Interval Weights Research Articles

Hybrid reliability analysis method for systems with random and non-parameterized p-boxes based on weight coefficients

This paper establishes a hybrid variable system failure probability optimization model based on sampling methods and weighting coefficients. By introducing auxiliary input variables, important sampling functions, and p-box, failure samples are mapped from the random variable space to the p-box variable space. The new weight coefficients are constructed, including important sampling weights and interval weights. Combining discretization methods and Monte Carlo simulation (MCS), the interval weights are transformed into variables, and constraints conforming to the p-box variable distribution are constructed. After calculating the weighting coefficients for all failure samples, the new failure probability optimization model is built. This model is independent of the performance functions and does not involve cyclic optimization, with computational complexity only related to the dimensions. Six cases are used for method comparison, validating that the new method exhibits higher efficiency and accuracy.

Research on the spacecraft ground equivalence test assessment problem: A comprehensive assessment method combining interval-type evaluation and prospect-two-dimensional cloud

For the complex dual-attribute qualitative assessment problem of spacecraft ground equivalence tests, the paper proposes a comprehensive assessment method that integrates interval-type evaluation with prospect theory and the two-dimensional cloud model. Firstly, to reduce the difficulty of determining indicator weights, the paper adopts interval-type evaluation and obtains reasonable interval weights of each indicator under dual attributes by interval analytic hierarchy process (IAHP). Secondly, to reduce the uncertainty of assessment and achieve the transformation of interval weights to value weights, the paper combines the prospect theory to obtain the value weight of each indicator that can maximize the personality preference satisfaction of the decision-maker by maximizing the integrated prospect value. During this period, to avoid the construction of a complex score function, the theoretical gain and loss values of indicator evaluation were obtained directly from the theoretical calculation based on the location of interval evaluation results in relation to interval psychological reference points. Again, to judge the validity of the interval evaluation of indicators, the paper theoretically derives an inverse cloud generator for interval-type samples and then realizes the validity analysis of the interval evaluation of indicators based on the 3-sigma principle of clouds. Then, to solve the problem of dual-attribute assessment of equivalence tests, the paper achieves the effective assessment of spacecraft ground equivalence tests through inter-cloud aggregation and similarity calculation of two-dimensional cloud models. Finally, the application of the method in a specific assessment case verifies the feasibility, validity, and practicality of the method in this paper.

Research on improvements of fraud detection system: basing on improved machine learning algorithms

Nowadays, commercial fraud behaviors commonly occur in many industries. However, due to obstacles like concept drift, imbalanced dataset and uneven distribution of fraud entries, Fraud Detection System (FDS) fails to identify such behaviors. Among the problems mentioned above, most research focus on dealing with skewed dataset. This paper first presents common application scenarios of FDS which consist of credit card fraud, insurance fraud and supply chain fraud. Then, this study introduces five representative methods in dealing with problems mentioned above, which are K Nearest Neighbors-Synthetic Minority Oversampling Technique-Long Short-term Memory Networks (kNN-SMOTE-LSTM), Generative Adversarial Nets-AdaBoost-Decision tree (GAN-AdaBoost-DT), Wasserstein GAN-Kernel Density Estimation-Gradient Boosting DT (WGAN-KDE-GBDT), Time-LSTM (TLSTM) and Adaptive Synthetic Sampling-Sequential Forward Selection-Random Forest (ADASYN-SFS-RF). KNN-SMOTE-LSTM adopts KNN as an identifying classifier so as to only retain true samples. GAN-AdaBoost-DT generates new samples without referring to real transactions. WGAN-KDE-GBDT uses Wasserstein Distance as distance measurement instead, and thus improves training speed and guarantees successful generation. TLSTM tires to consider the weights of different time intervals and measures the similarity between the simulated behavior and the genuine behavior. ADASYN-SFS-RF employs SFS algorithm, basing on RF, to only reserve optimal subsets of features. Finally, result metrics prove that those improved algorithms do improve the overall performance of FDS, even if with limitations at some indicators.

