Multi-scale Decision Research Articles

Hierarchical optimization by spatial-temporal indictor in multi-scale decision pyramid for constrained large-scale multi-objective problems

Most existing constrained multi-objective evolutionary algorithms (CMOEAs) are not so efficient when handling constrained large-scale multi-objective problems (CLSMOPs). To overcome CLSMOPs, a hierarchical optimization, based on the spatial–temporal indictor in the decision pyramid (HOSTI-DP), is proposed to determine the dynamic trade-off between feasible and infeasible solutions in the effectively shrunken searching area. The decision pyramid consists of multiple decision spaces with a set of descending numbers of variables; it is initially constructed to speed up the solution convergence by the layer-by-layer dimensionality reduction and increase the population diversity based on the accumulation of these layers. The spatial–temporal indictor considers both the optimization stage (time) and the hierarchy structure of the decision pyramid (space) and it is designed to restrain the prematurely feasible solutions and find the promising infeasible solutions. Finally, the hierarchical optimization strategy, which applies the spatial–temporal indicator to the evolutionary algorithms in every layer of the decision pyramid and dynamically arranging the proportion among them, is designed for comprehensive balance of objectives, constraints, and computational complexity. Nine representative and state-of-the-art CMOEAs have been compared with the HOSTI-DP to demonstrate its effectiveness through comparative experiments on CLSMOPs with equality and inequality constraints and 1000 decision variables. Experimental results show that HOSTI-DP can significantly improve the performance of these CMOEAs.

A novel approach to simplifying dynamic data through multi-scale decision systems

A novel approach to simplifying dynamic data through multi-scale decision systems

Multiscale collaborative representation for face recognition via class-information fusion

One of the most challenging issues in face recognition is having only a limited number of training images. Multiscale patch collaborative representation (MSPCRC) is an effective approach to address this problem. However, the existing MSPCRC methods only defined a single patch-scale weight vector for all classes to indicate the importance of different patch scales, ignoring the role of class information when fusing multiscale recognition results. In this work, we consider the effect of class information on face recognition and propose a novel multiscale collaborative-representation face recognition method. Specifically, we first construct the multiscale decision matrices of image subsets from different classes according to patch collaborative representation, and define a patch-scale weight vector for each class to describe the importance of different patch scales. Each element in a scale-weight vector represents the weight value of a certain scale in the corresponding class. Then, we construct the respective optimization objective function for each class, which takes into account the classification information both from the same class and from different classes. Finally, we propose a multiscale fusion-recognition output rule based on the patch-weight vectors. Experimental results demonstrate that the proposed method enhances classification accuracy by approximately 2% to 5% across multiple datasets, surpassing the majority of the competing methods.

Multi-scale decision systems with test cost and applications to three-way multi-attribute decision-making

Multi-scale decision systems with test cost and applications to three-way multi-attribute decision-making

A Three-Way Decision Methodology With Regret Theory via Triangular Fuzzy Numbers in Incomplete Multiscale Decision Information Systems

The three-way decision theory provides a three-way philosophical thinking to solve problems, and the regret theory quantifies the risk preferences of decision makers under different psychological behaviors. On the one hand, the combination of these two theories makes models more practical by considering the psychological behaviors of decision makers. On the other hand, we can effectively combine the advantages of the three-way decision theory with the regret theory to highlight the interpretability of decision making processes. In this paper, we propose a novel approximate estimation method for incomplete utility values via the regret theory and establish a wide sense of three-way decision model on incomplete multi-scale decision information systems. First, the degree of consistency for each scale is measured via using the dependency degree, then the optimal subsystem is selected by evaluating the scale selection cost. Further, the incomplete multi-scale evaluation information is transformed into triangular fuzzy numbers via linguistic term sets. Second, in light of fuzzy evaluation values and trade-off factors, an estimation method for incomplete fuzzy subsystems is constructed, which can be used to calculate the utility difference and regret-rejoicing values for pairwise comparisons. Finally, from the perspective of human cognition, the tri-partition and the corresponding decision rules are built by the tolerance degree, and the ranking of objects is calculated by the relative closeness degree. Additionally, multi-aspect comparative and experimental analyses are performed by extensive experiments, and the feasibility, validity and stability of the constructed model are shown by parametric analyses.

