Uncertain Problem Research Articles

Reverse triple I method based on the Pythagorean fuzzy inference model and its application

This paper is devoted to discussing the reverse triple I method based on the Pythagorean fuzzy set (PFS). We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO) and Pythagorean fuzzy biresiduum. The reverse triple I methods for Pythagorean fuzzy modus ponens (PFMP) and Pythagorean fuzzy modus tollens (PFMT) are also established. In addition, some interesting properties of the reverse triple I method of PFMP and PFMT inference models are analysed, including the robustness, continuity and reversibility. Finally, a practical problem is provided to illustrate the effectiveness of the reverse triple I method for PFMP in decision-making problems. The advantages of the new method over existing methods are also expounded. Overall, compared with the existing methods, the proposed methods are based on logical reasoning rather than using aggregation operators, so the novel methods are more logical, can better deal with the uncertain problems in complex decision-making environments and can completely reflect the decision-making opinions of decision-makers.

A global satisfaction degree method for fuzzy capacitated vehicle routing problems

There are several uncertain capacitated vehicle routing problems whose delivery costs and demands cannot be estimated using deterministic/statistical methods due to a lack of available and/or reliable data. To overcome this lack of data, third–party information coming from experts can be used to represent those uncertain costs/demands as fuzzy numbers which combined to an iterative–integer programming method and a global satisfaction degree is able to find a global optimal solution. The proposed method uses two auxiliary variables α,λ and the cumulative membership function of a fuzzy set to obtain real–valued costs and demands prior to find a deterministic solution and then iteratively find an equilibrium between fuzzy costs/demands via α and λ. The performed experiments allow us to verify the convergence of the proposed algorithm no matter the initial selection of parameters and the size of the problem/instance.

Robust Refinement of Built-in Network Information System Based on Nonparametric Density Estimation

In the research process of robustness refinement solution of built-in information systems for electronic networks, there are too many factors related to robustness in the current system robustness design, and different factors have different influences on robustness. In stochastic programming problems, uncertain variables usually obey a certain probability distribution, but in real decision-making, these determined distributions are often unknown or we only know part of the information of the distributions, and distributed robust refinement solution is just an effective solution to solve uncertain problems. The robustness measurement solution of information systems for electronic networks is analyzed. The robust refinement of information system is deeply studied by nonparametric density estimation solution, which is based on the strict robustness requirements put forward by users. Based on the research results of interdependent network theory and aiming at “improving the robustness of electronic information system,” this paper makes an in-depth study on the robustness refinement strategy of power information system. The comparison between the companies that adopted the robust refinement of built-in information systems for electronic networks based on nonparametric density estimation and the companies that did not adopt it shows that the refinement rate of the companies that adopted it in the first three years was 82%, while that of the companies that did not adopt it was only 57%, and the overall misjudgment rate was 43%. Therefore, it is proved that using the proposed reliability refinement solution to optimize, the embedded system can improve the service life, modeling accuracy, and availability of the system and has certain practicability.

GA/PD: a genetic algorithm based on problem decomposition for solving interval linear bilevel programming problems

For dealing with uncertain optimization problems, interval programming is a common model that can provide a risk range for decision makers between the best and the worst optimal solutions. Among all interval programming problems, the interval bilevel programming problem has always known as one of the hardest problems to solve. In this work, an efficient solution method is developed for general interval linear bilevel programs in which all coefficients and right-hand vectors are given by intervals. Firstly, a decomposition scheme is adopted to transform the original problem into two simplified subproblems in which only the follower's problem involves interval coefficients. Secondly, a genetic algorithm, one of the more effective evolutionary algorithms, is designed to search these intervals, and linear program optimality conditions are utilized to evaluate each individual in populations. Finally, by comparing the fitness values according to pre-determined rules, the best and the worst optimal solutions to the interval linear bilevel programming problem can be achieved. Simulation results show that the proposed algorithm is efficient and can obtain larger intervals of the optimal values on some computational examples than those in the literature.

