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In this paper, Protist algorithm (PA) and Otocyon megalotis optimization algorithm (OOA) are applied to solve the power loss lessening problem. Protist Algorithm (PA) is modelled based on the Protist's natural activities. Protist exists in moist places. The leading nutritious phase is Plasmodium, the energetic and vibrant phase of Protist. In this segment, the organic substance in Protist search for food in surroundings and conceals enzymes for digestion. Natural actions of Otocyon megalotis are emulated to design the OOA approach. In the projected OOA searching of regions in exploration, for foodstuff the Otocyon megalotis mark the prey in the space is indicated as a global exploration. Real power loss reduction and Voltage stability enhancement are the key objectives of the paper. To solve the problem, Protist algorithm (PA) and Otocyon megalotis optimization algorithm. In the course of the migration procedure, the anterior end outspreads and interconnected arterial system that authorize cytoplasm to stream inside. Then, mutation and cross-over probability are employed to augment the performance of the Protist algorithm (PA). With this integration engendering of the population is done. Mutation classes the population exploration agents (PN) in uphill order conferring to the agents appropriateness (fitness) cost. Consequently, the technique splits the organized agents into three fragments rendering to their fitness value. In which PN/3 denotes to the population possess pre-eminent (aptness) fitness values, subsequently with second pre-eminent and poorest aptness (fitness) values. Then, in this paper, Otocyon megalotis optimization algorithm (OOA) is applied for solving the Power loss lessening problem. In the subsequent segment, navigate during the haunt to seal prey previous to the hit was replicated as a local search. In exploration, the data obtained is shared to all the associates of the family unit for continued existence and growth. Examination of the nearby terrain is modelled with reference to the fitness of all entities. Most excellent entity has investigated the majority fascinating terrain and it will be shared with family unit of Otocyon megalotis. Primarily, Otocyon megalotis show that it not involved in hunting. Conversely, as soon as moving near to prey Otocyon megalotis will perform the attack in quick mode. This approach imitated and designed in the local search segment. Authenticity of the Protist algorithm (PA) and Otocyon megalotis optimization algorithm (OOA) is corroborated in 23 benchmark functions, IEEE 30, 57, 300 and 354 test systems. Power Loss reduction achieved with voltage stability enhancement. Real power loss reduction attained. Both the Protist algorithm (PA) and Otocyon megalotis optimization algorithm (OOA) performed well in solving the Power loss reduction problem. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method for solving the system of fuzzy relation equations (SFRE) with extended max–min composition for inverse inference problems. The properties of interval and constrained solutions with granular and relational structure of the solution set are investigated. The extended max–min SFRE can be represented in the form of the max–min subsystems aggregated using the min operator or dual min–max subsystems aggregated using the max operator. When decomposing the SFRE, the set of solutions can be decomposed into the lower and upper subsets bounded by the same aggregating solutions. Each lower (upper) subset is defined by the unique greatest (least) or aggregating solution and the set of minimal (maximal) solutions. Following Bartl et al. (Fuzzy Sets Syst 187:103–112, 2012), to avoid excessive granularity and ensure interpretability of the interval solutions when restoring causes through observed effects, the constraints in the form of linguistic modifiers are imposed on the measures of causes significances. The interval solutions are modeled by the complete crisp solutions, that is, the maximum solutions for the vectors of binary weights of the linguistic modifiers. The search for approximate solutions of the SFRE amounts to solving the optimization problem using the genetic algorithm. Due to the properties of the solution set, the genetic search for the lower and upper subsets is parallelized for each aggregating solution. The developed method makes it possible to simplify the search for the solution set based on the constraints on accuracy (interpretability) of the applied problem. [ABSTRACT FROM AUTHOR]

With the development of formal concept analysis, classical concept lattice cannot solve some problems in practice because of its strict conditions. Protoconcept, which is an extension of the formal concept, provides a new method of data processing. Three-way decisions is more in line with human cognition. Not like the decision of two ways, three-way cognition expands its scope of application. However, up to now, protoconcept is influenced by two-way decisions which leads to the restrictions of its applications. Hence, it is urgent to find a method to generalize protoconcept from the framework of two-way decisions. To give the solution to this urgent problem, the main contributions of this paper are the following: First, using the combination of protoconcept and three-way decisions, two models of three-way protoconcept are obtained. The algorithms for searching three-way protoconcept are built. Second, we investigate the constructions of three-way protoconcepts in double Boolean algebra. Third, the relationships between protoconcepts and three-way protoconcepts are found. Moreover, using examples that come from the real world, we explain the main results obtained above and show some applications. The two models for protoconcepts provided in this paper generalize the fields of thought from two-way decisions to three-way decisions. This follows that they are more in line with human thinking. Hence, the two models will certainly generalize the applications of protoconcept theory in the future. [ABSTRACT FROM AUTHOR]

The probabilistic linguistic term set (PLTS) shows great superiority in expressing decision-makers' opinions. The multi-attribute decision-making (MADM) problem under a PLTS environment has gained attention from numerous scholars. However, the majority of current studies are not precise enough in capturing information on PLTS. To address this problem, this paper presents a preference ranking organization method for enrichment of evaluations (PROMETHEE) based on the redefined PLTS and novel score function to solve MADM problems under a PLTS environment. First, an asymmetric normalized PLTS based on prospect theory (ANPLTSPT) is developed. Compared with the PLTS, ANPLTSPT offers a more realistic portrayal of decision-makers' psychological state while ensuring the superiority of the PLTS. Second, regarding the structural complexity of ANPLTSPT, this paper attempts to simplify the computational process through a score function that can embody the characteristics of ANPLTSPT. Inspired by previously formulated score functions, a novel score function called Score-InInHe is developed, the corresponding definitions are given, and some further properties are discussed. With the support of the proposed Score-InInHe, the total score entropy is defined and an objective method to determine the attribute weights is proposed. Finally, the proposed approach is applied to the selection of a green supplier and the determination of air quality. The validity and realistic applicability of the proposed approach are demonstrated through comparative analyses and discussions. [ABSTRACT FROM AUTHOR]