Information fusion for multi-scale data: Survey and challenges

Information fusion is a useful technique of combining and merging different information to form a more complete and accurate result. Traditional information fusion models mainly focus on the single-scale data in which each object has a unique value for any attribute. However, in practice, an object may take on different values under the same attribute, depending on the scale used to measure it. Information fusion of multi-scale data has become a hot topic in the field of intelligent computing. In the past decade, various models and algorithms of multi-scale information fusion (MIF) with rough set theory have been proposed. In this paper, a detailed and comprehensive review about the current research developments of MIF is carried out. First, the multi-scale decision system is introduced to perform the knowledge representation of multi-scale data. On the basis, the classical model of MIF, i.e., the Wu–Leung model, is presented. Second, some MIF models with different information granulation and information fusion strategies are summarized, respectively. Next, for optimal granularity selection, which is the key issue of MIF, existing information measurements interpreting consistency criteria are listed and analyzed, and the common strategies of scale fusion and attribute fusion in optimal granularity selection are summarized. Then, the local MIF and the applications of MIF are reviewed, respectively. Finally, the potential research directions and challenges of MIF are discussed.

On generalization reducts in incomplete multi-scale decision tables

On generalization reducts in incomplete multi-scale decision tables

Optimal scale selection and knowledge discovery in generalized multi-scale decision tables

In the real world, each attribute of data sets has multiple scales, whether it is a conditional attribute or a decision attribute. Knowledge mined from data based on the optimal scale can well meet the needs of real life. Hence, there is no denying that optimal scale selection is an problem to be solved urgently in the knowledge discovery field of multi-scale decision tables. The optimal scale combines coarser condition attributes with the finer decision attribute, so as to achieve a balance between efficiency and accuracy. With the aim of selecting the optimal scale combination, we firstly explore some related properties and theorems of generalized multi-scale decision tables. Then we define the optimal scale in generalized multi-scale decision tables and propose two algorithms for optimal scale selection. In addition, a knowledge acquisition algorithm and a multi-scale rough set classifier framework are proposed. Finally, numerical experiments are performed on some open data sets to test the effectiveness of the algorithms.

A YOLO-based AI system for classifying calcifications on spot magnification mammograms

ObjectivesUse of an AI system based on deep learning to investigate whether the system can aid in distinguishing malignant from benign calcifications on spot magnification mammograms, thus potentially reducing unnecessary biopsies.MethodsIn this retrospective study, we included public and in-house datasets with annotations for the calcifications on both craniocaudal and mediolateral oblique vies, or both craniocaudal and mediolateral views of each case of mammograms. All the lesions had pathological results for correlation. Our system comprised an algorithm based on You Only Look Once (YOLO) named adaptive multiscale decision fusion module. The algorithm was pre-trained on a public dataset, Curated Breast Imaging Subset of Digital Database for Screening Mammography (CBIS-DDSM), then re-trained and tested on the in-house dataset of spot magnification mammograms. The performance of the system was investigated by receiver operating characteristic (ROC) analysis.ResultsWe included 1872 images from 753 calcification cases (414 benign and 339 malignant) from CBIS-DDSM. From the in-house dataset, 636 cases (432 benign and 204 malignant) with 1269 spot magnification mammograms were included, with all lesions being recommended for biopsy by radiologists. The area under the ROC curve for our system on the in-house testing dataset was 0.888 (95% CI 0.868–0.908), with a sensitivity of 88.4% (95% CI 86.9–8.99%), specificity of 80.8% (95% CI 77.6–84%), and an accuracy of 84.6% (95% CI 81.8–87.4%) at the optimal cutoff value. Using the system with two views of spot magnification mammograms, 80.8% benign biopsies could be avoided.ConclusionThe AI system showed good accuracy for classification of calcifications on spot magnification mammograms which were all categorized as suspicious by radiologists, thereby potentially reducing unnecessary biopsies.