Urban livability and contextual uncertainties: An assessment of livability through the lens of urban dwellers in Guwahati, India

The frenetic pace of urban growth in India has caused major concerns regarding the quality of urban livability. Thus, constructing livable cities has become a major goal for new urbanization in India. But urban livability as a behavioral function of the interaction between urban environment and individual characteristics is still understudied. Therefore, to enhance urban livability and construct people-oriented livable cities, this research study aimed to understand the perception of the residents of Guwahati, India, on urban livability and its determinants. Following the notion of uncertain geographic context problem (UGCoP), the current study developed an appropriate conceptual and methodological framework that evaluated the residents’ satisfaction with urban livability and the effect of its dimensions using statistical methods, which were exploratory factor analysis, structural equation modeling and Spearman’s rank correlation. The empirical results of the study indicate that residents’ mean satisfaction with the city’s livable condition is above dissatisfaction level (2.735) and the four examined dimensions have a positive influence upon residents’ satisfaction with urban livability. Additionally, different socio-economic attributes also exert significant effects on the overall satisfaction with urban livability. Therefore, this study is a practical example and model reference for enhancing urban livability in India, particularly for fast-growing cities.

An uncertain production-inventory problem with deteriorating items

The uncertain production-inventory problem with deteriorating items is investigated and an optimal control model is developed in the present paper. The uncertain production-inventory problem is perturbed by an uncertain canonical process. Based on uncertainty theory, an optimistic-value optimal-based control model is established. The present study aims to find the optimistic value of revenue at a certain confidence level. The uncertainty theory is used to obtain the equation of optimality. Using the Hamilton–Jacobi–Bellman principle, a nonlinear partial differential equation that has to be satisfied by a value function is obtained. Assuming a specific form of the solution, backsubstituting the partial differential equation to find functions of time is conducted, and the functions are then used to solve the partial differential equation. Numerical experiments with different demand functions are used to assess the feasibility of this model and this method.

A new uncertain random portfolio optimization model for complex systems with downside risks and diversification

There are different types of securities yields in the financial market. The yields of these securities can be described as uncertain variables or random variables. This paper considers an uncertain random portfolio selection problem, in which uncertain and random return rates exist simultaneously. First, by considering downside risks and diversification constraints, an uncertain random bi-objective mean-variance-VaR-entropy model for portfolio selection problems is proposed. Here, investment return and risk are, respectively, quantified by uncertain random expected value and variance. Then the formulated uncertain random model is transformed into two equivalent deterministic models. Furthermore, we use the NSGA-II algorithm to solve the equivalent bi-objective model, and propose a new optimal solution criterion to find a single optimal solution in the Pareto optimal solution set. Finally, a numerical simulation is performed to verify the validity and the practicality of the proposed model and the NSGA-II algorithm.

Household Food Shopping Locations Beyond Residential Neighborhoods: An Exploratory Study Using a GPS-Based Household Survey

Understanding household food shopping locations is important as it could help policymakers develop effective place-based strategies to improve healthy eating and subsequently improve health conditions. Although a growing number of studies have examined food shopping patterns and their associations with food environment around home locations, evidence on food shopping locations relative to areas beyond residential neighborhoods remains scarce. We aimed to explore spatial dimensions of household food shopping locations relative to home, workplaces, and commuting routes. We defined three buffers to delineate potential food shopping geographies for home, workplaces, and commuting routes. We calculated home–grocery distances and work–grocery distances, and the percentage of grocery shopping locations falling inside each of the three aforementioned spatial units, respectively. Our findings suggest that people were more likely to visit food stores beyond immediate residential areas or workplace areas. They often bypassed the closest supermarkets near home or work, whereas they were more likely to shop along their commuting paths. Our findings provide an example of the uncertain geographic context problem in a context of food activities, highlighting that activity space is a more comprehensive measure for assessing food exposures and food shopping activities. Key Words: activity spaces, food shopping locations, healthy food environment, residential neighborhoods, workplace neighborhoods.