In the process of facial expression recognition, face detection is the prerequisite, image preprocessing is the foundation, facial expression feature extraction is the key, and facial expression classification is the target. Effective feature extraction in this process can improve the accuracy of facial expression classifications. On the other hand, traditional facial expression recognition methods are not only complicated in the feature extraction process, but also unable to obtain more in-depth high-semantic features and deep features from the original image. To solve the above problems, this paper proposes a facial expression recognition method based on multi-channel fusion and lightweight neural network. First, a cascade classifier based on Haar features is used to detect the face region of the facial expression image. Second, the local binary pattern (LBP) is used to extract the local texture features from the face region. Third, face edge features are simultaneously obtained by performing edge detection in the face region based on the Canny edge detection algorithm. Fourth, the obtained face image, LBP texture feature image, and edge detection Canny image are fused, and the fused image is input into the constructed lightweight neural network for training and recognition. Experiments are carried out on the public image databases Facial Expression Recognition 2013 (Fer2013) and extended Cohn–Kanade (CK +) using the hold-out cross-validation method. The experimental results show that the proposed method effectively extracts more complete image features by combining traditional feature extraction algorithms with deep learning feature extraction algorithms, improves the accuracy and robustness of facial expression recognition, and has better recognition rate and generalization ability compared to other mainstream methods. [ABSTRACT FROM AUTHOR]

How to handle conflict in Dempster-Shafer evidence theory is an open issue. Many approaches have been proposed to solve this problem. The existing approaches can be divided into two kinds. The first is to improve the combination rule, and the second is to modify the data model. A typical method to improve combination rule is to assign the conflict to the total ignorance set Θ . However, it does not make full use of conflict information. A novel combination rule is proposed in this paper, which assigns the conflicting mass to the power set (ACTP). Compared with modifying data model, the advantage of the proposed method is the sequential fusion, which greatly decrease computational complexity. To demonstrate the efficacy of the proposed method, some numerical examples are given. Due to the less information loss, the proposed method is better than other methods in terms of identifying the correct evidence, the speed of convergence and computational complexity. [ABSTRACT FROM AUTHOR]

This paper presents an effective approach for solving economic load dispatch problems contemplating the scheduling a set of thermal generating units to produce a specific power at low consumption costs. These problems can be thought of as nonlinear, non-convex, and highly constrained optimization problems with a large number of local minima. To cope with the above issues in solving such problems, a new meta-heuristic named capuchin search algorithm was adopted. To boost the search performance of this algorithm as well as to mitigate its early convergence and regression to the local optimum, it was hybridized with another algorithm and improved using several positive amendments. First, a memory element was added to this algorithm to ameliorate its position and velocity update mechanisms in order to exploit the most encouraging candidate solutions. Second, two adaptive parametric functions were used to manage the exploration and exploitation features of this algorithm and balance them appropriately. Finally, the hybridization was made using the gradient-based optimizer to strengthen the intensification ability of this algorithm and balance its searching ability to fulfill sensible search performance. The proficiency of the proposed algorithm was divulged by assessing it on computationally difficult economic load dispatch problems under 6 different tests with a generator of 3, 13, 40, 80, and 140 units, each with different constraints and load conditions. The proposed algorithm provided the best performance among many other competitors. Its superiority and practicality were revealed by obtaining optimal solutions for large-scale test cases such as 40-unit and 140-unit test systems. [ABSTRACT FROM AUTHOR]

The alternating direction method of multipliers (ADMM) is an effective algorithm for solving optimization problems with separable structures. Recently, inertial technique has been widely used in various algorithms to accelerate its convergence speed and enhance the numerical performance. There are a lot of convergence analyses for solving the convex optimization problems by combining inertial technique with ADMM, while the research on the nonconvex cases is still in its infancy. In this paper, we propose an algorithm framework of inertial regularized ADMM (iRADMM) for a class of two-block nonconvex optimization problems. Under some assumptions, we establish the subsequential and global convergence of the proposed method. Furthermore, we apply the iRADMM to solve the signal recovery, image reconstruction and SCAD penalty problem. The numerical results demonstrate the efficiency of the iRADMM algorithm and also illustrate the effectiveness of the introduced inertial term. [ABSTRACT FROM AUTHOR]

The minimum weighted vertex cover (MWVC) problem is to find a subset of vertices that can cover all the edges of the network and minimize the sum of the vertex weights in the vertex subset. MWVC is a generalization of the minimum vertex cover (MVC) problem and can be regarded as a combinatorial optimization problem. This paper proposes an evolutionary algorithm based on the snowdrift game to solve the MWVC problem. We use the evolutionary algorithm framework, and the snowdrift game is combined to construct and improve the initial solution. First, the network's vertex is regarded as an intelligent agent, and each vertex and its neighbors play a snowdrift game to form an initial solution. Then local search and global search are used to improve the initial solution. The solution is improved according to the proposed score function in the local search stage to obtain a better MWVC solution. The evolutionary algorithm is used in the global search stage to escape the local optimum. Experiments on different networks show that the proposed algorithm are effective on weighted networks. [ABSTRACT FROM AUTHOR]

The probability transformation of mass functions plays a crucial role for decision making in Dempster–Shafer evidence theory. From the perspective of information, the existing transformation methods just consider the information of original mass functions from the obverse side, and then use mathematical tools for information processing. However, the limited amount of information has a restriction on decision performance. To solve this problem, in this paper we provide a new insight for probability transformation. The negation operation is used to obtain additional information of mass functions from the opposite side. By the joint use of mass functions information from the obverse and opposite sides, the informative belief functions of different elements are obtained, then the conditional belief function is applied to calculate proportions of singletons in multi-subset elements, and finally mass functions can be transformed to probabilities by proportion reasonably. Experimental results and related analysis are provided to show the rationality of the new transformation method. [ABSTRACT FROM AUTHOR]

This paper addresses the electricity pricing problem with demand-side flexibility. The interaction between an aggregator and the prosumers within a coalition is modeled by a Stackelberg game and formulated as a mathematical bi-level program where the aggregator and the prosumer, respectively, play the role of upper and lower decision makers with conflicting goals. The aggregator establishes the pricing scheme by optimizing the supply strategy with the aim of maximizing the profit, prosumers react to the price signals by scheduling the flexible loads and managing the home energy system to minimize the electricity bill. The problem is solved by a heuristic approach which exploits the specific model structure. Some numerical experiments have been carried out on a real test case. The results provide the stakeholders with informative managerial insights underlining the prominent roles of aggregator and prosumers. [ABSTRACT FROM AUTHOR]

