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In many game theoretic environments, the precise crisp values of payoffs are not always easy to gather as real-life decision-making problems are not inevitably precise and symmetrically distributed in nature. Hence, there is a need to explore matrix games having unbalanced probabilistic linguistic information. To fill this research gap, this study proposes a concept of probabilistic multiplicative unbalanced linguistic (PM-UL) game in which the players express their responses in terms of PM-UL term. This type of PM-UL game is a useful technique for multiple criteria analysis. Further, to thoroughly capture the uncertainty involved in payoffs of such games, they are converted to probabilistic unbalanced linguistic clouds (PULCs) that describe the uncertainties of qualitative payoffs by implementing the uncertain transformation between PM-UL payoffs and quantitative values. The PULCs are represented by three numerical characteristics, i.e. expectation, entropy and hyperentropy. Hence, this model overcomes the inherent limitation of existing linguistic games where only the fuzziness of concepts is evaluated, by providing a PULC strategy and PULC value of the game. This procedure overcomes the loss of information occurring in the process of transformation of payoff values into quantitative ones. The defined methodology is implemented on a real-life working problem to demonstrate the effect and applicability in decision-making circumstances. [ABSTRACT FROM AUTHOR]

Architectural heritage health assessment is the basis of scientific repair and maintenance. However, existing methods do not adequately take into account the fuzziness, randomness and uncertainties unique to architectural heritage assessment. In this paper, a new evaluation model of VM-NCM is constructed by combining variable weight theory and normal cloud model theory. The model enables the combination of qualitative ratings and quantitative calculation, deals with the fuzziness in the assessment process, and resolves the randomness and reflects the uncertainty to a certain extent. Based on constructing the index system combining qualitative and quantitative indexes, the structural index values are acquired by the synergistic coupling of the fine laser point cloud model and finite element structural analysis model. The acquisition of surface index values is completed by the hyperspectral intelligent detection technology of surface materials and diseases. These reduce the generation of ambiguous information in the index detection process. An evaluation study is conducted using the Yingxian wooden pagoda in China as an example. The results show that this method takes into account the fuzziness and randomness in the evaluation process, and obtains more scientific and reliable evaluation results, which provides a research paradigm for assessing the architectural heritage health status. [ABSTRACT FROM AUTHOR]

DNA computing is one of the more popular computational methods currently studied, but the requirements for nucleic acid molecules in DNA sequences are high, and it is an important challenge to design reasonable and high-quality DNA sequences while satisfying various constraints. Evolutionary algorithms have good applications in DNA sequence optimization problems, but they still have some limitations. To this end, this paper proposes a JAYA algorithm based on normal clouds, referred to as IJAYA, which uses a combinatorial learning approach to update the optimal and worst positions, which is used to manipulate the subsequent merit search means, and then enhances the local search ability of individuals through the normal cloud model, and finally rejects the worst solutions through a harmony search algorithm to find more reasonable and high-quality solutions. The validity of IJAYA is verified in six benchmark functions, in comparison with multiple variants of JAYA and two statistical tests. In the DNA sequence design optimization problem, the average DNA metrics optimized by IJAYA are: 0 (Continuity), 0 (Hairpin), 59.43 (H-measure), 46.57 (Similarity) and 63.79 (Similarity). The feasibility and practicality of IJAYA was verified by comparing it with the solution algorithms proposed in recent years and ablation experiments. [ABSTRACT FROM AUTHOR]

In the consensus reaching process (CRP), experts are not infinitely compromising when adjusting opinions, and the "compromise limit" is used to reflect the limited compromise behaviors in the process of expert opinion adjustment. In complex and multiple social relations, experts tend to exhibit different behaviors according to their compromise limits. This paper aims to develop a novel CRP framework to promote a consensus that categorizes and manages experts based on their compromise limits. Firstly, the trust-interest network is defined to represent the multiple relations among experts, and the expert weights are calculated by considering the impact of interest manipulation on trust relations. Secondly, a novel cloud model-based minimum cost consensus model is established, which considers the mutual acceptance between the experts and the group, as well as the changes in the ranges of experts' hesitation and the collective acceptance. Thirdly, three behavior classifications are defined based on individual compromise limits and group acceptance ranges: cooperative behavior, hesitating non-cooperative behavior, and strong non-cooperative behavior, and a CRP optimization model is constructed to manage the three behaviors. Finally, a numerical example is given to illustrate the validity and superiority of the proposed model. [ABSTRACT FROM AUTHOR]