Application of the Cloud Model Synthesis Method in Ecological Evaluation of Waterways

The cloud model synthesis method based on the membership cloud theory combines the fuzziness and randomness of uncertain problems in reality and is a model that can realize the transformation between qualitative concepts and quantitative data compared with the traditional fuzzy theory system. The theory and method are relatively lacking in the research work of waterway ecological evaluation. In view of the abovementioned characteristics and the advantages of wide applications of the membership cloud model, this paper takes the ecological evaluation of the Jingjiang River waterway as an example and applies the cloud model synthesis method to the comprehensive evaluation of waterway ecology. The cloud generator MATLAB code is used as a tool to combine the expert scoring data of the Jingjiang ecological waterway comprehensive evaluation system, and the clouding principle of human scoring variables is applied to conduct a comprehensive evaluation of the ecological nature of the Jingjiang waterway from 2011 to 2015. The results show that the cloud model synthesis method is applicable to the ecological evaluation of waterways and has the advantages of being applicable to subjective and objective data as well as retaining the uncertainty of each element in the evaluation system in the calculation process. This research can play a supplementary and perfect role for the method of waterway ecological evaluation.

A probabilistic linguistic thermodynamic method based on the water-filling algorithm and regret theory for emergency decision making

Since thermodynamics can describe the energy of matter and its form of storage or transformation in the system, it is introduced to resolve the uncertain decision-making problems. The paper proposes the thermodynamic decision-making method which considers both the quantity and quality of the probabilistic linguistic decision information. The analogies for thermodynamical indicators: energy, exergy and entropy are developed under the probabilistic linguistic circumstance. The probabilistic linguistic thermodynamic method combines the regret theory which captures decision makers’ regret-aversion and the objective weight of criterion obtained by the water-filling algorithm. The proposed method is applied to select the optimal solution to respond to the floods in Chongqing, China. The self-comparison is conducted to verify the effectiveness of the objective weight obtained by the water-filling algorithm and regret theory in the probabilistic linguistic thermodynamic method. The reliability and feasibility of the proposed method are verified by comparative analysis with other decision-making methods by some simulation experiments and non-parametric tests.

A Weighted Bonferroni-OWA Operator Based Cumulative Belief Degree Approach to Personnel Selection Based on Automated Video Interview Assessment Data

Asynchronous Video Interviewing (AVI) is considered one of the most recent and promising innovations in the recruitment process. Using AVI in combination with AI-based technologies enables recruiters/employers to automate many of the tasks that are typically required for screening, assessing, and selecting candidates. In fact, the automated assessment and selection process is a complex and uncertain problem involving highly subjective, multiple interrelated criteria. In order to address these issues, an effective and practical approach is proposed that is able to transform, weight, combine, and rank automated AVI assessments obtained through AI technologies and machine learning. The suggested approach combines Cumulative Belief Structures with the Weighted Bonferroni-OWA operator, which allows (i) aggregating assessment scores obtained in different forms and scales; (ii) incorporating interrelationships between criteria into the analysis (iii) considering accuracies of the learning algorithms as weights of criteria; and (iv) weighting criteria objectively. The proposed approach ensures a completely data-driven and efficient approach to the personnel selection process. To justify the effectiveness and applicability of the suggested approach, an example case is presented in which the new approach is compared to classical MCDM techniques.

Extended Form of Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices

An extended form of robust continuous-time linear programming problem with time-dependent matrices is formulated in this paper. This complicated problem is studied theoretically in this paper. We also design a computational procedure to solve this problem numerically. The desired data that appeared in the problem are considered to be uncertain quantities, which are treated according to the concept of robust optimization. A discretization problem of the robust counterpart is formulated and solved to obtain the ϵ-optimal solutions.