This paper addresses the two-dimensional irregular bin packing problem, whose main aim is to allocate a given set of irregular pieces to larger rectangular containers (bins), while minimizing the number of bins required to contain all pieces. To solve the problem under study a dynamic hierarchical hyper-heuristic approach is proposed. The main idea of the hyper-heuristics is to search the space of low-level heuristics for solving computationally difficult problems. The proposed approach is "dynamic" since the low-level heuristic to be executed is chosen on the basis of the main characteristics of the instance to be solved. The term "hierarchical" is used to indicate the fact that the main hyper-heuristic can execute either simple heuristics or can run in a "recursive fashion" a hyper-heuristic. The developed solution strategy is evaluated empirically by performing extensive experiments on irregular packing benchmark instances. A comparison with the state-of-the-art approaches is also carried out. The computational results are very encouraging. [ABSTRACT FROM AUTHOR]

The graph coloring problem is an NP-hard problem. Currently, one of the most effective methods to solve this problem is a hybrid evolutionary algorithm. This paper proposes a hybrid evolutionary algorithm NERS_HEAD with a new elite replacement strategy. In NERS_HEAD, a method to detect the local optimal state is proposed so that the evolutionary process can jump out of the local optimal state by introducing diversity on time; a new elite structure and a replacement strategy are designed to increase the diversity of the evolutionary population so that the evolution process can not only converge quickly but also jump out of the local optimal state in time. The comparison experiments with current excellent graph coloring algorithms on 59 DIMACS benchmark instances show that NERS_HEAD can effectively improve the efficiency and success rate of solving graph coloring problems. [ABSTRACT FROM AUTHOR]

Cooperation search algorithm (CSA) is a new metaheuristic algorithm inspired from the team cooperation behaviors in modern enterprises and is characterized by fast convergence. However, for complex multimodal problems, it may get trapped into local optima and suffer from premature convergence for the shortcoming of population updating guided only by leading individuals. In this paper, the issue of low convergence efficiency and convergence accuracy of the CSA algorithm on complex multimodal problems is dramatically alleviated by integrating the mutation and crossover operators in DE algorithm. Experimental results demonstrate the better performance of CCSA on convergence speed and accuracy as compared to other existing optimizers. Furthermore, aiming at the problem that there is no universal approach for the multi-degree reduction in Ball Bézier surfaces under different interpolation constrains, we propose a new method to solve this problem by introducing metaheuristic methods, where the change of interpolation constrains is treated as the change of decision variables. The modeling examples show that the proposed method is effective and easy to implement under different interpolation constrains, which can achieve the multi-degree reduction in Ball Bézier surfaces at one time and can simplify the degree reduction procedure significantly. [ABSTRACT FROM AUTHOR]

This paper introduces a new meta-heuristic technique, named geometric mean optimizer (GMO) that emulates the unique properties of the geometric mean operator in mathematics. This operator can simultaneously evaluate the fitness and diversity of the search agents in the search space. In GMO, the geometric mean of the scaled objective values of a certain agent's opposites is assigned to that agent as its weight representing its overall eligibility to guide the other agents in the search process when solving an optimization problem. Furthermore, the GMO has no parameter to tune, contributing its results to be highly reliable. The competence of the GMO in solving optimization problems is verified via implementation on 52 standard benchmark test problems including 23 classical test functions, 29 CEC2017 test functions as well as nine constrained engineering problems. The results presented by the GMO are then compared with those offered by several newly proposed and popular meta-heuristic algorithms. The results demonstrate that the GMO significantly outperforms its competitors on a vast range of the problems. Source codes of GMO are publicly available at https://github.com/farshad-rezaei1/GMO. [ABSTRACT FROM AUTHOR]

The operations proposed by Dombi based on t-norn (TN) and t-corom (TCN) are generally known as Dombi operations, which offer versatility in the working behavior of parameters. Over the last decade, group decision-making has been a very active research field. Especially, the development of new operational rules, aggregation operators, and multi-attribute group decision-making techniques based on these rules and operators have recently piqued the interest of scientists. Acknowledging the importance of t-spherical fuzzy sets and linguistic variable in this paper, firstly, we define the notion of linguistic T-spherical fuzzy set (Lt-SFS) where membership degree, abstinence degree and non-membership degree are presented in the form of linguistic variables. Dombi operations, score function, accuracy function for linguistic T-spherical fuzzy numbers (Lt-SFNs) are defined and some prominent properties of Dombi operations are then investigated. Furthermore, two aggregations operators based on Dombi operations namely, linguistic t-spherical fuzzy Dombi weighted averaging operator and linguistic t-spherical fuzzy Dombi weighted geometric operator are also developed. At that point, these Dombi operators are used to establish an extension of the technique for order of preference by similarity to ideal solution (TOPSIS) method, and a multi-attribute group decision-making approach is proposed to solve decision-making problems which is the key innovation of this paper. Finally, we apply the proposed technique for the selection of the best variety of maize and a comparison analysis is provided to demonstrate its applicability and feasibility. [ABSTRACT FROM AUTHOR]

Due to the heterogeneity of program language and natural language query, it is difficult to identify the semantic relationship between them, which leads to the low efficiency of code recommendation. In order to solve the problems of the above code recommendation technology, a code recommendation method based on joint embedded attention network (JEAN) is proposed in this paper. The method uses GRU Network to embed code snippets and describe queries into vector representation, which solves the problem of heterogeneous code snippets and natural language queries. The Attention mechanism is then used to distribute totally different weights to different components of every mode of the code snippet. The reason for the Attention mechanism is that different components of every mode of the code snippet contribute differently to the semantic vector of the final code snippet, making it interpretable. Finally, two commonly used evaluation indexes of information retrieval, SuccessRate@k and MRR, are used for experimental comparison with other baseline models. The experimental results show that the code recommendation method based on joint embedded attention network proposed in this paper can effectively recommend appropriate code snippets according to the needs of developers, and its performance is better than other baseline methods. [ABSTRACT FROM AUTHOR]