Rockburst is one of the common geological disasters in deep underground areas with high stress. Rockburst prediction is an important measure to know in advance the risk of rockburst hazards to take a scientific approach to the response. In view of the fuzziness and uncertainty between quantitative indexes and qualitative grade assessments in prediction, this study proposes the use of a normal cloud model to optimize the theory of unascertained measures (NC-UM). The uniaxial compressive strength (σc), stress coefficient (σθ/σc), elastic deformation energy index (Wet), and brittleness index of rock (σc/σt) are selected as the index of prediction. After data screening, 249 groups of rockburst case data are selected as the original data set. To reduce the influence of subjective and objective factors of index weight on the prediction results, the game theory is used to synthesize the three weighting methods of Criteria Importance Through Intercriteria Correlation (CRITIC), Entropy Weight (EW), and Analytic Hierarchy Process (AHP) to obtain the comprehensive weight of the index. After validating the model with example data, the results showed that the model was 93.3% accurate with no more than one level of prediction deviation. Compared with the traditional unascertained measure (UM) rockburst prediction model, the accuracy is 15–20% higher than that of the traditional model. It shows that the model is valid and applicable in predicting the rockburst propensity level. [ABSTRACT FROM AUTHOR]

The cloud decision support model is an effective technique for describing an ambiguous mapping between qualitative notions and their quantitative manifestations. However, the existing research on cloud models is based on balanced linguistic term set and cannot address information in an unbalanced linguistic form. Henceforth, to thoroughly capture the intrinsic fuzziness and vagueness of decision information an accurate decision model is required to acquire good solution. In this direction, the proposed work aims to introduce a cloud model based on multiplicative unbalanced linguistic term sets. To match our research requirements, we initially propose a multiplicative unbalanced point-based cloud model. The innovation of the model overcomes the inherent limitation of the existing cloud and is competent of producing new solution according to the cloud model theory. Furthermore, a generalized multiplicative unbalanced linguistic scale function is introduced. The proposed generalized function creates a map between the linguistic data and numerical interval values. Based on this rational conversion method, interval cloud variables are transformed, which overcomes the loss of information existing in the point-based cloud models where linguistic variables are transformed into a specific numerical value. The process is then used to demonstrate the accuracy and efficacy of the suggested model using a numerical example, which is then followed by a comparison study. The overall results typically show that the cloud model has excellent performance and provides better solutions. [ABSTRACT FROM AUTHOR]

In image segmentation, one important problem is the indeterminacy of pixel value. Based on fuzzy and probability theory, Cloud Model can better solve this same concept problem in segmentation. Methods based on Normal Cloud Model have been proposed here for improving the segmentation performance. Single-Kernel Extraction (SKE) and Multi-Kernel Extraction (MKE) methods have been introduced which are used for determining expected value of the Cloud Model during Cloud Transformation. In addition, a Maximum-Similarity Concept Promotion (MSCP) strategy based on Minimum-Distance Concept Promotion (MDCP) has been proposed and its theoretical validity has also been introduced. Image segmentation experiment results show that our algorithms get a strong adaptability and better image segmentation effect evaluation coefficient. [ABSTRACT FROM AUTHOR]

Catenary plays an important role in electrified railway. It is of great significance to sense the status of catenary. However, the current status sensing methods of catenary select weighting coefficients artificially calculate similarity from only one aspect and only consider the fuzziness of indicators without the randomness. Thus, a status sensing system of catenary with multiple indicators is constructed. The main process of this system is as follows: Firstly, fuzzy analytic hierarchy process method and improved criteria importance though inter-criteria correlation are used to get the subjective and objective weights, and least square method is used to obtain the combined weights, which reduces the influence of artificial experience. Secondly, Grey-Technique for Order Preference by Similarity to an Ideal Solution is used to calculate weighted similarity, so as to obtain the health score of each sensing indicator. Thirdly, the normal cloud model is used to handle the health score to obtain the membership degree of sensing objects, which consider both the fuzziness and randomness. Finally, the principle of maximum membership degree is used to determine health status of each sensing object, and the weighted average principle is used to verify the sensing results. Selecting a Chinese railway catenary as an example for verification, the results show that the system can sense the status of catenary accurately. [ABSTRACT FROM AUTHOR]

Water inrush in karst tunnels is a dynamic process in which internal and external factors are involved. The evaluation of this process is fuzzy, complex, and uncertain. In the current research, few articles give full consideration to the fuzziness and randomness of the water inrush evaluation with useful dynamic feedback. A new assessment method has been proposed for the water inrush evaluation based on a combination of the weighting method and normal cloud model. Specifically, an evaluation index system is forged and each index is quantitatively classified into four grades. A synthetic weighted algorithm combining the analytic hierarchy process, entropy method, and statistical methods is proposed to assign the index weight rationally. Based on the cloud generator algorithm, three numerical characteristics are calculated and a sufficient number of cloud droplets are generated. The membership degree of each index belonging to each grade is constructed and the integrated certain grades are determined. In this paper, the multi-factor normal cloud assessment method is applied to the risk assessment of the Qiyueshan tunnel. The assessment result of the risk grade is accurate, that is, the water inrush risk of different samples at the same risk grade can be reflected in figures. The results not only show high consistency with other assessment methods but are also in good agreement with the excavation results. The proposed cloud model method demonstrates good practical reference for risk assessment of tunnel construction in karst areas and can be applied to tunneling, mining, and other engineering practices in the future. [ABSTRACT FROM AUTHOR]