An analytical framework for the best–worst method

Since the development of the best–worst method (BWM) in 2015, it has become a popular research focus in multi-criteria decision-making. The original optimization problem of the BWM is a nonlinear min–max model that can lead to multiple optimal solutions, while the linear model of the BWM produces a unique solution. The two models need to be solved by optimization software packages. In addition, although the linear model of the BWM can obtain a unique solution, it produces different feasible regions than the nonlinear model of the BWM, and it changes the objective function. This study aims to solve the nonlinear model of the BWM mathematically to obtain the analytical forms of the optimal solutions. First, we transform the original nonlinear model of BWM into an equivalent optimization model driven by the optimally modified comparison vectors. The equivalent BWM provides a solid basis for computing the analytical solutions. Second, for not-fully consistent pairwise comparison systems, we strictly prove that there is only one unique optimal solution with three criteria, and there might be multiple optimal solutions with more than three criteria. We further develop the analytical forms of these unique and multiple optimal solutions and the optimal interval weights. Third, we develop a secondary objective function to select a unique solution for the BWM. The secondary objective function retains all the characteristics of the original nonlinear model of the BWM, and we find the unique solution analytically. Finally, some numerical examples are examined, and a comparative analysis is performed to demonstrate the effectiveness of our analytical solution approach.

Choice of Solutions in the Design of Complex Energy Systems Based on the Analysis of Variants with Interval Weights

Ensuring high-quality and uninterrupted power supply to consumers is one of the main problems of creating reliable power systems of a new generation. It is associated with the implementation of an integral assessment of the technical state of equipment of the power stations and substations, based on technical diagnostics data. Integral assessment involves the choice of ranges of the set of parameters of the technical state for groups of constituent elements of equipment, as well as the determination of their weight coefficients. Currently, the problem is solved with the help of expert assessments, arbitrarily in each specific case, which may lead to an incorrect integral assessment of the state of the equipment. The principle of decomposition makes it possible to determine the individual performance characteristics of each of them. At the same time, their subsequent aggregation ensures that the emergent properties of the system are taken into account. Such an approach was used in this work to evaluate individual types of equipment and their constituent elements. The algorithm for constructing a tree with a minimum random weight, proposed in this paper, makes it possible to increase the validity of decisions. They are made at various stages of designing complex technical systems and include tasks with an integral assessment of the technical state of equipment of power plants and substations. In the proposed algorithm, as a result of using the tree of variants, a matroid is formed, on which, using the “greedy” algorithm, the optimal solution can be determined.

A Guide to Integrating Expert Opinion and Fuzzy AHP When Generating Weights for Composite Indices

Composite indices are a great tool for researchers and policymakers alike as they provide a simplification of reality of complex phenomena, as well as their enabling ability for cross-country comparisons. A troublesome issue with constructing composite indices is the selection of the weighting system as it can greatly influence the results of the index developed. One of the most reliable weighting systems is the expert weighting system, where experts on the topic being studied are delegated the weight selection process, and the average of their responses are then transformed into weights. The limitation of this method, however, is the high subjectivity, uncertainty, and inconsistency of the expert responses. This paper seeks to address this limitation by providing a guide to researchers on how to improve the expert weights by subjecting them to the fuzzy analytic hierarchy process (FAHP) method for multicriteria decision making (MCDM) to compute the fuzzy weights, a more objective and reliable weights relative to expert weights. That said, and despite the benefits of the FAHP method, it can produce weights that can skew the composite index results. To address this limitation, the study introduces the interval weights, which are calculated by finding the midpoint between the expert weights and the fuzzy weights. The resulting interval weights exhibit the benefits of both principal component analysis (PCA) and the FAHP process, the difference being that PCA cannot be applied for noncompensatory indices.

Bounded error modeling using interval neural networks with parameter optimization

Aiming at the issue of interval modeling of uncertain systems, this article proposes a data-based interval neural network (INN) optimization modeling method that combines interval analysis with a neural network and particle swarm optimization (PSO) algorithm, adopts an INN model with interval weights and interval thresholds, and constructs an interval multiobjective PSO (IMOPSO) algorithm to evolve the network, thereby modeling an uncertain system under an unknown-but-bounded error (UBBE) condition. Considering the cases of known and unknown error bounds in UBBE, two optimization objectives, i.e., interval coverage and interval width, are constructed to optimize the parameters of INN, aiming to improve the accuracy and reliability of prediction. The proposed method effectively solves many constraints such as the model structure demanded and error bounds known in UBBE modeling, and provides a new method of data-based interval system modeling. The method was applied to model linear and nonlinear systems, and simulation results showed that the established INN models have good prediction effects and dynamic characteristics, which demonstrate the effectiveness of the method.