The identification of apple leaf diseases is crucial to reduce yield reduction and timely take disease control measures. Employing deep learning for apple leaf disease identification is challenging because of the limited availability of samples for supervised training and the serious class imbalance. Hence, this paper proposes an accurate deep learning-based pipeline to solve the problem of limited data sets on farms and reduce the partiality due to serious class imbalance. Firstly, an improved cycle-consistent adversarial networks (CycleGAN) is used to generate synthetic samples to improve the learning of data distribution and solve the problems of small data sets and class imbalance. Secondly, ResNet is trained as a baseline convolutional neural network classifier to classify apple leaf diseases. The experimental results show that ResNet has the highest recognition accuracy on the test set, reaching 97.78%, and the classification accuracy is significantly improved by the generated synthetic samples (+ 14.7%). In addition, the experiment results of t-distributed stochastic neighbor embedding (t-SNE) and visual Turing test visually confirmed that the images generated by improved CycleGAN have much better quality and are more convincing. [ABSTRACT FROM AUTHOR]

Time-dependent reliability is a key index for reliability evaluation and life prediction of existing bridges, which can reflect the service status of bridges. Therefore, the time-dependent reliability of the bridge must be calculated and analyzed in time to ensure the safety of the bridge. Many scholars have established different time-dependent reliability models, but the model contains complex multiple integrals and is difficult to calculate. In this case, the current method for calculating time-dependent reliability is Monte Carlo method, which is inefficient and cannot meet the engineering needs. In order to solve the problem that time-dependent reliability is difficult to solve, this manuscript proposes a method for solving time-dependent reliability of bridges using neural networks, which is suitable for existing time-dependent reliability models. Then, compared with the results of Monte Carlo method, the results show that the neural network used in this paper is accurate. At the same time, it can also significantly improve the computational efficiency and has significant advantages compared with the existing calculation methods. [ABSTRACT FROM AUTHOR]

Multi-criteria group decision-making (MCGDM) problems, where correlations commonly exist among input arguments, are becoming increasingly complex. However, most of the existing consensus-reaching methods for MCGDM problems fail to adequately consider the effects of these interactions among criteria and experts, which may bring about inaccurate results. Therefore, this paper establishes a novel MCGDM framework based on the generalized Shapley value to solve the consensus-reaching problem with interval-valued Pythagorean fuzzy sets (IVPFS). First, experts' evaluations are collected using IVPFS, which offers a more flexible way to express this vague information. Second, the interval-valued Pythagorean fuzzy Choquet integral operator and the interval-valued Pythagorean fuzzy Shapley aggregation operator are developed to fuse the decision information with complementary, redundant, or independent characteristics. Third, an integrated consensus-reaching algorithm is established to improve group consensus by iteratively updating the evaluations until the group consensus level reaches the preset threshold. Then, the classical PROMETHEE method is extended using the generalized Shapley value within an IVPFS context to derive a more scientific ranking result. Finally, a case study for a sustainable supplier evaluation problem is presented to validate the proposed method. The results and comparative analysis show that the proposed method can represent experts' evaluations more flexibly, integrate inputs with interrelationships more effectively, and improve group consensus more efficiently. [ABSTRACT FROM AUTHOR]

Since frequent traffic accidents bring great losses to people's safety and social property, this paper takes the results of traffic accident risk prediction as the basis so that it can help city managers to reasonably deploy police force, relieve traffic pressure, avoid traffic accidents and provide safe guidance to pedestrians. Based on this paper, a deep learning framework including spatiotemporal attention mechanism is proposed to solve the problem of traffic accident prediction in urban areas, and the experimental simulation shows that the accuracy of traffic accident risk prediction proposed in this paper reaches 94%. [ABSTRACT FROM AUTHOR]

Generalized hesitant fuzzy numbers (GHFNs) are able to directly manage situations in which we may encounter a finite set of known values with a finite set of degrees of doubt as quantitative approximations of an uncertain situation/quantification of a linguistic expression. They are new extensions of hesitant fuzzy sets, which have been considered in this paper. In fact, in this paper, GHFNs will be utilized to model the uncertainty of the assessment values of options against criteria in multi-attribute decision making (MADM) problems. It means that all of the elements of decision matrix are GHFNs. Then, the technique for order of preference by similarity to ideal solution (TOPSIS) method, as a very successful method in solving MADM problems, will be updated to be used with GHFNs. To this end, the distance between GHFNs must be defined to obtain the distances between given alternatives from each of two subjective alternatives (positive/negative ideal solutions). Thus, three existing famous distance measures, i.e., general distance ( d g ), Hamming distance ( d h ), and Euclidean distance ( d e ) measures, have been updated for GHFNs firstly. Then, the new TOPSIS method will be proposed based on GHFNs. Finally, the numerical examples have been appointed to illustrate the proposed method, analyze comparatively and validate it. [ABSTRACT FROM AUTHOR]

Inverse data envelopment analysis technique is a useful tool in planning and management control to estimate the level of input/output of decision-making units to achieve the predetermined efficiency targets. In the real problems, data are time-dependent that also this technique is influenced by this parameter. The current paper studies this technique in a dynamic framework. In fact, the problem of estimating the input and output levels simultaneously is studied when data are time-dependent. This problem is solved using multiple-objective programming tools in the framework of dynamic inverse data envelopment analysis. The proposed models in the current study, unlike other existing models in the literature of inverse data envelopment analysis, can solve the problem of estimating the input and output levels such that the unit maintains or improves its current efficiency level to a pre-defined amount in the assessment window. Necessary and sufficient conditions are derived for the estimation of input and output levels through the linear multiple-objective programming problems. Also, the applicability and limitations of the provided method are explained via a real example of the banking sector on a period of six months. The proposed approach is confirmed according to the obtained numerical results as well. [ABSTRACT FROM AUTHOR]

This paper proposes an intelligent attendance monitoring system based on spatio-temporal human action recognition, which includes human skeleton gait recognition, multi-action body silhouette recognition and face recognition. Our system solves several problems, for example, when a mask is worn to conceal the face, which leads to a decrease in recognition accuracy performance, and when a 3D face mask is used to fake an identity. The skeleton gait feature of our intelligent attendance monitoring system uses a temporal weighted K-nearest neighbours algorithm to train the recognition model and carry out identification, while the multi-action body silhouette feature uses a multiple K-nearest neighbours algorithm to train the recognition model, identify the person and vote on the outcome. Using the proposed system, which integrates skeleton gait features, action silhouette features and face features, more effective recognition can be achieved. When the system encounters a situation with feature masking, such as when an individual is wearing a mask or has changed their clothes, or when the viewing angle is masked, it can continue to deliver good recognition ability through multi-angle skeleton synthesis gait recognition. Our experimental results show that the recognition accuracy of the system is 83.33% when a specific person wears a mask and passes through a monitored area. The intelligent attendance monitoring system uses a LINE messaging API as the access control notification function and provides a responsive web platform that allows managers to perform follow-up management and monitoring. [ABSTRACT FROM AUTHOR]