An integrated multicriteria group decision making methodology for property concealment risk assessment under Z-number environment

The complexity and opacity of individual property concealment seriously impede the court's judicial execution. Property concealment risk assessment can assist law enforcement officers in predicting the probability of judgment debtor’s concealment behavior in advance and improve enforcement efficiency. However, few studies have explored the property concealment risk assessment from the perspective of qualitative multicriteria decision making, considering the uncertainty of expert’s evaluation and the non-complementarity between assessing criteria. To fill this gap, we propose a novel integrated multicriteria group decision-making methodology (MCGDM) under the Z-numbers environment to rank the concealing risk of judgment debtors. First, Z-numbers are employed to characterize the uncertainty and reliability of cognitive information simultaneously. Next, we present an expert weight determining method based on the degree of group consistency and reliability under the Z-numbers environment (WCRZ). Then, an innovative score function is presented, extending the ELECTRE- III method to Z-number environment to obtain individual outranking relations. Moreover, we develop the weighted Copeland method to aggregate individual rankings and obtain comprehensive risk prioritizations. Finally, an application case in concealing property risk ranking illustrates the proposed method. Results show that the proposed method can be successfully applied to practical complex decision-making problems, and it obtains more reasonable outcomes than conventional methods, with lower computational complexity and higher group consensus. It is the first study to model the concealing risk of judgment debtors, and the proposed method can be employed to address complex, uncertain decision problems in the real world.

Hardness of uncertain segment cover, contiguous SAT and visibility with uncertain obstacles

In this paper, we prove that the uncertain segment cover problem is NP-hard. The uncertain segment cover problem, which appears in solving the question of visibility of a segment in the plane from a given point in the presence of uncertain obstacles, asks if a given interval can be covered by a collection of uncertain sub-intervals having two possible positions. This is done by showing that this problem is equivalent to a special version of the SAT problem that we will call contiguous SAT. In a contiguous SAT problem a CNF formula with a given ordering on its clauses is given such that any literal appears contiguously. We prove that contiguous SAT problem is NP-hard and as a consequence it follows that the uncertain segment cover problem is NP-hard. The approximation solution of this problem and its hardness are also studied.

Robust duality for nonconvex uncertain vector optimization via a general scalarization

ABSTRACT This paper concentrates on robust duality relations for uncertain cone-constrained vector optimization problems in more general nonconvex settings. First, different from the existing results, a new class of generalized Lagrange functions of the considered problem is introduced by combining the image space analysis method and scalarization technique. Then, the Lagrange robust vector dual problem is formulated. Subsequently, the results of robust weak duality, strong duality and converse duality are given respectively, which characterize vector dual relations between the primal worst and dual best problems. Simultaneously, some examples are given to illustrate our results.

Design and Application of BP Neural Network Optimization Method Based on SIWSPSO Algorithm

BP neural network method can deal with nonlinear and uncertain problems well and is widely used in the construction of classification, clustering, prediction, and other models. However, BP neural network method has some limitations in fitting nonlinear functions, such as slow convergence speed and easy local optimal convergence rather than global optimal convergence. In order to solve the insufficiency, the optimization approach applying BP neural networks is discussed. This paper proposes a simplified PSO algorithm based on stochastic inertia weight (SIWSPSO) algorithm to optimize BP neural network. In order to test the effect and applicability of the method, this paper established a quality safety risk warning based on SIWSPSO-BP network and selected the detection data of intelligent door lock products for risk warning experiment. The experimental results show that the convergence speed of SIWSPSO-BP model was increased by two times and the accuracy of product quality risk warning reached 85%, which significantly improves the accuracy and learning efficiency of risk warning.

Investigation of Spatial Orientation and Kinetic Energy of Reactive Site Collision between Benzyl Chloride and Piperidine: Novel Insight into the Microwave Nonthermal Effect.