The uniform sampling strategy is widely used in time series segmentation, but unable to handle time warping problem or preserve the latent patterns in time series. To solve these shortcomings, a brand new data-driven segmentation method is proposed, which could segment time series into subsequences with different lengths adaptively. Then a time series classification method under the bag-of-word framework is proposed. Two kinds of mutually complementary features, i.e., interval feature and normal cloud model feature, are extracted from subsequences. And then time series are encoded into Fisher Vectors. Finally, a linear support vector machine is used as the classifier. Experiments on 43 UCR datasets show that the newly proposed method has promising classification accuracies comparing with state of the art baselines. Moreover, due to the data-driven segmentation and timesaving local feature extraction, the method has low time complexity, which is also demonstrated in the experiments. [ABSTRACT FROM AUTHOR]

A systematic work has been presented for condition assessment of suspension bridges in this study. Initially, a four-layer index system is built up. Subsequently, 45 experts are invited to determine the index weights by processing the experts’ opinions using the Group Decision-Making (GDM). The assigned weights seem more reasonable (especially weights of the tower and auxiliary facility) when compared with those in the existing China’s code. Next, assessment algorithms, the Local Variable Weight Model (LVWM) and Normal Cloud Model (NCM), are established based on the characteristics of the bridge condition assessment. The LVWM adjusts weight properly to make assessment results in line with the actual situation under extreme cases. The NCM describes not only the fuzziness but also the randomness in the assessment process. Finally, a case study is illustrated to verify the effectiveness of the methodology. For sake of highlighting the advantages of the LVWM, two more models are subjected to the case study, which are the Constant Weight Model (CWM) and Traditional Variable Weight Model (TVWM). Consequently, the assessment result of the LVWM is more in keeping with the actual situation than those of the CWM or TVWM. [ABSTRACT FROM AUTHOR]

The Fruit Fly Optimization Algorithm (FOA) is one of the latest swarm intelligence-based methods inspired by the foraging behavior of fruit fly swarm. To improve the global search ability and solution accuracy of the FOA, a bimodal adaptive fruit fly optimization algorithm using normal cloud learning (BCMFOA) is proposed in this paper. Based on the labor allocation characteristics of the swarm foraging behavior, the fruit fly population is divided into two groups in the optimization process according to their duties of searching or capturing. The search group is mainly based on the fruit fly's olfactory sensors to find possible global optima in a large range, while the capture group makes use of their keen visions to exploit neighborhood of the current best food source found by the search group. Moreover, the randomness and fuzziness of the foraging behavior of fruit fly swarm during the olfactory phase are described by a normal cloud model. Using a normal cloud generator and an adaptive parameter updation strategy, the search range of the fruit fly population is adaptively adjusted. Therefore, the ability of FOA to avoid local optima is enhanced greatly. Twenty-three benchmark functions are used to test the performance of the proposed BCMFOA algorithm. Numerical results show that the proposed method can significantly improve the global search ability and solution accuracy of FOA. Compared with existing methods such as PSO, DE, AFAS, the experimental results indicate that BCMFOA has better or comparative convergence performance and accuracy. The application to the multi-parameter estimation of a permanent magnet synchronous motor further confirms its good performance. [ABSTRACT FROM AUTHOR]

Scientific surrounding rock classification (SRC) of underground water-sealed oil reservoir caverns is greatly significant for reducing risks and costs during construction. As to underground water-sealed caverns, not only the stability and deformation of the surrounding rock, but also the requirement of the water-sealed function must be considered. At present, there is no special standard for the SRC of underground water-sealed caverns. Based on the cloud theory and principal component analysis (PCA) method, a novel analytical model was proposed for SRC of underground water-sealed caverns. Five indexes: rock strength, rock integrity, discontinuity surface characteristics, groundwater, and the angle between the horizontal plane and the main discontinuity were selected to establish a multi-index evaluating system. With enough measured samples, the weights of the five indexes were determined based on the PCA method. According to cloud theory, five indexes affecting the SRC were investigated to establish five corresponding single-index normal cloud models. Subsequently, the single-index certainty degrees to every grade of surrounding rock were calculated. Finally, combined with the weights, a multi-index certainty degree was calculated as guidance to classify the surrounding rock. The proposed novel model was applied to a case study, i.e., the first underground water-sealed oil reservoir in China. The evaluating results were in broad agreement with the excavation results. The present findings imply that the proposed novel model is an effective method for the SRC in underground water-sealed caverns and can provide some useful references to similar projects. [ABSTRACT FROM AUTHOR]