Secret communication of sensitive data must progress in a trustworthy environment through data hiding. Using Mamdani fuzzy logic to identify color proximity at the block level and a shared secret key and post-processing system, this paper attempts to develop a robust data hiding scheme with similarity measures to ensure good visual quality, robustness, imperceptibility and enhance the security. In accordance with the Gestalt principle, proximity among the nearby objects is higher, whose value varies from expert to expert. Therefore, a possibility for type-I fuzzy logic to be used to evaluate proximity. Fuzzy proximity is computed by means of a difference in intensity (colordiff) and distance (closeness). Further, the block color proximity obtained from the proximity calculation network is graded using an interval threshold. Accordingly, data embedding is processed in the sequence generated by the shared secret keys. The tampering coincidence problem is solved through a post-processing approach to increase the quality and accuracy of the recovered secret message. The experimental analysis, steganalysis and comparisons clearly illustrate the effectiveness of the proposed scheme in terms of visual quality, structural similarity, recoverability and robustness. [ABSTRACT FROM AUTHOR]

The trisecting–acting–outcome model of a three-way decision is a practical approach to solving complex problems, consisting of three components: trisecting, acting, and outcome. Trisecting means dividing a complex problem into three parts based on an evaluation function, and acting means designing the corresponding action to apply to these three parts. The outcome denotes evaluation effectiveness based on the first two steps. Measuring this outcome is a challenging and moving question after trisecting-and-acting (T &A). This paper proposes a method to measure outcome based on object changes before and after T &A based on top-down and bottom-up perspectives, depending on the decision needs. First, evaluation functions are constructed that extend the traditional evaluation functions to measure changes. Then, based on the introduced evaluation functions, qualitative and quantitative of three-way changes are introduced and analyzed. Furthermore, we present the processes that determine the optimal strategy with the quantitative analysis. The analysis of several examples shows the effectiveness and practicality of our proposed method. [ABSTRACT FROM AUTHOR]

Classification is a technique in data mining that is used to predict the value of a categorical variable and to produce input data and datasets of varying values. The classification algorithm makes use of the training datasets to build a model which can be used for allocating unclassified records to a defined class. In this paper, the coronavirus herd immunity optimizer (CHIO) algorithm is used to boost the efficiency of the probabilistic neural network (PNN) when solving classification problems. First, the PNN produces a random initial solution and submits it to the CHIO, which then attempts to refine the PNN weights. This is accomplished by the management of random phases and the effective identification of a search space that can probably decide the optimal value. The proposed CHIO-PNN approach was applied to 11 benchmark datasets to assess its classification accuracy, and its results were compared with those of the PNN and three methods in the literature, the firefly algorithm, African buffalo algorithm, and β-hill climbing. The results showed that the CHIO-PNN achieved an overall classification rate of 90.3% on all datasets, at a faster convergence speed as compared outperforming all the methods in the literature. [ABSTRACT FROM AUTHOR]

The selection of a proper international freight transport route is one of the crucial tasks for decision-makers since it can affect costs, efficiency, and transportation performance. Besides, the selection of suitable and appropriate freight routes can also reduce external costs of transportation such as emissions, noise, traffic congestions, accidents, and so on. Route selection in international transportation is a complicated decision-making problem as many conflicting factors and criteria affect the assessment process. It has been observed that there is no mathematical model and methodological frame used for solving these selection problems, and decision-makers make decisions on this issue based on their own experiences and verbal judgments in the research process. Therefore, a methodological frame is required to make rational, realistic, and optimal decisions on route selection. From this perspective, the current paper proposes using the IVAIF CODAS, an extended version of the traditional CODAS techniques, and using the Atanassov interval-valued intuitionistic fuzzy sets (IVAIFS) for processing better the existing uncertainties. The proposed model is applied to solve the route selection, a real-life decision-making problem encountered in international transportation between EU countries and Turkey. According to the results of the analysis, option A6 (i.e., Route-6 (Bursa–Istanbul–Pendik–Trieste (Ro-Ro)–Austria–Frankfurt/Germany) has been determined as the best alternative. These obtained results have been approved by a comprehensive sensitivity analysis performed by using different MCDM techniques based on interval-valued intuitionistic fuzzy sets. Hence, it can be accepted that the proposed model is an applicable, robust, and powerful mathematical tool; also, it can provide very reliable, accurate, and reasonable results. As a result, the proposed model can provide a more flexible and effective decision-making environment as well as it can provide valuable advantages to the logistics and transport companies for carrying out practical, productive, and lower cost logistics operations. [ABSTRACT FROM AUTHOR]

Decision making is a universal behavior based on human cognitive information. In the real world, information related to human cognition is characterized by uncertainty and partial reliability, which is challenging to express with traditional and precise concepts. To better describe this type of uncertain information, Z-number is introduced by Zadeh, which contains uncertain information with both probability and fuzziness. Recently, Yager proposed the fusion of multiple multi-criteria aggregate functions, especially the fusion of multiple OWA-type aggregate functions, to deal with the group decision problem. However, such aggregation functions exhibit limitations in facing the uncertainty of expert information in real-world decision-making scenarios. To overcome this shortcoming, this paper extends Yager's aggregation method to the Z-number field and further propose a new group decision-making method based on the OWA aggregation operator and Z-number. The maximum entropy optimization model based on a genetic algorithm is used to determine the hidden probability distribution in Z-numbers to aggregate the Z-numbers, which solves the problem of information loss caused by ignoring the hidden probability distribution in the existing Z-number aggregation methods, and greatly preserves the original meaning of Z-number. Some numerical examples are used to demonstrate the rationality and effectiveness of the proposed method. Finally, a comparative analysis with existing methods expounds on the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

A fuzzy equivalence relation can be used for clustering. But when using it in applications, we often get a similarity relation rather than an equivalence one because of various reasons. We need to reform it into an equivalence relation close to it to cluster. A commonly used method is transitive closure method, but it usually results in serious distortions about the relation. This paper further studies fuzzy similarity and equivalence relations using fuzzy graphs, and obtains some new results. The defects of transitive closure method are analyzed, and an improved clustering algorithm is given, but it cannot eliminate the inconsistency phenomenon in classification hierarchy structure. To solve this problem, the optimal fuzzy equivalence relation of similarity relation is studied. An optimization model which can derive it exactly is given, but it is too complex for applications. An effective approximation algorithm to get the optimal equivalence relation is thus presented. Several examples and some discussions are also given to illustrate the given methods. [ABSTRACT FROM AUTHOR]