Microwave nonthermal effect in chemical reactions is still an uncertain problem. In this work, we have studied the spatial orientation and kinetic energy of reactive site collision between benzyl chloride and piperidine molecules in substitution reaction under microwave irradiation using the molecular dynamics simulation. Our results showed that microwave polarization can change the spatial orientation of reactive site collision. Collision probability between the Cl atom of the C-Cl group of benzyl chloride and the H atom of the N-H group of piperidine increased by up to 33.5% at an effective spatial solid angle (θ, φ) of (100∼110°, 170∼190°) under microwave irradiation. Also, collision probability between the C atom of the C-Cl group of benzyl chloride and the N atom of the N-H group of piperidine also increased by up to 25.6% at an effective spatial solid angle (θ, φ) of (85∼95°, 170∼190°). Moreover, the kinetic energy of collision under microwave irradiation was also changed, that is, for the collision between the Cl atom of the C-Cl group and the H atom of the N-H group, the fraction of high-energy collision greater than 6.39 × 10-19 J increased by 45.9 times under microwave irradiation, and for the collision between the C atom of the C-Cl group and the N atom of the N-H group, the fraction of high-energy collision greater than 6.39 × 10-19 J also increased by 29.2 times. Through simulation, the reaction rate increased by 34.4∼50.3 times under microwave irradiation, which is close to the experimental increase of 46.3 times. In the end, spatial orientation and kinetic energy of molecular collision changed by microwave polarization are summarized as the microwave postpolarization effect. This effect provides a new insight into the physical mechanism of the microwave nonthermal effect.

Deep reinforcement learning for the dynamic and uncertain vehicle routing problem

Deep reinforcement learning for the dynamic and uncertain vehicle routing problem

Wide-area damping power system control based on robust self-triggered model predictive control

Unavoidable random disturbances during the operation of large-scale interconnected power systems may undermine their stability. To prevent this problem, we propose a damping control method based on robust self-triggered model predictive control. First, we linearize the power system model and determine the controller installation location and feedback signal through geometric measurements. Subsequently, the model order is reduced by applying Schur method for balanced truncation. According to the assumed distribution and boundary range of random disturbance, the multi-cell robust predictive control minimax optimization problem described by the vertex is established. By deriving the upper bound of the maximum problem, the minimax problem is transformed into minimizing the upper bound problem to deal with the uncertain problem, which is transformed into linear matrix inequality for controller design. Finally, we introduce a self-triggered control strategy that avoids solving a constrained optimization problem at every time step. This strategy reduces the number of controller responses and resource requirements for sampling and communication, thereby improving computational efficiency. Selecting the two zone four-machine system as the test system, the simulation results demonstrate that the proposed control strategy can effectively eliminate the effect of random disturbances on the stable operation of power systems, improve the damping characteristics of power systems, and suppress low-frequency oscillations.

Approximate Analytic–Numeric Fuzzy Solutions of Fuzzy Fractional Equations Using a Residual Power Series Approach

In this article, we consider a reliable analytical and numerical approach to create fuzzy approximated solutions for differential equations of fractional order with appropriate uncertain initial data by the means of a residual error function. The concept of strongly generalized differentiability is utilized to introduce the fuzzy fractional derivatives. The proposed method provides a systematic scheme based on generalized Taylor expansion and minimization of the residual error function, so as to obtain the coefficients values of a fractional series based on the given initial data of triangular fuzzy numbers in the parametric form. The obtained approximated solutions are provided within an appropriate radius to the requisite domain in the form of rapidly convergent fractional series according to their parametric form. The method’s performance and applicability are verified by applying it on some numerical examples. The impact of r-levels and fractional order γ is presented quantitatively and graphically, showing the coincidence between the exact and the fuzzy approximated solutions. Moreover, for reliability and accuracy, our obtained results are numerically compared with the exact solutions and with results obtained using other methods described in the literature. This indicates that the proposed approach overcomes the difficulties that appear in other approaches to create fractional series solutions for varied uncertain natural problems arising within the fields of applied physics and engineering.