Regret Theory-Based Three-Way Decision Method on Incomplete Multiscale Decision Information Systems With Interval Fuzzy Numbers

In realistic decision-making environments, human behaviors bring influences to various decision-making procedures, and classic multiattribute decision-making approaches based on utility decisions own some deviations from actual situations. The behavioral decision theory modifies classic decision-making theories to make the new method more applicable. Regret theory, as one of the important components in behavioral decision theories, has been widely used in theories and applications. Based on regret theory, we establish a generalized three-way decision method on incomplete multiscale decision information systems with interval fuzzy numbers. First, we select an incomplete optimal subsystem for the incomplete multiscale information system, and convert the multiscale evaluation information into an interval fuzzy number by using a linguistic term set. Second, based on the probability distribution of evaluation values and tradeoff factors, we propose a target-dependent approximation estimation method for the incomplete interval fuzzy subsystem. Then, the regret–rejoicing preferences between objects are obtained. Finally, a tripartition and ranking method based on a max-bipartition and preference index is established. Moreover, the incompleteness experiments show that the decision-making results of our method can still maintain more than 97% consistency in an incomplete information system with a missing rate of at most 20%. In addition, the parameter analysis shows that the proposed method maintains an accuracy rate of more than 98% and a classification error rate of no more than 0.6%.

PRNU-based Image Forgery Localization with Deep Multi-scale Fusion

Photo-response non-uniformity (PRNU), as a class of device fingerprint, plays a key role in the forgery detection/localization for visual media. The state-of-the-art PRNU-based forensics methods generally rely on the multi-scale trace analysis and result fusion, with Markov random field model. However, such hand-crafted strategies are difficult to provide satisfactory multi-scale decision, exhibiting a high false-positive rate. Motivated by this, we propose an end-to-end multi-scale decision fusion strategy, where a mapping from multi-scale forgery probabilities to binary decision is achieved by a supervised deep fully connected neural network. As the first time, the deep learning technology is employed in PRNU-based forensics for more flexible and reliable integration of multi-scale information. The benchmark experiments exhibit the state-of-the-art accuracy performance of our method in both pixel-level and image-level, especially for false positives. Additional robustness experiments also demonstrate the benefits of the proposed method in resisting noise and compression attacks.

Optimal scale generation in two-class dominance decision tables with sequential three-way decision

Optimal scale selection is studied widely at present to obtain scale rules in multi-scale decision tables. However, one limitation of this method is that it cannot directly extract scale rules from single-scale decision tables. In this study, we determine how to generate an optimal scale in two-class dominance decision tables with sequential three-way decision (S3WD). First, we use the variance of each attribute to describe its importance in a single-scale two-class dominance decision table. Then, we arrange all attributes in descending order in accordance with their importance. Second, we examine each attribute by following the aforementioned order. Thereafter, we construct different object granules on the basis of the numerical size of attribute value and different decision values and then expand them individually until their limit is reached. Third, we label and delete objects that are already in the object granules. Then, we continue to construct object granules for the remaining objects by following the preceding method until all the objects are labeled (if the information system is inconsistent, then it should be labeled with ”until it cannot be marked”). In the process above, we adopt the idea of S3WD and successively classify the objects into positive, boundary, and negative regions in accordance with the three states of objects (i.e., object classification has been confirmed, to be confirmed, and cannot be confirmed). We perform experiments on some UCI datasets and demonstrate the effectiveness of our method. In summary, our work provides a method for generating an optimal scale in single-scale decision tables and extracting scale rules from the generated tables.

Stepwise updating of optimal cut in multi-scale decision systems considering the dynamic changes of attributes

Stepwise updating of optimal cut in multi-scale decision systems considering the dynamic changes of attributes

DeepDSFusion: A General Multiscale Decision Fusion Method for Segmentation Tasks on High-Resolution Imagery With Deep Learning

DeepDSFusion: A General Multiscale Decision Fusion Method for Segmentation Tasks on High-Resolution Imagery With Deep Learning

Rule acquisition in generalized multi-scale information systems with multi-scale decisions

In this paper, knowledge acquisition in the sense of deriving IF-THEN rules in multi-scale information systems with multi-scale decision attributes is investigated. Specifically, the concept of a generalized multi-scale information system with a multi-scale decision attribute, called generalized multi-scale decision information table (GMDIT for short), is first introduced. Such a system is a multi-scale decision table in which each condition or decision attribute at each object can take different values under different scales. The notion of scale selections for a GMDIT, which is mainly used to determine individual decision tables, is then defined. Information granules and their properties with different scale selections in GMDITs are also described. Optimal scale selections which are used to determine proper decision tables for final decision in inconsistent GMDITs are further formulated. Local optimal scale selections to obtain more concise decision rules for different objects are presented. Finally, attribute reducts based on optimal scale selections are derived and decision rules hidden in inconsistent GMDITs are unraveled.