As one of the indirect causality, cascaded causality can be used to construct the event knowledge graph, causal inference, scenario analysis, etc. The existing GCN methods lack the mining of context information and relevant entity information, resulting in the poor ability of causality inference, which inevitably affects the extraction accuracy of cascade causality. To solve this problem, this paper proposes a causality extraction model based on a two-stage GCN to improve the extraction accuracy. To obtain rich features of entities, this work combines sentiment polarity and knowledge base to get the causality candidate entity library. Firstly, the BERT model is pre-trained using context information and relevant entity information extracted from the entity library to obtain the final entity nodes. Secondly, using the semantic dependency graph, each possible edge between any two entity nodes can be obtained, which are input into the first stage GCN to get a preliminary directed graph of causality. Finally, the directed graph of causality is input into the second stage GCN to achieve deep causality multi-hop inference. Thus, the cascade causality is inferred and extracted by the two-stage GCN model. Experiments show that the extraction accuracy of cascade causality has been further improved. [ABSTRACT FROM AUTHOR]

Multi-verse optimizer (MVO) algorithm is one of the recent metaheuristic algorithms used to solve various problems in different fields. However, MVO suffers from a lack of diversity which may trapping of local minima, and premature convergence. This paper introduces two steps of improving the basic MVO algorithm. The first step is using opposition-based learning (OBL) in MVO, called OMVO. The OBL aids to speed up the searching and improving the learning technique for selecting a better generation of candidate solutions of basic MVO. The second stage, called OMVOD, combines the disturbance operator (DO) and OMVO to improve the consistency of the chosen solution by providing a chance to solve the given problem with a high fitness value and increase diversity. To test the performance of the proposed models, fifteen CEC 2015 benchmark functions problems, thirty CEC 2017 benchmark functions problems and seven CEC 2011 real-world problems were used in both phases of the enhancement. The second step, known as OMVOD, incorporates the disruption operator (DO) and OMVO to improve the accuracy of the chosen solution by giving a chance to solve the given problem with a high fitness value while also increasing variety. Fifteen CEC 2015 benchmark functions problems, thirty CEC 2017 benchmark functions problems and seven CEC 2011 real-world problems were used in both phases of the upgrade to assess the accuracy of the proposed models. [ABSTRACT FROM AUTHOR]

An equity warrant allows warrant holders to buy stocks of listed companies at a certain price on a promissory day. Classified by the time of exercise right, there are two types of equity warrant, namely European equity warrants and American equity warrants. The European equity warrants allow the buyers to exercise their rights only on the expiring date. In contrast, American warrants enable the buyers to exercise their rights before or on the expiring date. Based on the assumption that the firm's value follows an uncertain exponential Ornstein–Uhlenbeck process instead of a stochastic process, this paper mainly solves the pricing problems of European and American equity warrants. The most significant advantage of this paper is offering the corresponding formulas to calculate equity warrants, which are not complicated compared with the classical stochastic financial theory. Besides, the minimum cover estimation method is applied to estimate the parameters in an uncertain exponential Ornstein–Uhlenbeck equation, and a simulation example is provided to show the effectiveness of the proposed pricing formulae. [ABSTRACT FROM AUTHOR]

In this paper, ant colony optimization (ACO) and grey wolf optimization (GWO) algorithms are used for solving the joint user and receive antenna scheduling problem of multi-user multiple input multiple-output systems in the uplink channel. A subset of users among all the available users should be allowed to send their data to the appropriate receive antenna of the base station (BS). The search space for assigning appropriate user with the appropriate receive antenna of the BS is very large. Searching through this large search space is quite time-consuming process which cannot be accomplished within the real-time frame. To overcome this, ACO and GWO soft computing techniques have been implemented for this problem. In this paper, it is shown that both ACO and GWO accomplish this huge task with very low computation complexity. Simulation results presented in this paper are verifying the effectiveness of ACO and GWO for solving such complex problems. Moreover, it has also been showcased that GWO performs better than ACO and binary particle swarm optimization (BPSO) techniques. Both GWO and ACO attains the system sum-rate very close to that of exhaustive search algorithm. Furthermore, different statistical parameters for these soft computing techniques like BPSO, ACO, and GWO have been presented and compared to assess the efficacy of these meta-heuristic methods. [ABSTRACT FROM AUTHOR]

This paper presents an evolutionary approach-based solution of multi-objective transportation-p-facility location problem (MOT-p-FLP) that minimizes overall transportation time, cost of transportation, and carbon emission (CE) from available sites to facility sites by seeking transported product quantities and the facility locations in the Euclidean plane. Genetic algorithm (GA), non-dominated sorting genetic algorithm (NSGA-II and NSGA-III), and modified Self-Adaptive Multi-Population Elitism Jaya Algorithm (SAMPE JA) are utilized to solve the problem. We compared obtained compromise solutions of the problem by evolutionary algorithms with population size, the maximum number of generations, crossover probability, mutation probability, and computational time. Sensitivity analysis for supply, demand, and carbon cap parameters is incorporated in the model's solution, which helps the decision maker make the appropriate decision. These evolutionary algorithms (NSGA-II and NSGA-III) give Pareto-optimal solutions, and it helps management decide on the selection of p-facility locations. They could transport their product to the facility locations easily, with minimum transport, CE costs, and transportation time. As a result, management can give equal attention to their profit and environment, which helps to build world market credibility. At last, the paper concludes the results. [ABSTRACT FROM AUTHOR]

In this research paper, we will solve problems of Bi-level linear fractional programming (BL-LFP) by proposing an interactive approach. Based on the imposition of the relationship DM. to obtained adequate solution, DMs will updating the minimal adequate level at upper level permanently, and that is through. Firstly, the decision makers uncertainty is described by introducing the membership function and non-membership function. Secondly, the opting of minimum adequate degree, leads to obtain the adequate solution, with the overall adequate balance considerations among two levels. For more, this paper gives an algorithm of the proposed approach. At the end, we give a numerical example to explain the feasibility of that approach. [ABSTRACT FROM AUTHOR]