Various approaches to multiobjective linear programming problems with interval costs and interval weights

Various approaches to multiobjective linear programming problems with interval costs and interval weights

Multicriteria assessment of biomass gasification‐based hybrid energy systems in remote areas

AbstractThis study proposes an approach to multicriteria assessment of biomass gasification‐based hybrid energy systems in remote areas using the modified SMARTS method. This approach involves comparing two groups of hybrid energy systems: those based on biomass gasification and those based on diesel generation, which is already widely used in remote areas. The hybrid energy system configurations are developed using the HOMER software in terms of the maintenance schedule of biomass gasifiers. Alternatives are compared according to the criteria of economic, technical, environmental and social efficiency. The proposed modification of the SMARTS method uses both crisp and interval weights of criteria and criteria estimates for decision making under uncertainty of the preferences and input data, especially in terms of initial capital and operating costs, feedstock and diesel fuel prices. The final choice of a hybrid energy system is based on the relative dominance indicator. Two case studies of isolated rural settlements show that biomass gasifiers when supplemented with diesel generation and other renewable energy sources are the best sustainable solution as compared with other feasible alternatives. These conclusions are robust to sufficiently significant changes in preferences and input data. © 2022 Society of Chemical Industry and John Wiley & Sons, Ltd.

Neutrosophic approach to Dynamic Programming on group Decision Making problems

In this article, complicated group decision-making situations where the preference data is represented by linguistic variables are addressed using the dynamic programming approach. Making conclusions clear through accurate figures is difficult for decision-makers due to the complexity and ambiguity of reality. Neutrosophic is used to encode the linguistic variables because they cannot be directly computed. Neutrosophic sets are used to manage indeterminacy in a practical situation. The relationships between single and interval Neutrosophic sets are then measured using novel distance and similarity models. The suggested dynamic programming interval-based clustering methodology is then used to group the decision-makers. Additionally, a novel method for computing the interval weights of decision-makers and clusters is described, accounting for both the cluster center and group size. A centroid-based ranking system is then used to compare and order the possibilities, and illustrated experiments are presented to demonstrate how effectively the suggested technique operates. Comparisons and discussions are also done to show its superiority.

Evaluation of Vehicle Handling Stability Based on Interval TOPSIS and Entropy Weights

The purpose of this study is to evaluate the handling stability of vehicle from the perspective of users using a multi-criteria decision-making approach with interval numbers. In order to achieve this purpose, the evaluation criteria easy for drivers to understand were constructed based on questionnaire, the interval weights of the criteria were calculated using the entropy weight method with interval numbers, and the interval TOPSIS method was used to evaluate the vehicle handling stability. As the improvement of the method, a new method to determine the crisp value of the interval weight was given, and the relative closeness index used for ranking alternatives was extended to a new additive ranking index. The proposed method was used to evaluate the handling stability of 12 vehicles, and the results may provide some basis for vehicle R & D and design.

A type-1 OWA operator for Extended Comparative Linguistic Expressions with Symbolic Translation

Recently, a new representation model has been proposed to improve the interpretability and accuracy of Computing with Words (CW) processes, the so-called Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT). It extends the concept of comparative linguistic expressions based on hesitant fuzzy linguistic term sets into a continuous domain by means of the symbolic translation used in the linguistic 2-tuple model. The aggregation of this kind of information is vital when solving decision making problems, but as the field of ELICIT information is still quite new, not many aggregation operators have been defined for it. Therefore, taking into account the need to deal with the fuzzy representation of ELICIT information for its aggregation, we propose the ELICIT type-1 OWA (ELICIT-t1-OWA) operator based on the equivalent α−level type-1 OWA operator to simplify the CW processes by using ELICIT trapezoidal fuzzy representations. The ELICIT-t1-OWA operator will use interval weights induced by an interval-valued linguistic quantifier to aggregate ELICIT expressions and then its properties will be studied. Additionally, a way to deal with both the weights and arguments of the ELICIT-t1-OWA operator is provided in the form of fuzzy numbers. Finally, a decision making model dealing with ELICIT information that carries out the aggregation by using the proposed ELICIT-t1-OWA operator is developed and a numerical example to show its effectiveness is introduced.