Update of optimal scale in dynamic multi-scale decision information systems

The problem of optimal scale selection for multi-scale decision information systems is an important issue in the field of granular computing research, especially when data are dynamically updated. Determining the changes of the optimal scale for dynamic data is a goal that has drawn increasing attention from scholars in related fields. For the case of object updating, solving this problem requires finding which characteristic conditions should be satisfied by newly added objects when different cases of the optimal scale occur. However, existing studies only include the sufficient and necessary condition of the optimal scale becoming smaller for dynamically updating objects. Therefore, to complete the theory regarding how the optimal scale will be changed when objects are dynamically updated, it is still necessary to explore the sufficient and necessary conditions for the optimal scale being unchanged or becoming larger. In this paper, we use three-way decision theory to study this problem. Concretely speaking, the uncertain region of three-way decision is used to reveal the change of knowledge at different scales. That is, the obtained results, combined with existing work, provide a nice solution to the problem of finding the changing laws of the optimal scale for object updating in multi-scale decision information systems.

Sequential 3WD-based local optimal scale selection in dynamic multi-scale decision information systems

The multi-scale decision information system (MDIS) is a typical granular computing model. In the research of MDIS, uncertainty is an important factor in making decision analysis, and the selection of optimal scale is a core problem. Therefore, the uncertainty of decision is an important factor in the scale selection. With the rapid increase of data size, the amount of feature information will increase greatly, and the uncertainty of the system will become more and more complex, which makes the optimal scale selection more difficult. The purpose of this study is to investigate the updating law of the local optimal scale under the condition of the dynamic increase of objects. The criterion of scale selection is to keep the uncertainty of the system unchanged. Firstly, the updating law of uncertainty for the decision class in a decision information system under the case of object increment is explored. Secondly, the definition of local optimal scale which keeps the uncertainty of decision classes is given by the sequential three-way decision theory, and the updating law of optimal scale is given by using the updating mechanism of the uncertainty of decision classes. Finally, experiments are conducted to verify the correctness and effectiveness of the proposed method in the calculation of local optimal scale by comparing the algorithms for adding multiple objects directly and adding objects one by one.

A prospect-regret theory-based three-way decision model with intuitionistic fuzzy numbers under incomplete multi-scale decision information systems

As a new data representation in the big data era, a multi-scale decision information system (MSDIS) realizes “multi-level, multi-angle and multi-view” evaluations in various problems. However, most of existing multi-scale data analysis models are built for complete information systems (CISs), whereas the research on incomplete multi-scale decision information systems (I-MSDISs) is not perfect. Additionally, the irrational behavior of one decision-maker (DM) often has an impact on decision outcomes. On this basis, this paper develops a prospect-regret theory-based three-way decision (3WD) model with intuitionistic fuzzy numbers (IFNs) under an I-MSDIS, which is abbreviated as PR-3WD-I-MSDIS. Specifically, we first select the optimal scale combination of I-MSDISs by the matrix theory to complete the information extraction of incomplete optimal sub-systems. Then, we further propose an attribute weight evaluation strategy under the incomplete optimal subsystem, which fully considers the neighborhood information of each object. Subsequently, the concept and calculation method of aggregated weighted fuzzy conditional probabilities are constructed from the perspective of intuitionistic fuzzy sets. Furthermore, a prospect-regret theory-based relative profit function is proposed, which sufficiently takes into account the loss and utility in decision-making processes. Finally, a novel three-way classification and ranking method is developed for solving incomplete multi-scale problems. The experimental results on real-world datasets demonstrate that the PR-3WD-I-MSDIS model achieves excellent performance.

Multi-granulation-based knowledge discovery in incomplete generalized multi-scale decision systems

Multi-granulation-based knowledge discovery in incomplete generalized multi-scale decision systems

Dominance-based fuzzy rough sets in multi-scale decision tables

Dominance-based fuzzy rough sets in multi-scale decision tables