The capsule network (CapsNet) is a promising model in computer vision. It has achieved excellent results on MNIST, but it is still slightly insufficient in real images. Deepening capsule architectures is an effective way to improve performance, but the computational cost hinders their development. To overcome parameter growth and build an efficient architecture, this paper proposes a tensor capsule layer based on multistage separable convolutions and a dense capsule architecture. Multistage separable convolutions can effectively reduce the parameters at the cost of a small performance loss. In the dense capsule architecture, the use of dense connections allows the capsule network to be deeper and easier to train. Combining these two can achieve a novel lightweight dense capsule network. Experiments show that this network uses only 0.05% of the parameters of the CapsNet, but the performance is improved by 8.25% on CIFAR10. In addition, the full tensor capsule method is proposed to solve the problem of capsule network parameters changing with image scale. Experiments prove that this method can keep the parameters unchanged while affecting the performance in a small amount. In order to lighten the fully connected capsule layer, a dynamic routing based on separable matrices is proposed. In addition to applying it to our models, this algorithm also compresses the CapsNet by 41.25% while losing only 0.47% performance on CIFAR10. The parameter utilization index is proposed to quantify the relationship between parameters and performance. To our knowledge, this is the first paper to study lightweight capsule network. [ABSTRACT FROM AUTHOR]

In this paper, new concepts to use clique covering of a fuzzy graph are introduced for optimization of parameters involved in business strategy. For this purpose, four algorithms are designed for finding necessary parameters and sets of a fuzzy graph which is helpful for constructing a cordon of linear programming problems. The linear programming problems are constructed with suitable optimization functions and constraints. The strengths of the cliques present in fuzzy graph get a new look in this paper. Facility location problems are characterized and solved with a new strategy optimization problems by using concept of clique covering of fuzzy graphs for a smooth business strategy to have a maximized total gain. This optimization process will help for developing a part of sustainable economic growth all over the world. Some new definitions are given with relevant examples of fuzzy graphs. An illustration is given to elaborate all mathematical terminologies. Also, a real-life application to optimize different parameters in a business network by solving the programming problems with the help of the mathematical software "LINGO" keeping the fuzziness of the parameters involved in the considered fuzzy graph. [ABSTRACT FROM AUTHOR]

In order to solve the problems of low learning efficiency and slow convergence speed when mobile robot uses reinforcement learning method for path planning in complex environment, a reinforcement learning method based on each round path planning result is proposed. Firstly, the algorithm adds obstacle learning matrix to improve the success rate of path planning; and introduces heuristic reward to speed up the learning process by reducing the search space; then proposes a method of dynamically adjusting the exploration factor to balance the exploration and utilization in path planning, so as to further improve the performance of the algorithm. Finally, the simulation experiment in grid environment shows that compared with Q-learning algorithm, the improved algorithm not only shortens the average path length of the robot to reach the target position, but also speeds up the learning efficiency of the algorithm, so that the robot can find the optimal path more quickly. The code of EPRQL algorithm proposed in this paper has been published to GitHub: https://github.com/panpanpanguoguoqian/mypaper1.git. [ABSTRACT FROM AUTHOR]

Due to the extent and existence of multiple branches in the distribution network, one of the main challenges in this network will be the issue of fault location. Gradually, with the expansion of smart grids and the use of smart meters in the distribution network, various methods are proposed to use these devices to the fault location. In this paper, fault location in the distribution network is defined as an optimization problem with an objective function based on network voltage changes before and after the fault. The objective function of the problem consists of the difference between the two approaches. In the first approach, the combination of the power flow (PF) method with smart meter data is used to calculate voltage changes before and after the fault in each network node. In the second approach, by calculating the network impedance matrix per the hypothetical fault location in each node of the network, these voltage changes are calculated, and by comparing the results of these two approaches, when the objective function of the problem is minimized, the optimal answer will be the fault location in the network. Therefore, in this issue, two objective functions of the difference between these two approaches are defined, one to identify the faulty section and the other to fault location has been used. The required data are extracted from the network partly before the fault and partly after the fault. Due to the need to process these data, the volume of calculations and the wide distribution network, a genetic algorithm (GA) has been used to solve the problem. To evaluate the speed and accuracy of the proposed method in fault location, the proposed method has been implemented on the largest distribution network, namely the IEEE 123-node distribution test system through MATLAB software. The results showed that the proposed method had a good performance for types of faults and different fault resistance so that it was able to detect the location of the fault with an accuracy of 1.501% in less than 60 s. [ABSTRACT FROM AUTHOR]

This paper considers a passive target localization problem based on the noisy time of arrival measurements obtained from multiple receivers and a single transmitter. The maximum likelihood (ML) estimator for this localization problem is formulated as a highly nonlinear and non-convex optimization problem, where conventional optimization methods are not suitable for solving such a problem. Consequently, this paper proposes an improved adaptive hybrid firefly differential evolution (AHFADE) algorithm, based on hybridization of firefly algorithm (FA) and differential evolution (DE) algorithm to estimate the unknown position of the target. The proposed AHFADE algorithm dynamically adjusts the control parameters, thus maintaining high population diversity during the evolution process. This paper aims to improve the accuracy of the global optimal solution by incorporating evolutionary operators of the DE in different searching stages of the FA. In this regard, an adaptive parameter is employed to select an appropriate mutation operator for achieving a proper balance between global exploration and local exploitation. In order to efficiently solve the ML estimation problem, this paper proposes the well-known semidefinite programming (SDP) method to convert the non-convex problem into a convex one. The simulation results obtained from the proposed AHFADE algorithm and well-known algorithms, such as SDP, DE and FA, are compared against Cramér–Rao lower bound (CRLB). The statistical analysis has been performed to compare the performance of the proposed AHFADE algorithm with several well-known algorithms on CEC2014 benchmark problems. The obtained simulation results show that the proposed AHFADE algorithm is more robust in high-noise environments compared to existing algorithms. [ABSTRACT FROM AUTHOR]