Practical approximate indoor nearest neighbour locating with crowdsourced RSSIs

In the indoor space, finding the nearest neighbour is of great importance in location-based services. Received Signal Strength Indication (RSSI) has received much attention due to its simplicity and compatibility with existing hardware, which has been widely used for indoor localization. Existing indoor nearest neighbour search methods are based on the real walking distance, which need ground survey and much labor work to measure many real distances. Crowdsourcing is a low-cost and efficient way to collect the RSSI of indoor space without expert surveyors and designated coordinates for RSSI collection points. The crowdsourced RSSIs can reflect the location of indoor objects and RSSI-based localization method is the simplistic method as it needs low hardware requirements, low deployment cost and no survey indoor distance. So we study how to search the nearest neighbour of indoor objects with crowdsourced RSSIs. To address this problem, we propose a graph with interval weights, called I-graph, which can connect the RSSIs and represent the topology of indoor space. We also construct a search tree index D-tree, which can index the graph with interval weights and search the nearest neighbour objects efficiently. We also propose a novel distance metric for RSSI and study the relationship between the RSSI distance and the indoor distance. To locate nearest neighbour of indoor objects with crowdsourced RSSIs, we devise efficient search algorithms and pruning strategies for computing the nearest neighbour query. We demonstrate the efficiency and effectiveness of the proposed solution through extensive experiments with two real data sets.

Air Pollution Assessment in China: A Novel Group Multiple Criteria Decision Making Model under Uncertain Information

Assessment of and controlling air pollution are urgent global issues where international cooperation is deemed necessary. Although a very relevant data source can be obtained through continuous monitoring of air quality, measuring air pollutant concentrations is quite difficult when compared to other environmental indicators. We mainly have three different aims for the current study: (1) we propose the computation of the interval weights of decision makers (DMs) based on a group multiple criteria decision making (GMCDM) model; (2) we aim to rank the overall preferences of DMs by the possibility concepts; (3) we aim to evaluate the air quality in China using the most recent data based on our proposed method. We consider three monitoring stations, namely Luhu Park, Wanqingsha, and Tianhu, and the data for SO2, NO2, and PM10 are collected for November 2017, 2018, and 2019. The results from our innovative model show that November 2019 had the best air quality. Finally, robustness analyses are also performed to confirm the discriminatory power of the proposed approach.

An acceptability index based approach for solving shortest path problem on a network with interval weights

Based on the acceptability index for comparison of any two imprecise values, efficient algorithms have been proposed in the literature for solving shortest path (SP) problem when the weights of connected arcs in a transportation network are represented as interval numbers. In this study, a generalized Dijkstra algorithm is proposed to handle the SP problem with interval weights. Here it is shown that once the acceptability index is chosen, the interval SP problem is converted into crisp one, which is easily solved by the standard SP algorithms. The main contribution here is the reduction of the computational complexity of the existing algorithm for solving interval SP problem. To show the advantages of the proposed algorithm over existing algorithm the numerical example presented in literature is solved using the proposed algorithm and the obtained results are discussed. Moreover, an small sized telecommunication network is provided to illustrate the potential application of the proposed method. Finally, the practical relevance of the proposed algorithm is evaluated by means of a large scale pilot case where a pharmaceutical shipment between the cities in Iran should be transported.

Customer-oriented product and service design by a novel quality function deployment framework with complex linguistic evaluations

Quality function deployment (QFD), as a widely-used quality management method, can effectively capture customers’ preferences of products and services by involving lots of evaluations including the weights of customer requirements, the performance of alternatives under different design requirements and the interactions of design requirements. However, there are challenges to use this tool to solve complex customer-oriented design problems because of the uncertain information regarding customer requirements, design requirements and alternatives’ performances. To address the inherent uncertainty of qualitative information in the framework of QFD, this paper incorporates the continuous interval-valued linguistic term set, a novel information representation model, to depict the complex linguistic evaluations of experts, and then introduces a novel QFD framework with complex linguistic evaluations. Such a QFD framework is constructed with three phases: the first step is to determine the importance degrees of customer requirements and additional requirements, which are important for product deployments, with the help of the best worst method; the second step is to determine the relative importance of design requirements; the third step is to calculate the interval weights of alternatives according to the uncertainty degrees of evaluations and the weights of design requirements. The inner-element correlations are considered in the whole procedure of the proposed QFD. The proposed method is applied to the aviation service development for Sichuan Airlines in China to illustrate its practicability. It is noted that this method can also be applied to various cases about product and service design.

