarantee the operability and interpretability of the recommendation results, this paper presents a new information fusion operator and an probabilistic linguistic three-way recommendation process. Finally, a case study is used to demonstrate the complete procedures, and the parameter and comparative analyses highlight the effectiveness of the new operator and recommendation method.

Social network group decision-making method based on stochastic multi-criteria acceptability analysis for probabilistic linguistic term sets

In social network group decision-making (SNGDM) problems, decision-makers (DMs) often express their opinions or preferences using probabilistic linguistic term sets (PLTSs). In this paper, a novel SNGDM method for probabilistic linguistic information is proposed. Firstly, to obtain the prioritization of DMs in the clustering process, a DM clustering method for SNGDM is developed considering the influence of trust relationships and opinions similarity among DMs. Then, to satisfy the requirements of the consensus reaching process in SNGDM, a dynamic consensus threshold calculation method based on an optimization model is introduced. Furthermore, in the consensus measure stage, a novel consensus measure method for both DMs and subgroups is proposed, using a stochastic multi-criteria acceptability analysis (SMAA) method. Based on the consensus measure method, a novel SNGDM method based on SMAA for PLTSs is proposed. Finally, a case study of service quality evaluation in institutional pensions is used to illustrate the effectiveness of the proposed method. The results of case show that the proposed method can adjust consensus thresholds dynamically based on each round of collective opinions, and can solve the SNGDM problems when DMs can not provide their preferences for criteria weights.

Probabilistic and Average Gel’fand Widths of Sobolev Space Equipped with Gaussian Measure in the Sq-Norm

In this article, we mainly studied the Gel’fand widths of Sobolev space in the probabilistic and average settings. And, we estimated the sharp bounds of the probabilistic Gel’fand (N,δ)-widths of multivariate Sobolev space MW2r(Td) with mixed derivative equipped with the Gaussian measure in the Sq-norm by discretization methods. Later, we estimated the sharp bounds of the p-average Gel’fand N-widths of univariate Sobolev space W2r(T) and multivariate Sobolev space MW2r(Td) with mixed derivative equipped with the Gaussian measure in the Sq-norm.

An Integrated CREAM for Human Reliability Analysis Based on Consensus Reaching Process under Probabilistic Linguistic Environment

Human reliability analysis (HRA) is widely used to evaluate the impact of human errors on various complex human–machine systems for enhancing their safety and reliability. Nevertheless, it is hard to estimate the human error probability (HEP) in reality due to the uncertainty of state assessment information and the complex relations among common performance conditions (CPCs). In this paper, we aim to present a new integrated cognitive reliability and error analysis method (CREAM) to solve the HRA problems under probabilistic linguistic environment. First, the probabilistic linguistic term sets (PLTSs) are utilized to handle the uncertain task state assessments provided by experts. Second, the minimum conflict consensus model (MCCM) is employed to deal with conflict task state assessment information to assist experts reach consensus. Third, the entropy weighting method is used to determine the relative objective weights of CPCs. Additionally, the CPC effect indexes are introduced to assess the overall effect of CPCs on performance reliability and obtain the HEP estimation. Finally, the reliability of the proposed CREAM is demonstrated via a healthcare practical case. The result shows that the new integrated CREAM can not only effectively represent experts’ uncertain task state assessments but also determine more reliable HEP estimation in HRA.