Comparing the probability distribution, basic probability assignment in evidence theory is more efficient to deal with uncertain information. However, the uncertainty measure of basic probability assignment is still an open issue. In this paper, a new uncertainty measure based on Tsallis entropy is proposed to solve problems when the basic probability assignments are not given or being transformed into interval probability distribution. The proposed entropy is an extension of Tsallis entropy in continuous space. Some numerical examples are illustrated to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Multiobjective optimization techniques have much importance while solving real-life problems. There may get chances of neutral thoughts and hesitations in real-life problems. This paper has studied the multiobjective programming problems (MOPPs) under neutrosophic hesitant fuzzy uncertainty. The degrees of neutrality and hesitations in MOPPs were introduced, and simultaneously, we have developed the neutrosophic hesitant fuzzy multiobjective programming problems (NHFMOPPs) under a neutrosophic hesitant fuzzy environment. Besides, a new robust solution scheme, namely neutrosophic hesitant fuzzy Pareto optimal solution to the NHFMOPPs, is investigated, and two different optimization techniques are suggested to evaluate it. The validity and applicability of the proposed methods are unanimously implemented on different multiobjective real-life problems. Finally, conclusions, comparative study, and future research direction are addressed based on the presented work. [ABSTRACT FROM AUTHOR]

The weapon target assignment (WTA) problem is an important task to tactical arrangements in military commitment operations. It describes the optimal method to allocate defense in opposition to threats in fighting situations. It is an NP-complete issue in which no accurate outcome for all conceivable situations is known. The time performance of created algorithms is a major challenge in modeling the WTA problem, which has only been lately considered in related papers. This article improves the recently developed algorithm called improved Tunicate Swarm Algorithm (iTSA) which is inspired by the natural behavior of tunicates to solve the WTA problem. The suggested method is compared with well-known metaheuristic approaches. The experimental findings show that the method presented works better than previous competing metaheuristic approaches. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a new classifier using a multiple-attribute decision-making (MADM) model for fuzzy classification. First, we form a decision-making matrix. Its elements are membership functions of a fuzzy set constructed by training datasets. Then, for any test data, we form an MADM problem, and by solving this problem with a method from the MADM techniques, we obtain a fuzzy classification. For this purpose, we utilize the technique for order of preference by similarity to ideal solution (TOPSIS) method as a well-known method in the MADM techniques. Additionally, we use a new criterion for determining a weight vector for features in this approach. We evaluate the obtained results of the new approach with five well-known algorithms on ten datasets. Also, we compare our new approach with the weightless algorithm and weighed algorithm by the generalized Fisher score in feature selection methods. Finally, to show the superiority of the new approach, we use a statistical comparison with other methods. [ABSTRACT FROM AUTHOR]

An inherent difficulty in dynamic distributed constraint optimization problems (dynamic DCOP) is the uncertainty of future events when making an assignment at the current time. This dependency is not well addressed in the research community. This paper proposes a reinforcement-learning-based solver for dynamic distributed constraint optimization. We show that reinforcement learning techniques are an alternative approach to solve the given problem over time and are computationally more efficient than sequential DCOP solvers. We also use the novel heuristic to obtain the correct results and describe a formalism that has been adopted to model dynamic DCOPs with cooperative agents. We evaluate this approach in dynamic weapon target assignment (dynamic WTA) problem, via experimental results. We observe that the system dynamic WTA problem remains a safe zone after convergence while satisfying the constraints. Moreover, in the experiment we have implemented the agents that finally converge to the correct assignment. [ABSTRACT FROM AUTHOR]

Resource Planning Optimization (RPO) is a common task that many companies need to face to get several benefits, like budget improvements and run-time analyses. However, even if it is often solved by using several software products and tools, the great success and validity of the Artificial Intelligence-based approaches, in many research fields, represent a huge opportunity to explore alternative solutions for solving optimization problems. To this purpose, the following paper aims to investigate the use of multiple Artificial Neural Networks (ANNs) for solving a RPO problem related to the scheduling of different Combined Heat & Power (CHP) generators. The experimental results, carried out by using data extracted by considering a real Microgrid system, have confirmed the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with an extensive variant of the inverse p-facility maxian location problem on networks in which the set of vertices is considered as the existing client points and the aim is to modify (augment or reduce) the underlying vertex weights and the arc lengths at the minimum overall cost with respect to the modification bounds so that a given set of p vertices, denoting the predetermined facility sites, becomes a p-facility maxian location of the perturbed network. A novel modified directional bat algorithm, as a meta-heuristic approach, is developed to solve the problem under the bottleneck-type Hamming, sum-type Hamming, rectilinear and Chebyshev cost norms. Through computational tests, the effectiveness of the proposed algorithm is shown. [ABSTRACT FROM AUTHOR]

Many real-world datasets consist of multiple views of data items. The rough method of combining multiple views directly through feature concatenation cannot uncover the optimal latent structure shared by multiple views, which would benefit many data analysis applications. Recently, multi-view clustering methods have emerged and been applied to solving many machine learning problems. However, most multi-view clustering methods ignore the joint information of multi-view data or neglect the quality difference between different views of data, resulting in decreased learning performance. In this paper, we discuss a multi-view clustering algorithm based on concept factorization that effectively fuses useful information to derive a better representation for more effective clustering. We incorporate two regularizers into the concept factorization framework. Specifically, one regularizer is adopted to force the coefficient matrix to move smoothly on the underlying manifold. The other regularizer is used to learn the latent clustering structure from different views. Both of these regularizers are incorporated into the concept factorization framework to learn the latent representation matrix. Optimization problems are solved efficiently via an iterative algorithm. The experimental results on seven real-world datasets demonstrate that our approach outperforms the state-of-the-art multi-view clustering algorithms. [ABSTRACT FROM AUTHOR]

Solving fuzzy relation equations (FRQs) can be used to determine the weight vector in fuzzy synthetic evaluations, etc. However, the solutions of FRQs derived by real problems usually are infinite, so the vector cannot be determined. Many real problems need use FRQs to determine an objective and unknown vector, a particular solution. This paper discusses this problem for FRQs with max-continuous t-norm composition, which contain the two most frequently used types, max-min and max-product FRQs. It further analyzes the traits that FRQs have a unique solution, gives a sufficient condition that any vector can be determined by FRQs, and points out that it does for max-continuous T FRQs. Generally, when the FRQs cannot determine the vector, we need do some new tests and add those new equations into the system so as to the new system can determine it. But the new equations derived by blind testing often are redundant, or have little value, so the vector still cannot be determined, even if we add a lot. To solve this problem, the paper investigates how to extract valuable information from the old system and then to do new tests purposely so as to let the new system efficiently determine the vector. A procedure to realize it is thus given. Besides, three examples are also given to show the study content. [ABSTRACT FROM AUTHOR]