A hesitant fuzzy wind speed forecasting system with novel defuzzification method and multi-objective optimization algorithm

Owing to the nondeterministic nature of wind speed, the conventional fuzzy time series forecasting model has difficulty in establishing a common membership level. Therefore, in this study, the fuzzy series forecasting model was improved based on hesitant fuzzy sets. A hesitant fuzzy wind speed forecasting system with a novel defuzzification method and multiobjective optimization algorithm was developed. First, an advanced decomposition model is employed to extract the effective feature and remove the noise component from the raw wind speed series. Then, the universe of discourse is partitioned into equal and unequal intervals by multifuzzification methods and merged by aggregating hesitant information. A multiobjective intelligent optimization algorithm is applied to determine the optimal weights of different intervals accurately and stably. Furthermore, a novel defuzzification model based on an ordered weighted averaging operator and a regular increasing monotone quantifier is proposed to calculate the final forecasting results. The crucial strengths of the developed system are verifying the possibility of enhancing the performance of wind speed forecasting models by improving conventional fuzzy time series forecasting models and integrating them with decomposition models and artificial-intelligence models. Typical wind speed series datasets with different resolutions were selected to evaluate the performance of the proposed system, and experimental results prove that the proposed system outperforms other comparison models with high forecasting accuracy and computing efficiency.

Distance-Based Consistency Measure and Priority Weights of Best-Worst Multi-Criteria Decision Making Method

Best-Worst method (BWM) is a new multi-criteria decision-making method based on pairwise comparisons, but only the comparisons concerning the best and the worst alternatives or criteria. This method shows some significant advantages in the simplicity with a less requirement of comparison data and reliability with better consistency. This paper proposes a new consistency measure method based on the distance of the vectors of reference comparisons in BWM because the difference of the preference in two vectors directly affects the reliability of results. Through the establishment of the threshold of consistency ratio, we supplement the definition of satisfactory consistency of the comparisons in BWM. With comparisons satisfying the acceptable consistency, we use linear programming models to find all possible priority weights between the preferences given by decision maker and derive interval weights. For comparisons with unacceptable consistency, another approach is presented to find the interval weights meeting the consistent requirement. At last, several examples are used to illustrate the details of process.

On consistency and priority weights for interval probabilistic linguistic preference relations

When expressing preferences with different probability weights for different linguistic terms, only partial assessment information is usually to be provided. Then the probability information can be normalized to the interval probability, hence, using interval probabilistic linguistic term sets (IPLTs) is more appropriate. Considering this situation, interval probabilistic linguistic preference relation (IPLPR) is proposed. To measure the consistency of IPLPR, the consistency definition of IPLPR is put forward. For the consistent IPLPR, from which an expected consistent PLPR can be obtained, we can obtain interval weights as the final priorities by using the pairs of linear programming models. We also create the probabilistic linguistic geometric consistency index (PLGCI) of PLPRs to judge whether the IPLPR is satisfactorily consistent. For an unsatisfied consistency IPLPR, the adjusting algorithm is proposed. Probability information is firstly considered to be adjusted. If it is not possible to achieve satisfactory consistency through the adjustment of probability information, then the linguistic terms will be adjusted. In addition to examples of different situations, such as the consistency, satisfactory consistency and consistency improvement, the application example is also given to show the practicability of the proposed methods.

A smart adaptive particle swarm optimization–support vector machine: android botnet detection application

Support vector machine (SVM) is a renowned machine learning technique, which has been successfully applied to solve many practical pattern classification problems. One of the difficulties in successful implementation of SVM is its different parameters (i.e., kernel parameter(s), penalty parameter (C) and the features available in the dataset), which should be well adjusted during the training process. In this paper, a new approach called smart adaptive particle swarm optimization–support vector machine (SAPSO–SVM) is developed to adapt the parameters of optimization algorithm (i.e., inertia weight and acceleration coefficients) to the latest changes in the search space, so that each particle explicitly explores the search space based on the latest changes made to Personal best, Global best and other particle locations. In this algorithm, using the changes in Personal best and Global best at each stage of execution, the new evolution factor values are designated and the interference of the intervals of inertia weight is eradicated. Then, the states of each particle (i.e., convergence, exploitation, exploration, jumping-out) at each stage of administration, based on the interval weights, are specified accurately. By fine tuning the parameters of SAPSO, this algorithm can acquire the best optimal responses for SVM parameters. The results obtained from the SAPSO–SVM method demonstrate the superiority of this method in four different measures (i.e., sensitivity, specificity, precision, accuracy) in comparison with the other three similar ones. Finally, the top 20 features of Android botnets are somehow introduced by the proposed approach and three other approaches; firstly, these features are not encrypted by Android botnets, and secondly, are selected based on the best results.